_TL_^J. ^ ,.,............. , ., , - - . n_jy J jT_j " I-..-. :P .-.-_- REESE LIBRARY OF THE UNIVERSITY OF CALIFORNIA. Class A HANDBOOK ON REINFORCED CONCRETE FOR ARCHITECTS ENGINEERS, AND CONTRACTORS BY F. D. WARREN MASSACHUSETTS INSTITUTE TECHNOLOGY, 1900 NEW D. VAN NOSTRAND COMPANY 1906 REESE l> COPYRIGHT, 1906, BY D. VAN NOSTRAND COMPANY Stanbope press p. H.GILSON COMPANY BOSTON. U.S.A. PREFACE. IN preparing this volume, I have endeavored to produce a reference handbook that would be par- ticularly adapted to the wants of architects, en- gineers, and contractors. Appreciating the value of a reference book to a designer in any of these branches, and especially when business methods and competition demand an economy of time, such a choice in preference to a text-book, re- sulted. All clue care has been exercised to avoid conflicts with data compiled in the many valuable text-books on the subject. It was purposed to produce a work treating upon a general form of design rather than upon any one particular or patented system, but to which any of the latter may be applied. The treatment of the many phases entering the de- sign has been carried out along well-known for- mulae based upon the theory of elasticity, but modified by the usual assumptions, such as the "conservation of planes" and "Hookes' Law," and not upon empirical formula? based upon ex- periments. Attention should be called to the fact that before applying the theory of elasticity to any particular part of the design, a sufficient number of tests were carried out along this basis 5 144173 6 PREFACE. to approve it, and determine the coefficients and constants. The book is divided into four parts: Part I gives a general but concise resume of the subject from a practical standpoint, bringing out some of the difficulties met with in practice, and suggest- ing remedies. Under Part II is compiled a series of tests justifying the use of various constants and coefficients in preparing the tables under Part III, as well as bearing out the theory of elasticity. Part III contains a series of tables from which it is hoped the designer may obtain all necessary information to meet the more common cases in practice. It was not intended to cover the more intricate designs, as this is a feature that requires considerable thought and time, both of which may be profitably applied. Part IV treats of the de- sign of trussed roofs from a practical standpoint. Finally, if this volume will* tend to do away with the use of some of the "empirical formulae" and "rule of thumb' 7 methods of designing rein- forced concrete structures, and tend to concen- trate all toward a standard and universal system, as well as remove some of the prejudicial influ- ences at work tending to demerit its worth be- cause of unfamiliarity with its design, it will have accomplished its purpose in the mind of the writer. CONTENTS. PART I. PAGES Tensile Strength of Cement . 13 Classification of Trap-rock Sizes . 19 Caring for Crushed Stone upon the Works 19 Sand 22 Proportion of Ingredients for the Various Mixes ... 22 Incorporation 26 Protecting Newly-laid Work 32 PART II. Tensile Strength of Concrete-Steel 37 Test of Beam No. 1 40 Test Beam No. 2 43 Cut Showing Failure of Beam No. 1 45 Cut Showing Failure of Beam No. 2 45 Remarks Concerning Tests No. 1 and No. 2 46 Cut Showing Arrangement of Apparatus for Conduct- ing Tests No. 1 and No. 2 ,.-.. 47 Floor Tests Nos. 1-13 49-57 Results of Floor Tests Nos. 1-13 58-59 Remarks Concerning Floor Tests 60 Floor Tests Nos. 86 and 14 61-62 Roof Test No. 22 63 Remarks upon Plots Showing the Relationship between Expansion and Temperature 64 Plot Showing Expansion in Fifty Feet 65 Plot Showing Expansion hi Thirty Feet 67 Conclusions 68 Combined Plot Showing Expansion in Ten Feet ... 69 7 8 CONTENTS. PART III. PAGES Description of Table I 75 Tables Giving Safe Bending Moments for Different Sizes of Beams or Girders, Called Table I 82-94 Description of Tables la and 16 95-97 Tables Giving Safe Bending Moments for Different Sizes of Continuous Girders (with Two Spans), Called Table la 98-105 Key to Using Tables I, la, 16, and II ....... 106 Tables Giving Safe Bending Moments for Different Sizes of Continuous Girders (with Three or More Spans), Called Table* 16 107-114 Description of Table II 115-116 Tables Giving Safe Loading for Different Spans, Called Table II 117-128 Description of Table III 129-137 Tables Giving Safe Shearing Forces for Different Sizes of Beams or Girders, Called Table III 138-144 Description of Table IV 145-146 Tables Giving Safe Spans for Different Sizes of Beams or Girders, Allowing a Safe Deflection of 3 ^Q of Span, Called Table IV 147-149 Description of Table V 150 Table Giving Safe Bending Moments for Different Thicknesses of Floors, Called Table V 152 Description of Table Va 153 Table Giving Amount of Steel to Resist Various Temperature Changes in Floors, Called Table Va . 154 Description of Table VI 155 Table Giving Safe Loadings and Spans for Different Thicknesses of Floors, Called Table VI 157-165 Description of Table VII 166 Tables Giving Safe Loads for Different Sizes of Col- umns, Called Table VII 167-169 Description of Table VIII 170 CONTENTS. y PAGES Comparative Costs, Beams for Equal Strength, CaUed Table VIII 172-173 Description of Table IX 174 Comparative Costs, Floors for Equal Strength, Called Table IX 175 Description of Table X 176 Comparative Costs, Floors for Equal Deflection, Called Table X 173 Description of Table XI 177 Comparative Costs, Columns for Equal Strength, Called Table XI 178-1 S3 Cost of Reinforced Concrete Columns, Octagonal Sec- tion, for Different Sizes 184-186 Amounts of Cement, Sand, and Stone Required for Concrete Mixtures of Various Proportions, Called Table XII 187-188 Description of Table XIII ...... 189 Relative Strength of Different Proportions of Mixture, Called Table XIII 190 PART IV. Trussed Roofs 193-200 Reinforced Concrete Roofs 201-202 Description of Table XIV "... . . . 202 Roof Designs, Called Table XIV . . 203-205 Description of Table XlVa 205 Costs of Roofs, Called Table XlVa 206 Description of Table XV 206 Table XV. Truss Designs 208-213 Description of Table XVa 214 Weights of Trusses. Table XVa . -r-r~-. .... 215-216 Description of Plots . . 217 Plots of Costs. Table XV 218-222 Description of Table XVI 223 Table XVI. Truss Designs 224-230 Description of Table XVIa 231 10 CONTENTS. PAGES Weights of Trusses. Table XVIa 232 Plots of Costs. Table XVI 233-237 Description of Table XVII 238 Table XVII. Truss Designs 239-242 Plot of Costs. Table XVII . 243 Description of Table XVIIa 244 Weights of Trusses. Table XVITa 244 Description of Table XVII6 245 Table XVII6. Truss Designs 246-248 Plots of Costs. Table XVII . 249 Weights of Trusses. Table XVII^ 250 Description of Table XVIIc 251 Table XVIIc. Truss Designs 251-253 Description of Table XV lid 254 Table XVIId. Truss Designs 254-256 General Description of Trusses of Types Treated under Tables XVII-XVIId 257 Description of Table XVIII 258 Plot to Determine Factor K in Formula ....'.. 261 Table XVIII. Truss Designs 262-266 Plot of Costs. Table XVIII 267 Plots Showing Comparative Costs of Different Kinds of Trusses 268-269 Weights of Trusses. Table XVIIIa 270-271 PAET I. TENSILE STRENGTH OF CEMENT. 11 HANDBOOK ON REINFORCED CONCRETE. THE tensile strength of a cement enters into the design of a reinforced concrete structure only indirectly. However indirectly as it may be, it is of the utmost importance, since the possibility of realizing a satisfactory design depends entirely upon the obtaining of a satisfactory value for the same. The prime object of knowing the tensile strength of a given cement which is being used on works of magnitude, is to safeguard the owners that they are receiving from the makers the qual- ity of cement specified by the architects. Thus it may "be seen thatrthe time when this factor enters the problem is not during the design, but during the erection of the plant. SPECIFICATIONS. For instance, a cement is sometimes specified to be calcined from given pro- portions of given constituents, which are known to render a first-class cement of a high tensile strength. This measure, although used for cau- tion, seems too exacting upon the cement makers, as doubtless there are secrets in the manufacture of the cement, known only to the makers, which are of great value to it, and which would be en- tirely upset by such stringent requirements. It 13 14 HANDBOOK ON REINFORCED CONCRETE. should rather be specified, and more properly, that the cement delivered on the works must stand a certain tensile strength per square inch when made into the standard briquette of neat cement, and allowed to set in air for a given time before testing, or shall stand another stated stress per square inch when made as before, but allowed to take its initial set in air, and then immersed, and allowed to remain a stated time in water of a given temperature before testing. Sometimes one or the other of these figures of tensile strength per square inch is given, and the second given as a ratio in terms of the first that must not vary over a certain amount. In either case, the briquette should take its initial set without a perceptible rise in temperature. Again, it may be specified that the cement in question shall be thoroughly burned during cal- cination. To satisfy ourselves in this respect, we have but to carefully watch the above-mentioned briquettes or other samples while setting. Should these show a rise in temperature while setting, we are at once convinced that the cement was not properly burned. Yet, if this fact be lost sight of at this time, the results from the tensile strength will show that something is wrong, and if this something reduces the test below the fixed speci- fied amount, we are justified in condemning the lot, provided sufficient tests to give an average of the lot show the deficiency, without troubling ourselves as to the exact cause. TENSILE STRENGTH OF CEMENT. 15 Thirdly, it may be specified that the cement be ground to a certain degree of fineness by requiring a certain part, or all, to pass a sieve of specified number, and all, or but a small per cent, to be retained on a second sieve of smaller mesh. If the cement be improperly or rather too coarsely ground, there will be grains in more or less num- bers of too large proportions to bond with the finer and more uniform mass, and the only mis- sion these can have is to act as so much sand, and necessarily lower the tensile strength. So, again we resort, or should resort, to the results of the tensile tests. But this fault may also be de- tected by weighing, for it is generally known that, bulk for bulk, a coarser ground grade will' weigh in excess over a finer ground grade. It is not practical to be too severe with this measure, for there is danger, if the brand be too finely ground, and especially if the sand used be fairly coarse, that the particles of cement will be too small to fill the voids in the sand, unless we make our- selves doubly sure, and use a larger ratio of cement to overcome the danger, which, to say the least, is a remedy too extravagant for the most scrupulous. Fourthly, caused by the improper mixing of materials, or by insufficient burning during calci- nation, a pat of neat cement when worked up in the hand, and placed upon a piece of glass under water, will creep and draw up along its outside perimeter where it meets the glass. Also, pri- marily due to the same cause, a pat of neat cement 16 HANDBOOK ON REINFORCED CONCRETE. made as before, and placed under water, will blow, liberating bubbles of air and indicating chemical action taking place. Both these influences tend to lower the tensile strength. Attention has already been called, first to the mixture of constituents composing the cement; second, to the proper burning of these constitu- ents; and thirdly, to the degree of grinding after the calcining process. These I consider the three important steps in the making of cement, and a slip in any of these during manufacture renders a product totally unfit for use. To guard against the use of .any lot, deficient in this manner, and especially in reinforced concrete construction, is the prime object of what has been written; and finally, as a safeguard, I make an urgent appeal for the more general adoption of making tensile tests, and to an extent to give a fair average of the lot in order to show up the quality of the cement which is being used at any time upon the works. Now, the brand of cement which has been specified, and which is supposed to meet all the requirements, has arrived on the works. To be sure, one has his faculties of sight and feeling, which can be used to good advantage in passing superficial judgment upon the lot, provided his judgment has had the necessary training through experience. For instance, the color of the lot will tell the more experienced in a general way the composition of the mixture, when the locality from TENSILE STRENGTH OF CEMENT. 17 which the constituents were taken is known, since the ingredients vary greatly in texture in different localities. This, at the best, can be of only pass- ing importance, as the exact proportions of the constituents, which so largely affect the chemical reaction to make the proper compound, will not always appeal to the eye in the same way when so many things enter into the process which may upset any fast rules. But very fortunately there is the privilege of applying the tensile tests to satisfy oneself that the combination of ingredients is such as not to impair the strength. Again, the sense of feeling may be used. The expert can, by running his hand through the lot and by rubbing together the particles, in a meas- ure tell whether there are too many unground or too coarsely ground particles to affect the results so as not to meet the requirements. Once more, if one is not thus skilled, and in all cases as a precautionary measure, the tensile strength should be relied upon to determine whether the lot is not too diluted by coarse particles, before accepting the lot. Thus, one has his faculties to guard him against two of the many faults; and how often does not this suffice to accept a lot, which, had tests been taken, would never have been unloaded from the car. In summing up, it may be expected that two lots of cement, made .from the same ingredients, taken from the same locality, and mixed in the same proportions, will, if made into neat cement 18 HANDBOOK ON REINFORCED CONCRETE. briquettes, using the same care as regards mixing, proportion and temperature of water used, and the place and conditions of setting, give fairly uniform results by tensile tests. Hence, it re- mains for the architect merely to fix upon the tensile strength of a cement known to be good when allowed to set for a given time under given conditions, and to see to it that every shipment, when a sufficient number of samples have been taken to warrant the average lot, shall meet the requirements, when the briquettes have been made, set, and tested under similar conditions which governed the standard. No little stress should be laid upon this matter, for it seems to the writer, that in works of magnitude, where every other precaution is taken to insure the obtaining of proper materials, and where a large amount of money is at stake, this primary function of qual- ity and endurance to the structure, second not even to workmanship of mixing and deposit- ing the concrete, should not be overlooked nor deemed too expensive to maintain throughout the time during which the concrete is being placed. By what has just been said, do not imagine that the workmanship is a matter of inconsiderable importance. On the contrary, it is second in im- portance only to the grade of cement. It should be remembered that the life and endurance of the structure are dependent upon both conditions, and anything lacking in one cannot be compensated for in the other, and the whole suffers in accordance. TENSILE STRENGTH OF CEMENT. 19 CLASSIFICATION OF TRAP ROCK SIZES. It seems to the writer that one of the necessary steps in the specifications of the architect is to classify the sizes of trap rock that may properly be used in the different parts of the building. Thus, it may be arbitrarily fixed that the sizes of rock to be used in the foundation must all pass a 2J-inch ring, and all be retained on a 1-inch screen. For exterior walls and piers, where the sizes of the same will permit proper rodding, it may be specified that all rock shall pass a 1-inch and all be retained on a J-inch screen. For gird- ers, beams, and floors above the steel members, also for columns, all rock should pass a screen of J-inch mesh, and all be retained on a J-inch mesh. Below and around the steel members in girders, beams, and floors, in order to obtain proper rod- ding and perfect work, no stone should be used that will not pass a screen of J-inch mesh, and should include everything under except the dust. This is ordinarily known as pea size. CARING FOR CRUSHED STONE UPON THE WORKS. Under the heading of Classification it may be perceived that in cases where a crusher is used on the works, all grades of the trap rock may be used from 2J inch down, excluding the dust. As screened, the different grades should be deposited in bins or piles properly labeled, so there can be 20 HANDBOOK ON REINFORCED CONCRETE. no mistake made by the man in charge of the mixer or the different gangs of men when there comes a call for a change in mixture. If, on the other hand, the trap rock is received on the works by the carload, it should be seen to that each carload is labeled as to its grade, and that it is unloaded into its proper bin or pile. As a safeguard where the rock is received by the carload, and not inspected as to its grade, and especially when coming from an unreliable yard, it is well to run the rock through screens so ar- ranged and spouted beneath that the different grades reach their proper piles. Accordingly, four bins or piles will be required; and if circumstances will allow, and machine mixing be adopted, the hopper feeding the mixer should have four compartments. Yet this is not absolutely necessary, for it is not probable that there would be calls at any one time for the four grades from any one mixer. Before charging the hopper, or its different compartments, it is abso- lutely necessary that the rock be thoroughly washed free from dirt and dust in order that every opportunity may be given to the cement to completely coat the exterior surface. No little stress should be laid upon this matter of classifying the different grades of rock, and keeping each within its sphere for its proper in- stallation in the building. For each grade of stone there is a definite amount of sand and a fixed proportion of cement within limits required TENSILE STRENGTH OF CEMENT. 21 to make a homogeneous concrete; and without this homogeneity of mass, we are putting weak links in the chain, just as would be done provided we allowed poor cement to enter. As there is a safeguard against this latter, so there is against allowing the different grades to be interchanged, and this is care. To be more explicit in regard to the consequences which are bound to exist with- out this due amount of care, let me add: Sup- posing the mixture which is being run through the mixer is for beams or floors, and the measuring devices are set for the proper amount of sand and cement for a j J gauge stone. Through careless- ness, let us suppose that the mixer hopper has been charged with a few buckets of the 2J-1 gauge stone along with the J J gauge.. When this enters the measuring hopper, there is neither time nor ready means of changing the sand and cement to agree, provided the tender knew enough. Con- sequently, the larger stone goes through with the proportions of sand and cement for the smaller stone, in other words, with voids unfilled, and the concrete far from being homogeneous. But the trouble does not end here. The mass, already diluted, is deposited upon the floor, and shoveled into the beams, and other men follow along with tamps to rod the same into place. Although going through their usual mechanical motions, what is the result? With the large size of stone it is impossible to work them into a small beam, or around steel members without allowing voids to 22 HANDBOOK ON REINFORCED CONCRETE. form, and again we are sacrificing homogeneity. Thus a slip in one respect has weakened the chain twofold. SAND. Where practicable, two grades of sand should be specified, one to be a very coarse and angu- lar crushed quartz; the other to be a finer river or bank sand, also angular. The proportions of the two may be determined thus : Take a given bulk of the coarse sand, and determine the voids after the manner described later on. The ratio of the voids to the original volume of coarse sand will be the ratio of fine sand to coarse to be used. The two grades of sand should be measured out, thor- oughly, mixed in the above proportions, washed free from dirt, and deposited in a pile or bin ready for the sand compartment of the mixer. If but one grade of sand can be conveniently obtained, it should be of medium grade, very irregular as to size of granules, and, of course, sharp and angular. Besides, it should be tested at frequent intervals for voids to insure the proper amount of cement at all times to obtain a homo- geneous mass. PROPORTIONS OF INGREDIENTS FOR THE VARIOUS MIXES. Now that we have the ingredients for making the concrete, namely, the cement, which has TENSILE STRENGTH OF CEMENT. 23 passed the tensile requirements, the cleaned sand in its compartment, and the rock in its various compartments fixed by the arbitrary grades es- tablished, next comes the fixing of the ratio of these ingredients, determined by the grade of rock and the grade of sand, to make a proper concrete as regards homogeneity. To do this, take a form impervious to water, that will hold just one cubic yard by its actual inside dimensions. Fill this shovel by shovel with the grade of stone from which is required the proper mix, compacting the same as much as pos- sible. Then obtain, by measuring the volume of water required to fill the voids between the stones, the amount and ratio of the voids to the whole. Then remove the stone and water, and with the volume of sand as just determined by the volume of water thoroughly mixed with the measured cubic yard of stone, replace the mixture into a water-tight form of the same width and length, but of somewhat greater depth than before, tamp- ing the same well as it is placed shovel by shovel into the form. Then the increase in depth will give the relative increase in proportions by add- ing the sand. After leveling and tamping the contents into the form, measure again the amount of water required to fill the remaining voids just to the level of the top of the sand and stone. Remove, and with other stone of the same grade, and other sand of like grade, and both of the same volumes already determined, and with the 24 HANDBOOK ON REINFORCED CONCRETE. volume of cement determined by the last measure- ment of water added, all thoroughly mixed, re- place the same into the measuring form shovel by shovel, tamping and leveling as before. Again note the. increase of height and hence the increase of volume by adding the cement. Undoubtedly we could add a considerable volume of water to the mass before same stood at the level of the mixture in the form, showing voids remaining un- filled. These, however, are due to improper mix- ing of the materials, and insufficient ramming into place, and should be compensated for as stated farther on. Now we have determined not only the proper ratio of ingredients for the grade of stone and sand in question to make a homo- geneous mix, but also the ratio of the final to the initial volume, which will be from 1.1 to 1.3, depending upon the grade of stone. So we may expect that every cubic yard of crushed stone will fill a space in the structure of 1.1 to 1.3 cubic yards after the same has been made into its proper mix of concrete. After water has been added, which should be enough to make a plastic mass in order to insure the filling of the mold properly, and especially plastic where it is difficult to incorporate the mass thoroughly by rodding, tamping, and rolling, the mass will have gained in bulk nearly in proportion to the water added, provided that the voids have been properly filled when mixed dry, that the cement is in proper condition as already deter- TENSILE STRENGTH OF CEMENT. 25 mined by the tensile tests, and that the rock and sand have been thoroughly wetted beforehand, as both have a certain avidity for water depending upon climatic conditions. This gain in mass will probably amount to 2 to 5 per cent over its volume when dry, depending upon the amount of water added. While setting, this water is gradually ab- sorbed by chemical action and outside influences, and the mass gradually diminished, tending to assume its normal state when dry. Thus, what is generally known as the shrinkage of concrete dur- ing set is merely the tendency of the mass to attain its original bulk when dry. As previously mentioned, voids remain in the mass after seemingly the proper proportions of ingredients have been fixed. These are bound to occur, for in practice, because of so many variables entering to upset the best of calculations, it is impossible to obtain nearly the results which are obtained when determining the proportions. Then again, when the plastic mass is deposited into the molds, it is impossible to prevent a leakage of water, and this leakage will carry away with itself some of the cement. To overcome such difficul- ties, which must necessarily happen, we have to resort to a factor of safety, as we might term it, by adding to the proportions already determined an excess of cement varying from 5 to 10 per cent as best seems required to meet each particular case. In what has been said, it may appear how 26 HANDBOOK ON REINFORCED CONCRETE. difficult it is to obtain the proper proportions of ingredients, even when the utmost care is taken. Hence, all the more reason for being careful. In summing up the matter of proportions of ingredients, we may derive some general figures, which we will term mixes, all of which can be only approximate, and all subject to the variables already mentioned tending to change them more or less. For instance, for the 2 J-inch- 1-inch grade of rock, the proportions of cement to sand and to stone should be about 1-2J-5. This we will term a 1-2J-5 mix. For the 1-inch-J-inch grade of work, a 1-2-4 mix seems to be about the proper thing in round numbers. Likewise from the f-inch-J-inch grade, a 1-1 J-3 mix results, and from the pea-size grade, a 1-1-2 mix results. By comparing these mixes with what has been said concerning the proper sizes of rock for indi- vidual locations in the structure, it can be readily seen that Foundations require the 1-2^-5 mix Outside walls, piers, etc., require the 1-2 -4 mix Girders, beams, floors, and roofs above the steel members, also inside columns, require the . 1-1 $-3 mix Girders, beams, floors, and roofs below the steel require the 1-1 -2 mix Wearing surface for floors requires .... 1 cement-2 sand INCORPORATION. After the different mixes have been settled upon, and we are sure these are coming from the mixer in due form, the next important step seems TENSILE STRENGTH OF CEMENT. 27 to be the distribution of these mixes into their proper places. Whatever else goes wrong, it is necessary to have the 1-1-2 mix to work around the steel in the beams and girders and for the first spreading upon the floor to receive the steel. If not, the penalty is paid later on, when the false work is stripped, and a honeycombed surface presents itself. There is no excuse for the 1-2J-5 mix ever reaching the superstructure, so we may eliminate this from our cares. It should be care- fully watched that the 1-1^-3 and the 1-2-4 mixes reach their destination, but the danger resulting from the interchanging of these two mixes is the least of any of the combinations. That proper incorporation should result by care- ful and scientific rodding, cutting, tamping, and rolling, the plastic mass must be a realized fact, and this can be so only by using all care and by putting the proper man in the proper place. But first of all, before we can rod, tamp, or roll the mass successfully, we must have a mass that is in such a physical state as can be so rodded, tamped, or rolled. By this is meant a concrete made from a moderately slow-setting cement, one containing the proper mix, and one sufficiently plastic. A cement that will begin to take on its initial set to any extent within half an hour after mixing has no place in the superstructure of a building, and yet how often do we see such a cement in use that will set up so hard as to require hoeing or picking out of the bucket. 28 HANDBOOK ON REINFORCED CONCRETE. How can this be properly rodded, tamped, or rolled? The time of thirty minutes' grace, as we may term it, is arbitrarily fixed upon as under ordinary conditions ; the rodding, tamping, rolling, leveling, and walking over a section require that amount of time at least, before it can be left for nature to take her course. In many cases it is required that the top finish shall be floated on immediately after the base is laid. This seems to the writer quite unscientific and very impracticable. It is held by the sup- porters of this method that the strength of the floor is increased, and that perfect bond between the base and the finish is realized. That this latter is accomplished, no one can dispute. In regard to the former supposition, there seems to be just grounds to take exceptions. If any strength is gained thereby, it is by adding more area to the concrete to resist compression. Al- ready, before the addition of the 1-inch finish, the floor is as able to resist compression as it is tension. Any addition of strength to one link of a chain does not increase the durability of the whole chain. It may be argued that this will increase the moment of resistance of the steel, which un- doubtedly would be true if it could be practically realized, but this is not the weak point of the floor if properly designed. The weak point is the ad- hesion of the concrete surrounding the steel mem- bers. By adding the finish at this crucial time, it would be necessary to keep walking over the TENSILE STRENGTH OF CEMENT. 29 soft base, which has already begun to set; and in so doing, you are all the while destroying the bond between the setting concrete and the steel, thus impairing the adhesion between the two, without which, the steel is more or less unsup- ported, and, when undergoing tension by bending, may be so separated from the concrete that the latter is unable to take the stress, caused by the elongation of the steel fibers while bending, from the steel. In other words, instead of having a compact mass so constrained, one member by another, that any stress in one may be trans- mitted to another, and the entire stress distributed throughout the number of members, we have a more or less mutilated and disconnected whole. All our former carefulness to obtain a homogene- ous compact mass has been set at naught, and we are only undoing what we have already tried so hard to do. Then there is another consideration. The top finish should be considered as the top floor of a house or mill, a part which takes the wear. What strength it imparts to the lower floor, we do not stop to figure or think of. It is put there for one sole purpose, to take wear, no more nor less. To take wear, the cement finish should be uniform throughout, both as regards breadth and depth, and to attain this, the top surface must be screeded off perfectly level. To do this, the screeds cannot be set on a soft surface and the same leveled both ways over any con- siderable amount of area with the ordinary level 30 HANDBOOK ON REINFORCED CONCRETE. and straight edge. It requires the accurate work of an engineer with an instrument to establish a level grade by setting nails in the base floor after the latter has set for twelve to twenty-four hours, and for careful workmen to bring the screeds to the nails, to attain anything like proper results. Provided the mason could level the screeds prop- erly, how long would they remain so, resting as they would on a soft base, which is all the while being disturbed by walking over it? The effect of screeding off a floor, out of level, is for the water to flow by gravity to the low places, carry- ing with it cement from the high places. The cement which has collected in the hollows, after the surface has been floated and finished, forms into a thin skin with no body, and instead of bonding with the particles below, seems to keep apart from them, sets slower, and later on when the floor is put in use, scales off by wear. The high places have lost a considerable amount of the cement which should be there in order to float and trowel the same to a smooth, hard sur- face, but instead, the surface is rough and sandy, in such condition that trucking and wear keep removing the rough particles; hence the spot or spots grow more and more uneven, and more extensive. Again, the water insuring a proper set, has run from the high places to the low places, allowing the latter to become oversupplied. Consequently, the surface is not uniform, and when one part is TENSILE STRENGTH OF CEMENT. 31 ready for floating or smoothing, another part is not ready, thereby increasing the chances of allow- ing one part to go too long to be properly worked. Ultimately, the high places set faster than they should, because of insufficient water, while for the opposite reason, the low places do not set so quickly. The only thing that can be expected, under such conditions, is a network of cracks between the two surfaces, and these expectations are usually realized. Now what has been gained? Strength may have been added to the floor by hurrying up the finish, but instead of obtaining a surface to meet wear, a rough substitute is ob- tained, uneven in surface, and far from homo- geneous, and the consequences, a series of repairs to keep the floor intact. On the other hand, if the base is allowed to set for twelve to twenty-four hours, all danger of destroying the adhesion between the concrete and steel has passed. The surface of the base is un- even, it may be scratched with a rake to make it more uneven, and it should be well-wetted down before applying the finish. With these things attained, there is no reason why there should not be a sufficient bond between the base and the finish. Then everything is favorable for obtaining a level surface by bringing the screeds to nails set in the base to exact grade, and the men applying the finish may have daylight by which to see what they are doing, all of which tend toward good results. 32 HANDBOOK ON REINFORCED CONCRETE. PROTECTING NEWLY-LAID WORK. Now, having obtained a floor surface properly laid to take wear, the next step in sequence seems to be to properly care for the results already obtained by protecting them from outside influ- ences. We have seen that, if some portions of the surface set earlier than others, the result is a network of hair cracks dividing such surfaces. It is perfectly well-known that concrete of a given mix requires a given amount of water to cause proper setting; any water in excess will be left free to be absorbed by the air; any deficiency will leave parts of the concrete improperly set. Along this line of reasoning, it may be easily seen that if a newly-laid floor surface be left unprotected from the sun on a dry, hot day, the result will be that the rays of the sun, and the surrounding dry air will extract from the upper surface a considerable amount of water. Being robbed of what it should require to set properly, and at the same time, being forced in places to set much earlier than it otherwise would, it tends, by shrinkage of the affected portion, to separate the same from the lower and less-affected layers. The result is im- perfect bond between the successive layers and cracks between the more or less effected parts of the exposed surface, which, of course, are detri- mental to wear, as well as unsightly in appearance. To overcome such influences, and to hold nature somewhat in check, the writer would suggest that TENSILE STRENGTH OF CEMENT. 33 just as soon as an area, however small, had re- ceived its final troweling, and had become con- sistent enough to support a covering of burlap or canvas, the same be spread over the area and wetted by spraying gently with a hose. As the surface below becomes harder and harder, water should be sprayed over the covering in increasing amounts, and just as soon as the surface will allow it, the whole covered area should be flooded. In about twenty-four to thirty-six hours, this temporary covering may be removed, when the surface should be covered with a layer of saw- dust or fine sand sufficiently thick and evenly distributed to protect all parts. Preferably saw- dust should be used, as the particles are more elastic, and are not so harsh upon the finished surface when walked upon. Coarse sand or gravel should be infrequently resorted to, for upon areas which require much walking over, the surface will become very spotted and marred, because of the coarse particles being pressed into the surface not already hard. This covering should be flooded with water, and kept wet, or at least damp, just as long as practicable, or until ready for occupancy, if possible. This covering not only protects the surface from atmospheric influ- ences, but also from wear which the newly-made surface could not otherwise withstand. In this way, work upon or above the newly-placed area may not be delayed more than thirty-six to forty-eight hours. PART II. TENSILE STRENGTH OF CONCRETE-STEEL. 35 TENSILE STRENGTH OF CONCRETE STEEL, OR THE EFFECT OF STEEL MEMBERS UPON CONCRETE WHEN EMBEDDED IN THE LATTER, AND THE WHOLE IS UNDERGOING TENSION CAUSED BY BENDING. WHEN we come to determine the tensile strength of concrete, when lying just around or between steel rods, as in case of the layer containing the tension members near the bottom of a concrete- steel beam undergoing tension caused by bend- ing, we have a more complicated problem to deal with than with the simple tensile strength of a cement briquette. Experiments galore have shown just how much may be expected from a tensile specimen of concrete alone, when the history of its manufacture is known, and the treatment it has undergone, and under what conditions. It yet remains for experimenters, after many and careful trials, to enlighten us concerning the in- fluence the steel members have upon the concrete when embedded in it, and the combination is undergoing tension caused by bending. That this influence is enormous, no one can dispute when examples, and these from reliable sources .no 37 38 HANDBOOK ON REINFORCED CONCRETE doubt, are cited, where tests to destruction of concrete-steel beams, by bending, have ruptured the steel members. Since the ratio of the con- crete section to the steel section in the layer con- taining the steel has not been furnished us, we are unable to compute the stress in the concrete section, which, indeed, is to be exceedingly re- gretted. We are, however, quite justified in say- ing that in such layers, where, for instance, the section of the concrete between the steel members just equals that of the steel itself, that the stress in the concrete is one-tenth that in the steel, allowing the ratio of the modulus of elasticity of the concrete to steel to be 1 to 10. As there are several cases in actual practice where the equality of the sections of steel and concrete in the layer in question actually exists, and where, from the actual loading, the stress per square inch of steel figures 15,000, it is but fair to assume that the stress caused in the concrete thereby is one-tenth of this, namely 1,500 pounds per square inch. Critics who are wont to call the ultimate tensile strength of concrete 200 to 300 pounds per square inch will no doubt either laugh this reasoning to scorn, or will refuse to use a construction which imposes such exacting conditions upon a material weak in itself, before stopping to consider that we are not dealing with the elements alone, but with a carefully selected (or at least it should be) combination of materials. That this combination TENSILE STRENGTH OF CONCRETE-STEEL. 39 has proved itself in practice to be equal to the conditions just stated should, until experimenters have shown otherwise, be evidence enough to justify its adoption. How many materials in actual use of construction, and which go appar- ently free from criticism, are there which in them- selves are weak and unfit for any use, but when in combination with, or constrained by other mem- bers, do excellent service. Yet we are just as unable to give this combination a fixed limit of strength and endurance as are we in the case at hand. To determine a value for this tensile strength of concrete within the extreme fibre, the writer had two test beams made which were designed to be weak in concrete-resisting area between the steel members in order to facilitate this method of failure if possible. The results and conclusions drawn from these tests are given further on. To be sure, the manner of failure was as anticipated, namely by tension in the concrete between the steel members. As may be noted from the tests at the time of failure, the tensile stress in the three rods of Beam No. 1 was 55,000 pounds per square inch, and in those of Beam No. 2 at the time of failure, 64,000 pounds per square inch. From No. 1 beam, provided the resisting areas of both concrete and steel were equal, the tensile stress at the time of failure would have been one- tenth of 55,000, namely 5,500 pounds per square inch, but the resisting area of the concrete was 40 HANDBOOK ON REINFORCED CONCRETE. 206 -s- 168 in excess over that of the steel, which would reduce the ultimate stress in the concrete by the reciprocal of this ratio, namely, to 4,500 pounds per square inch. From the test of No. 2 beam, this value, by like treatment, becomes 5,200. Allowing a factor of 3.5, which is allowed in all cases, as may be seen in the explanations of tables, for safety, brings the safe allowable work- ing stress between 1,000 and 1,500 pounds per square inch. From the tables, in all cases, the safe-working stress of the concrete in tension has been kept between 1,000 and 1,500 pounds per square inch. It is not intended to assert that the value of the tensile strength of concrete can be obtained from these two experiments. They are given merely to illustrate what may be expected, and, as they bear out common practice, they are cited as fair examples of the ordinary run of experiments, which may be carried on with the object of determining the tensile strength in view. TEST BEAM No. 1. Duration of set 59 days. Kind of cement used Portland Alpha. Ratio of ingredients 1-2-4. Proportion of steel 3-f-inch bars. Proportion of steel 8-1-inch U-bars 45 to axis of beam. Distribution of steel f-inch bars 2 inches from bottom. Distribution of steel f-inch bars, distances vary- ing from 4 inches at ends to 12 inches toward mid- dle. TENSILE STRENGTH OF CONCRETE-STEEL. 41 Manner of applying load . . . Gradually. Application of load At center of span. One-fourth load weighed on scales. Deflection measured by micro- meter calipers. Length of beam 10 feet 6 inches. Span 10 feet inches. Width of beam 5 inches. Depth of beam 15 inches. Results of Test. 1 j "o jl Deflec- tion read- Aver- age deflec- tion Deflec- tion read- ings load ige deflec- readings removed . Total set. tion recov- >y removal load. jrement of deflection. 5 deflection 100 Ibs. load. 1 o c ings. read- ings. re- moved. ill 3*! IF Q a .2 J3 "a! 11 s 0. .0405 .0405 .0405 488. 488. .0472 .0471 .0410 .0410 .0005 .0061 .0061 .00125 .0470 .0410 740. 252. .0545 .0545 .0424 .0418 .0013 .0127 .0066 .00172 .0546 .0412 1140. 400. .0635 .0635 .0437 .0439 .0034 .0196 .0069 .00172 .0635 .0440 1748. 608. .0678 .0682 .0425 .0425 .0020 .0257 .0061 .00147 .0685 .0425 2300. 552. .0784 .0784 .0450 .0447 .0042 0337 .0080 .00147 .0784 .0440 3448. 1148. .1050 .1050 .0640 .0640 .0235 .0410 .0073 .00119 .1050 .0640 4960. 1512. .1300 .1297 .0675 .0687 .0282 .0610 .0200 .00123 .1295 .0700 5760. 800. .1530 .1537 .0778 .0778 .0373 .0759 .0149 .00132 .1545 .0778 6960. 1200. .1820 .1815 .0790 .0788 .0383 .1027 .0268 .00148 .1810 .0785 8160. 1200. .2145 .2145 .0856 .0857 .0452 .1286 .0259 .00158 .2140 .0858 42 HANDBOOK ON REINFORCED CONCRETE. Failed under 15,000 pounds. Manner of failure See illustration Average elastic deflection per 100 pounds load 00144. 1 WL 3 Formula for elastic beam D = 4o liiL D = elastic deflection corre- sponding to load W ' . L = length of span in inches. E = modulus of elasticity _ Stress per square inch Strain per inch 7 = moment of inertia of beam section about neutral axis. 1 X 100 X 120 3 48X1X926 E = modulus of elasticity, 2,640,000. Neutral axis (when determined as al- ready explained) above the under- side of the beam 7.4 inches. Or, below the central axis 1.35 inches. Maximum bending moment = \ X 15,000 X 120 450,000 inch-pounds. Concrete. Moment of inertia / = ( T V X 5 X 12.5 3 ) + (5 X 12.5 X 1.35 2 ) = 926. Distance from neutral axis to extreme fiber or layer in compression Y 7.6 inches. I _ 9?6 Y " 7.6 ' Ultimate compressive stress at extreme fiber or layer / = ' 3,700 Ibs. sq. in. TENSILE STRENGTH OF CONCRETE-STEEL. 43 Steel. I area of section X (distance of steel to neutral axis) 2 3 X .56 X 4.9 2 ......... 40.4 Y ............... 4.9 7 40 ' 4 8 23 Ultimate tensile stress at extreme layer f = 450.000 ........... 8.23 Ultimate tensile stress of concrete within this layer 55,000 X X ...... 4,500 Ibs. sq. in., 10 , 6 modulus of elasticity of concrete modulus of elasticity of steel 168 area .of steel in tensile layer 206 = area of concrete in tensile layer TEST BEAM No. 2. Duration of set Kind of cement used Ratio of ingredients Proportion of steel Proportion of steel Distribution of steel Distribution of steel Manner of applying load Application of load .. One - twenty - fourth weighed on scales. Deflection measured micrometer calipers. Length of beam Span Width of beam Depth of beam load b 62 days. Portland Alpha. 1-2-4. 3-f " bars. 8-i" U-bars, 90 to axis of beam. J-inch bars, 3 inches from bottom. J-inch bars, distances varying from 4 inches at ends to 12 inches toward middle. Gradually. At center of span. 10 feet 6 inches. 10 feet inches. 5 inches. 15 inches. HANDBOOK ON REINFORCED CONCRETE. Results of Test. c 5 "o c . Deflec- Aver- age Deflec- tion it! 1*1 ent ection. c o 11 Total Ic Increme load tion read- ings. deflec- tion read- ings. read-* ings load re- moved. Average c tion reac load remi Total set. Defied recovere removal oi fi 53 jfS-S .s ~ 1 * 111 If W 0. .2714 .2714 .2714 960. 960. .2883 .2884 .2714 .2714 .0000 .0170 .0170 .00177 .2884 .2714 2230. 1270. .3304 .3304 .2868 .2872 .0158 .0432 .0262 .00194 .3305 .2880 2810. 580. .3435 .3437 .2740 .2733 .0019 .0704 .0272 .00251 .3440 .2725 3650. 840. .3548 .3574 .2795 .2783 .0069 .0791 .0087 .00217 .3600 .2770 4800'. 1150. .3815 .3817 .2895 . 2880 .0166 . 0937 .0146 .00195 .3820 .2865 5040. 240. .4010 .4010 .2950 .2045 .0231 .1065 .0128 00212 .4010 .2940 5930. 890. .4190 .4195 .2960 2945 .0000 .1250 .0195 .00211 .4200 .2930 Failed under 16,200 Ibs. Manner of failure See illustration Average elastic deflection per 100 Ibs. load .00208. .00208 100 X 120 3 48 X E X 732 ; whence E = modulus of elasticity Neutral axis (above underside of beam) Neutral axis (below central axis) . . . Maximum bending moment 2,420,000. 7.95 inches. 1.30 inches. X 16,000 X 120 480,000 in.-lbs. TENSILE STRENGTH OF CONCRETE-STEEL. 45 CUT SHOWING FAILURE OF BEAM No. 1. CUT SHOWING FAILURE OF BEAM No. 2. 46 HANDBOOK ON REINFORCED CONCRETE. Concrete. Moment of inertia / = (rV X 5 X 11.5 3 ) + (5 X 11.5 X 1.30 2 ) 732. Y 7.05 inches. 7 - 732 104 Y ~ 7M> Ultimate compressive stress at extreme layer 480,000 / = ^4 4610 Ibs. sq. in. Steel. I = 3 X 56 X 4.45 2 t . 33.4. Y 4.45. Y 7.5. Ultimate tensile stress at extreme layer ,= 64,000 lb,sq. in. / .> Ultimate tensile stress of concrete within this layer = 64,000 X -^ X i5| 5;2 00 Ibs. sq. in. AU ^Uo REMARKS CONCERNING TESTS No. 1 AND No. 2. These tests were carried out, as the cuts will clearly illustrate, by applying a central load at the center of the span by means of a screw-jack, and determining same by means of allowing a portion of same to be weighed upon a set of scales. The deflection readings were obtained by fixing a pair of micrometer calipers to the beams at the center of the span, and by taking successive read- TENSILE STRENGTH OF CONCRETE-STEEL. 47 ings when the screw of same just came into con- tact with a steel piano wire stretched across pins set into the ends of the beam at the neutral axis, and directly over the supports. The contact was determined more closely by allowing the microm- eter screw to make an electric circuit through the piano wire, two dry cells, and an induction ringer. CUT SHOWING ARRANGEMENT OF APPARATUS FOR CONDUCTING TESTS No. 1 AND No. 2. All readings were checked by two individuals to .0005 or .0010 of an inch. It will be noted that in working up the results, no attention was paid to the concrete below the tension layer of steel, and hence in Beam No. 1 the effective depth was 12.5 inches, while in Beam 48 HANDBOOK ON REINFORCED CONCRETE. No. 2 only 11.5 inches, instead of the nominal depth of 15 inches as given. As before stated, these beams were designed to be weak in concrete-resisting area in the tensile layer between the steel, expecting this manner of failure. In one case it was clearly marked, and in the other, the first indications were tending in this direction, but which ultimately developed in- to a shear-crack, the failure being a compromise between the two. CONCLUSIONS CONCERNING TESTS. It may be observed, by referring to the sets of deflection readings given, that like successive in- crements of load did not produce like increments of deflection. On the other hand, each successive like increment of load produced a deflection 10 to 30 per cent in excess over the preceding incre- ment of deflection. RESULTS OF TESTS. 49 Floor Test No. 1. 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 \b3. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 1A Sq. ft. 36.5 137 Inches. .0310 1638 Sq. ft. .0850 1195 Inches. Inches. Inches. 249. .2412 .0969 249. .3700 .1484 1A-1B 280. Lin. ft. 822.5 .4607 Inches. .0780 .1648 Lin. ft. .0095 .4688 .3438 .1250 3170. .0938 .0296 4365. .1300 0298 4365. .1720 .0394 IB 5600. Sq. ft. 63.7 .2750 Inches. .0360 .0492 Sq. ft. 0390 .2750 .2230 .0520 249. 312. .1260 1585 .0506 0509 312. .2065 .0662 1B-1C 420. Lin. ft. 1265 .4888 Inches. 0620 .1165 Lin. ft. 0049 .5900 .3340 .2560 3713. .0940 .0025 4635. .1300 .0028 1C 4635. 6300. Sq. ft. 125 .1700 .2800 Inches. 0522 0037 .0045 Sq. ft. 0418 .2800 .1300 .1500 245. .1175 0480 303. .1475 .0488 303 .2125 .0702 420. .4950 .1180 .5900 .3560 .2340 50 HANDBOOK ON REINFORCED CONCRETE. Floor Test No. 2. 1 2 3 4 5 6 7 Mean increment Loca- tion in Total load. Mean deflec- deflec- tion per 100 Ibs. per Greatest deflec- Amount deflec- tion Perma- nent section. tion. sq. ft. or per 1000 tion. recov- ered. set. Ibs. lin. ft. 2C Sq. ft. 205 Inches. 1190 Sq. ft. 0580 Inches. Inches. Inches. OCA 1428 0571 ocn 1962 0785 250. .2241 .0898 .2450 .2031 .0419 1C-2C Lin. ft. 9ORO Inches. 0469 Lki. ft. 0228 2500 0780 0313 9K.OO 0780 0313 2^00 0780 0313 0780 2C-3C Lin. ft. Inches. Lin. ft, 2060 Oil 0053 ornn 033 0132 2500 2500. .035 .0140 .0700 2C-2B Sq. ft. Inches Sq. ft. 125 080 0640 125 080 0640 125 094 0753 125. .125 .1000 .1250 Floor Test No. 3. 3C Sq. ft. Inches. 032 Sq. ft. 057 250 248 0835 250. .255 .1020 .2550 .2550 .0000 51 Floor Tests No. 3. Continued. 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 Ibs. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 3C-4C Lin. ft. 1500 Inches. .046 Lin. ft. .0370 Inches. Inches. Inches. 1500. 1500 .062 078 .0414 0520 2500. .078 .0312 3750. .094 .0251 3O3B 5000. Sq. ft. 1250 .209 Inches .120 .0418 Sq. ft. .0960 .2090 .1630 .0460 1250. .125 .1000 .1250 .1250 .0000 Floor Test No. 4. 4C Sq. ft. 1250 Inches. .1075 Sq. ft. Inches. Inches. Inches. 2500. .1938 2500. .2250 4C-5C 2500. Lin. ft. 1250. .0150 .2700 .2550 .0150 1250. .0400 5000. .1500 5000. .1700 2500. .1700 4C-4B Sq. ft. 60. .0320 125. .0900 125. .0480 125. .0650 .0900 52 HANDBOOK ON REINFORCED CONCRETE. Floor Test No. 5. 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 Ibs. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 5C Sq. ft. 250. Inches. .2500 Sq. ft. .1030 Inches. Inches. Inches. 250. .2500 . 1030 250. 250 .2812 3200 .1200 1280 250. 2187 250. .1900 .3180 .3180 .000 5C-6C Lin. ft. Lin. ft. 2500. 2500 .010 032 .0040 0128 3750. 5000 .062 095 .0165 0190 5000. .218 .0436 5000. .156 .0312 2500. .010 .0400 .2180 .1830 .035 5C-5B Sq. ft. 125 050 Sq. ft. 040 125. 125 .093 130 .0743 1041 125 124 0991 125 069 125. .050 . 1300 .1300 .000 RESULTS OP TESTS. Floor Test No. 6. 53 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 Ibs. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 6C Sq. ft. 125 Inches. Sq. ft. Inches. Inches. Inches. 250. 250 .2180 2300 250 2530 250. .2480 6C-7C 250. Lin. ft. 2500 .2300 1250 .3250 .2550 .0700 2500 . 1 250 5000 2750 5000 1900 5000. .1600 5000 2450 2500 .1950 .2450 .0890 1560 6C-6B Sq. ft. 62 0310 125. .0650 125 125. 0940 125 1000 125. .1000 .1000 .0000 Floor Test No. 7. 7C Sq. ft. 125 Inches. 1000 Sq. ft. Inches. Inches. Inches. 250 2200 250 250 2812 250 2812 250. 250. .2770 .2812 .1512 .1300 54 HANDBOOK ON REINFORCED CONCRETE. Floor Test No. 7. Continued. 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 Ibs. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 7C-8C Lin. ft. 1250. Inches. .0570 Sq. ft. Inches. Inches. Inches. 2500 0900 2500. .0980 2500 1200 3750. .1562 5000. 5000 .1900 1500 7C-7B 2500. Sq. ft. 62 .1600 .1150 .1900 .1330 .0570 125. 125 .1300 1900 125. .1800 125. .1900 125 1850 125. .1900 .0400 .1500 Floor Test No. 8. 80 Sq. ft. 125. 250. Inches. .0500 2750 Sq. ft. .0560 .1025 Inches. Inches. Inches. 8C-9C 250. 250. Lin. ft. 1825 .3075 0310 .1230 Lin. ft. 0169 .3075 .1875 .1200 5000. .1560 0276 5000. 5000. .2300 .3700 .0460 .0740 8C-8B 2500. Sq. ft. 62. .2700 .092 Sq. ft. 148 .3700 .2175 .1525 125. 125. .3125 3075 .250 246 125. .3125 .0650 .2475 RESULTS OF TESTS. 55 Floor Test No. 9. 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 Ibs. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 9C Sq. ft. 62. 250 Inches, .093 234 Sq. ft. .150 094 Inches. Inches . Inches . 250 247 098 250 345 138 9C-10C 250. Lin. ft. 620 .329 015 .132 Lin. ft. 024 .345 .160 .185 2500 030 012 5000 129 0258 5000 281 9C-9B 5000. Sq. ft. 31 .219 063 .0438 Sq. ft. 201 .219 .074 .145 125 205 164 125 234 187 125 313 250 125. .290 .232 .313 .037 .276 Floor Test No. 10. IOC Sq. ft. Inches . Sq. ft. Inches. Inches . Inches . 125 189 1514 250 380 1520 250. .370 .1480 .3800 .0675 .3125 56 HANDBOOK ON REINFORCED CONCRETE. Floor Test No. 10. Continued. 1 2 3 4 5 6 7 Mean increment Loca- tion in section. Total load. Mean deflec- tion. deflec- tion per 100 Ibs. per sq. ft. or per 1000 Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. Ibs. lin. ft. 10C-11C I An. ft. Inches. Lin. ft. Inches. Inches. Inches. 2500 2500. .375 0750 2500. .406 .0810 2500. .348 .1394 .4060 .1270 .2790 10C-10B Sq. ft. Sq. ft. 62. .156 252 125. .284 .227 125. .268 .214 .2840 .0000 .2840 Floor Test No. 11. 11C Sq. ft. Inches. Sq. ft. Inches. Inches. Inches. 125. .1175 .0940 250. .4375 .175 250. .4688 1876 250. .5600 .2220 .5600 .1200 .4400 11C-12C Lin. ft. Lin. ft. 1250. .1875 .150 2500 2188 0877 3750 3080 0821 5000. .4640 .0926 .4640 .0340 .4300 11C-11B Sq. ft. Sq. ft. 62 2790 455 125 3280 263 125 4040 324 125. .4970 .397 .4970 .0000 .4970 RESULTS OF TESTS. 57 Floor Test No. 12. 1 2 3 4 5 6 7 Loca- tion in section. Total load. Mean deflec- tion. Mean increment deflec- tion per 100 Ibs. per sq. ft. or per 1000 Ibs. lin. ft. Greatest deflec- tion. Amount deflec- tion recov- ered. Perma- nent set. 12C Sq. ft. Inches. Sq. ft. Inches. Inches. Inches. 125. .2180 .1742 250. .5050 .2020 .5050 .1925 .3125 12C-13C Lin. ft. 2500 0660 Lin. ft. 0264 5000. .4690 .0938 .4690 .0940 .3750 12C-I2B Sq. ft. Sq. ft. 62. .0940 .1516 125. .3780 .3022 .3870 .0795 .3075 Floor Test No. 13. 13C Sq. ft. Inches. Sq. ft. Inches. Inches. Inches. 125. .1230 .0984 250. .5800 .2320 .5800 .2360 .3440 13C-14C Lin. ft. Lin. ft. 1250 1510 1210 5000. .5780 .1158 2500. .5630 .5780 .2950 .2830 13C-13B Sq. ft. Sq. ft. 62 0625 1010 125. .4687 .3760 .4687 .0987 .3700 58 HANDBOOK ON REINFORCED CONCRETE. Results of Tests. 1 2 3 4 No. of bays. Location in bay. Average of greatest deflection. Average of least deflection. S 03 C fe 83 32 O 5 6 . W>T3 2 Q; ^ i M E st \s YL V \ \\ < j : c 3 I \ * 10 K > c i| m D - f \ \ \ \ 4^ ^ *" 4 ^ 1 = = C \ i \ - ~n 3 - r T \ \ C 1-- : ' r n o \ "c n > < \ s g g c 3 O i ^ \ CP ) VO \ \ } . - i n ^ i \ ^ ? . ; \ \ \ 1 7 * V \ o. \, o \ j M ^ ^ c ^ ' . \ ^ G \ 1 \ [ o ^ \ * \ Y . V '^ \ V- ' * k v y t^ \ > ^> ^5> y _\j^ y ij 1 r. V *, \^i ^ V^ V* Y- ^ p 3 , 'A ^ \ i f r V c j 68 HANDBOOK ON REINFORCED CONCRETE. to any extent, because the base of the column, the footing of same, and the curtain walls between this column footing and its neighbors, were sur- rounded by frozen earth and ice. However, any slight variation, when it was known not to be in error, was allowed for. Readings were taken on the four corner columns, and in both directions, namely, east-west and north-south, on each of the four columns. This required eight set-ups. The building in question had an expansion joint fifty feet from the ends in a north-south direction, and was sixty feet wide, thus allowing a length for expansion in an east- west direction of thirty feet for each of the two corner columns at either end. CONCLUSIONS. By referring to the combined plot, it may be seen that the data contained there is* sufficient to determine the coefficient of expansion. Take the point, for instance, whose coordinates are 42.5, .0029. This means that for a change in tempera- ture of 42.5, there was a corresponding change in length of .0029 feet per ten feet, or .00029 feet per one foot. The corresponding change in length per one degree may be represented by the ex- pression .00029 -&- 42.5 equals .00000682, which is the coefficient of expansion. By using the point whose coordinates are 42.5, .0026, the resulting coefficient of expansion becomes .00000601. The COEFFICIENT OF EXPANSION. 69 og b Expansion in Feet 70 HANDBOOK ON REINFORCED CONCRETE. mean of the two is .00000642, and this value is used in the following. In temperate climates a change of temperature of 70 F. may be considered a maximum either way from the temperature under which the origi- nal setting ordinarily takes place. This change would cause a strain of .00000642 X 70 = .000448 inches in the concrete, and, since the coefficient of expansion of steel is .00000657, the strain in the steel would be .000459 inches, or practically the same as that in the concrete. This strain causes a stress of 13,780 pounds per square inch in the steel, calling the modulus of elasticity 30,000,000. To determine the percentage of metal required for a change of 70 when there is developed in the steel a stress not greater than the elastic limit, which may be considered 52,000 pounds per square inch with a high carbon steel, we may proceed as follows: The amount of stress which may be brought to bear upon the steel by the concrete, when the same has reached its ultimate tensile stress, = 52,000 - 13,780 = 38,220 pounds per square inch. The ultimate tensile stress of the concrete may be considered to be 300 pounds per square inch. Hence the remaining stress of 38,220 pounds per square inch would resist the stress of 38,220 -5- 300 = 127 square inches of con- crete stressed to 300 pounds per square inch. In order to develop the ultimate stress in a square foot section of concrete would require a section of steel that would resist the stress of COEFFICIENT OF EXPANSION. 71 72 square inch concrete after the same hag reached its ultimate tensile stress. Under this condition the steel section would offer half the resistance to elongation, while the concrete would offer the other half, and the square foot section, which might be treated as 72 square inches of concrete and its equal of steel, each stressed to its elastic limit, or as 144 square inches of con- crete stressed to 300 pounds per square inch, its ultimate tensile stress. Consequently, since 1 square inch of steel stressed to 52,000 pounds per square inch is equivalent to 127 square inches of concrete stressed to 300 pounds per square inch in tension, to care for one square foot of concrete, considered as 72 square inches of con- crete and its equivalent of steel, would require 72 -* 127 = .57 or practically .6 square inches of steel. PAET III. DESIGNS OF CONCRETE STRUCTURES. 73 TABLE I. DESCRIPTION OF TABLE I. IN using Table I, all that is required to be known, in order to design the beam or girder, is the maximum bending moment. When this is known, either in inch-pounds or foot-pounds, pick out the next larger value in column 5, if in inch- pounds, or in column 6, if in foot-pounds, pro- vided the designer will accept a factor of safety of 3.5 as ample; if not ; use columns 7 or 8 in a like manner, which allow for a factor of safety of 5. From the location of the proper moment to fit the case at hand, by following horizontally to the left, column 1 will give the size of beam as far as concrete is concerned. This size includes the concrete protection below the steel tension members and the base of the floor, but does not allow for the top 1-inch finish. In other words, the depth of the beam given in column 1, which in all cases is the second of the two dimensions, takes into account the entire depth save 1 inch, which is to be added to the top of floor for wear. Column 5 gives the total moment that the size can withstand allowing the specified factor of safety, which total includes the moment due to 75 76 HANDBOOK ON REINFORCED CONCRETE. the dead load of the concrete itself as well as that due to the live load. To facilitate computations, in column 2 is given the weight per lineal foot of the beam, from which the moment, due to the dead load, can be ascer- tained by taking a trial size. Column 4 gives the ratio of the moment of in- ertia of the section about the neutral axis which is lettered /, to the distance of the upper layer of fibers, which layer in all cases has the most stress to withstand by compression, from the neutral axis, lettered y. This ratio, of course, is the same as that of the safe maximum bending mo- ment, expressed in inch-pounds, to the safe allow- able stress per square inch of the concrete in compression. It is given more as a check than from any practical use it bears to the u^e of the table. Under column 5 is given the section of the steel member or members, which, by virtue of being embedded in the concrete, is able to with- stand the tensile stress in the worst layer resist- ing tension, allowing the same factor of safety as was allowed in the concrete, namely, 3.5 or 5.0. Of course, as long as the extreme layer remains strained below the elastic limit, all layers ap- proaching the neutral axis, which must necessarily be less strained, are obliged to remain intact, and there can come undue stress on these layers only after the extreme layer has been strained beyond the elastic limit. Accordingly, in designing the DESIGNS OF CONCRETE STRUCTURES. 77 beam for tension, it is necessary only to put enough steel in the extreme layer to withstand the tension in that layer, allowing the proper factor of safety. All layers approaching the neu- tral axis will have their corresponding tensile stresses properly resisted by the concrete, as long as the extreme layer remains intact. The steel section as here given in all cases, is designed to be placed in the beam or girder with its lower- most part, at the center of the span, just 1 inch above the underside of the beam, but never less, in order to be sufficiently protected by the con- crete in case of fire. At the center of the span, the location should never be more than 1 inch above the bottom, without making allowance for the lessening of the moment of resistance. Under column 10 is given what is termed by the heading, "The Proper Size of Bars." This, at first- thought, may appear uncalled for, as long as the area of section is given, but after reading what is outlined under the "Tensile Strength of Concrete," in another section, the reason may appear. Briefly, in cases where it is required to use two or more rods to equal the section, a num- ber might be selected leaving very little concrete between the different steel members in the layer along with them. This total resisting area of the concrete between the rods might, in extreme cases, be so reduced that it would be incapable of transferring the tensile stress from member to member, because of an excessive stress per square 78 HANDBOOK ON REINFORCED CONCRETE. inch upon the area. In such a case it might be practically impossible to work in the concrete between the steel members without leaving voids, or allowing the members to rub together with only a film, if any, of concrete between. With this in view, the items under this column were so selected as to leave sufficient area of concrete between the steel so that this latter would not have to carry over 1,000 to 1,500 pounds per square inch in tension, and at the same time allow space to properly work in the concrete between the rods. This area is given under column 12, and the cor- responding tensile stress per square inch under column 13. Column 11 gives the distance below the center of gravity of the section to the neutral axis. This is determined after the steel section is known, and the rods selected, by substituting an area of con- crete, which, when placed at the location of the steel, would give the same tensile resisting power at the extreme layer as does the section of steel. This area is considered attached to the beam so that its depth is equal to one side of the square rod or rods, and its width ten times the total width of the rod or rods ten times because the modulus of elasticity of the steel is ten times that of the concrete. By so doing, we obtain an inverted T section, and it remains, in order to determine the neutral axis, only to determine the center of gravity of this section by the method of moments. DESIGNS OF CONCRETE STRUCTURES. 79 It has just been stated that the steel section was so designed as to be protected by 1 inch of concrete at the center of the span. This was fixed at 1 inch by balancing up two important factors, each directly opposed to the other. For instance, to render the beam or girder fire resist- ing, it is well to have the steel members thoroughly protected from below by concrete, w r hich tends to have the tension members approach the neutral axis. On the other hand, in order to obtain the greatest moment of resistance in tension, the tendency is to have the tension members approach the underside of the beam or girder. Along this same reasoning, in order to prevent hair cracks, caused by excessive tension due to deflection, across the underside of the beam which, although they do not to any extent effect the strength of the beam, are very unsightly, the tendency is to have the tension members approach the under- side of the beam, since this adds to the stiffness of the beam, and thereby lessens the tension in the concrete below the steel. By equating these fac- tors, judgment will fix the location, especially at the center of the span, about 1 inch from the underside of the tension members to the under- side of the beam or girder. Finally, to give an outline how the values y. and the safe allowable resisting moments, both of compression and of tension, were deduced, the following routine is given: 80 HANDBOOK ON REINFORCED CONCRETE. Let M = Maximum bending moment. b = Width of beam or a width of floor corresponding to bending moment above. d = Depth of beam or thickness of floor down to center of tension members. M 1 bd? Then = - - whence assuming b, d is com- 500 4 d puted. This is a preliminary step, but after the neutral axis is located, and using the value of d just found, the fiber stress at top fiber figures about 850 pounds per square inch. Calling the ultimate compressive stress 3,000 pounds per square inch, which should be attained in a 1-2-4 or a 1-1 J-3 mixture, the stress just found gives a factor of safety of 3. The next step is to find the area of steel which, when taking all the stress in the worst position of tension, takes a stress of 15,000 pounds per square inch. This is figuring a factor of safety of 3.5, with an ultimate stress of 52,000 or 53,000. To do this, I assume the neutral axis to be from 1.5 to 2.0 inches below the center of gravity, and figure the area of the steel thus: M ah 2 15,000 h Where a = area of steel. h = distance from center line of steel to neutral axis assumed above. DESIGNS OF CONCRETE STRUCTURES. 81 With this area of steel, the neutral axis can be located by taking moments, after transposing the area of steel into an area of concrete, etc., as stated before. If this location does not come sufficiently near 1.5 or 2.0 inches below the center of gravity of the section to fulfil the assumption previously made, use this value to determine h in in the last formula M (Namely = ah), and solve for a again. 15,000 This new value of a will probably not change the location of neutral axis, found previously, enough to effect the results. Now we are able to figure the fiber stress of the concrete in compression and so check the 850 pounds per square inch with the sizes we had determined, or else fix new sizes to give no more than 850 pounds per square inch for the concrete in compression. 82 HANDBOOK ON REINFORCED CONCRETE. 1 1 ^ b- b- ^ oo oo t" 00 O S 1. fe! I ^ *^3535 ,. SSi ^SiS8 a *.<*. CD OCOOO OOOOO D 1C OS b- ^ 1C 00 1C 1C O o o o CO CO CO rh CO iC i-T csf co" 5 O O O O O O -H O' C 1C 1C >C 10 S M CO ^ rH N ^ ; OOOO OOOOO OOO coc32!2 tSioS^M ^w^ ^ r-T U5 1C J l>>CCb. OSOOOiCCO i-lC O 00 1C i-I b.' CO CO i-I O O CN1 O CM ^ O Cl XXXX XXXXX XXX csi ^ DESIGNS OF CONCRETE STRUCTURES. ^OOOOO i"* CM l^ -^1 CO rH T-H t> 00 O> O CO TiJ -i CN 00 O O O t> 00 p I-H CN -i CO OOU300t-OCNTt J co" oo t>T I-H" oT CN" oo co" rC co o" -H" 10" o o o o o oo ooooooo -i rH COCNTtlOOOi-HCO 00 rn O 00 t- O o" TjT oo* CN" t>T co" of co r-T co" CN od c iHi-li-(C 0 t^OOOJOCNCO^ OS^HCN^iOCOCOOS CN p p CN O CO 00 CO CM CN CO CO lO CO W CO t^ 00 XX XXXXXX XXXXXXX XXXXXXXX HANDBOOK ON REINFORCED CONCRETE. '35 $ ^'^ & JiW! . 9 M c3 S3 II: ;ooo>oioooioo oooo ;Tfit^iO i 000(MOt- 000 * 35 00 C l> CO * SCO CO 1C CO O5 C5 O oioooooooio o 10 o o o o u: osoor-^oios oiosoocoo'Ci-HOicoosio -^ T-I as o os co t^ CO O i-< Ol T)< Tf OOr-fOlOOrHOIOlOlCO O) CO CO O4 O) O C h. ,-1 i-< O O Gi-ii-ii-iO500>CiCOOCO O Ol Ol O O 1C CO C l> I> 01 01 Or-iWOJp'-iOIOlCOCOCO p -! 1-1 O >O t^ 00 1C CO CO CO CO CO COCOCOCOOOOOOOOOOOOOOO CO CO CO t~ t^ OS OS O O O TP h. t^OSOCO00OOOOOTi< O CO 0} OJ>M rt< f- CO OCOO oo iCCiCO OOOOOOOOOOO OOO^COOO oo" to" oo o* O CO 1> OS OOOO 00 IM (M O 00 O of 10" 1> OS O rH tCt-COC COCO^O)O1 iciccot-ocor^i-Hoo o o i- 1 co to o iOcO^-OOO'-iOIM H C lOcOt'-OOOS'-i CO Ol" tC o" I-H" T^ ~rf O" -^ O" o" 10" of of 1C o" Os" 00 Ol" tC 1C ^OOOIOO CiCCOOOi-HCOCOCOOO i-HOJiCOiCOl OSOOICO TjilCCOt^OSOOlCOiCt^OS CO I s * 00 O i 'CO COOOOOOt^iO OOOliCiC O O O CO i~< TJH CO "^ i( i * oo o oi -* 3OOOOOOOOO OlTfHcOOOOOlTM MTfcOOOOOl^COOOO TflCOOOOCOiCt- NOlOlOlCOCOCOCOCOrf< OIOIOICOCOCOCO . <. OOO-iCO OOlCt~-.O3rHCOCI>.OSi-H lCt>-OSOlTtlCD 04COCOCO 040)04O1OlCOCOCOCOCOrt< OIO1O1COCOCO COOOOOlrlHcO OO)rt I> 00 00 00 iOcOCOCOl>t^OOGOOO Us oooo oooooooo Tf CO O 1~- COCOOOiOOt^OSCO rH O OS I-l TjHCDOOCDOCOCOlO 8 8 S GO 00 r-i t^ CO 1> l ooooo ooooooooo CO1>OSOO)COIOCOOO fl cq oo o co s t o o_ 00 10 i-^ 00 3 O - GO O i-T r-T of O rH CO rH CO 1O I> CO OS 00 iO *O *O |>- C^ t^- CD 00 00 O t> CO O CD rH CO O CO -t 1C CO 1C CO* .-H~ O O IO <* t rH CO_ . >O t^ O CO CO ^ * t rfl-^TfO t> t^ CO 00 00 O O T i ; cor-io>tN.'-H-ICO>OOOOCOO I-H W Tt< CO 3 4- i OC^IfO 00 t^, CO CO O co" ^ S of 2" O IN. O O OO Tfi O >O t> O CO IO GO >O 00 ^H CD 00 O3 r-l * r^ (N C4 jf 10 O O O O O 00 U5 00 >-i ^ b- 1> TjH Tfl IO O IO . b- 00 O O IN ,-! CD O CO CD 00 ^ o o m xxxxxxxxx xxxxx DESIGNS OF CONCRETE STRUCTURES. 89 IOOOIOOOO OOOiOOOiOOOO O>OiO I-H CO O O Tfi h- O GOC500COCOOOINOOCOCO O5lNO OOiOOOOiOOiOO -ICO . OS * i ^ OCOCO oooo OOO Sao 10 00 M S 2' d 04 CO CO o o ^o o *o o o i i O C^ iO t^ O t^- O 1C co" co" i-l O O N- IO CO O CO I-H IN CO CO CO CO 10" 10 10 S 8 O TJH 00 SSi?: CO-tfOOOiOOOOCOiN COcOO3COCDO^Ht^-'-iCO (N(NINCOCOTt<-*T}HiOiO O 00 00 00 (N * CO CO 00 00 1^ 00 O CO i-H >O CO t^ l> I-H CO t^ iO t^ O5O5 lOiOCOCOCOt^-t^t^OOOO xxxxxxxxxxx (N-*COOOO(NTfcOOOO (N-^cO COCOCOCO-^TfiTtlTti't | iO IOOIO xxxxxxxxxx xxx COCOCOCOCOCOCOCOCDCO COCOCO 90 HANDBOOK ON REINFORCED CONCRETE. S g 85 r=c J |i 8282 li 8^88 28882 ^i i-H (N IN o co r-lTH(N(N(NO CO T OOOOOO -H.-iiooocort.-HcO'^ OO-l>.CSpp b-p'-i'-it>. 2 88 Si S3 Si SS S S2222 V ">< H-i HM Hci *M O CO 00 O - OS 00 OS ^ -H rf CO CO OS O COCO r-l(N(N(NCOOSOTfri O>OOOOOO O'OOCOO'OOOOOOO *^ 00 ^O !O CO ' ^O COCOC^OOt s - | OCOOC^Ot N "t N -COO^CCOO o>ooooo 1010010 OOOOOSOiOi"* COCO^Tt^ S 8 S cS o " i-J" i-T 00 (N CO O (N CO OS CO OS O5 OS O 3 8 $ Ss- 3 CO b~ t^ t^- 00 OO5'O lOO^OOiOO^OO OCN ^COOOOOOCOCOCOCOCO COCCTft^f^t^ OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOQO 92 HANDBOOK ON REINFORCED CONCRETE. 00*000000*0 iOOiCOO3'OCOt>.rtiO COOO>OOC5OO O5OOOOO OOOOOiOOOOt-H rH (N (M CM I-H T-I (N (M 01 CN o >O h- O . 10 p CO I-H r/T - r iC^TjHioO^O h il O O CO CN O CO Slili $ O o" i-T O* t^-" tO^Ot^-^O^OO^OOC CO- iOOO5C33fOOiTtiCOCOl^ CO O O'-H .555^.^!* 3 s 2 3 cOO^CMcOCMpCOCOpt>T-iO5 poqicppt^Oi_wcq i . TtiTfiTffTjiiCiCiCCOCO CM ^f CO 00 -i-iW OSCMCOt^-OCOOOi^^COOCOI^i iCOi-^ & So 00 CM t^ I-H CO r-l "' ooooooooo cococor^oi>cococo OOCOOOCO'CCOOOCO_CO_ ic" co" o" TH I>OOOOOSOSOO CD --I CO O 00 OS CO ^ n if o" IN oo" 00 O ^t 1 00 C^l 1^* O 000 t^ 1C t^ 1-1 I> o o iC O COGOCOI>CMOOCOOOTfiOCOcMOO 00 OS OS O O I-H 8OOOOOOOO OiCOOiCiOOOOOOOOO OSOOOCO'^'^t^-t^- C^OSC^I^-CMi-HOS-^iCCOOOcMt^-^ O 00 CO S 8 oooooooo '*OOCNCOO'<* I 00(N OOi-irHCMOJCMCO V W ^J "V 1- t- ^^' r^ I-H co t^- i-i ws o * C 00 00 OS OS O O- TfTtTtiTti'*iCC>CiCCcOCOCOcOcot>- xxxxxxxxx xxxxxxxxxxxxxxxx i-lt-lr-Hi-li-lr-li-li-li-! CMiM(NCMCMC^ .S 50 O O 00 IN CO O O p i^ *-< >O O T-H (N o o o o fl iO t- O CO <* hH (N OJ. t>; -*_ t^ O l> 00 X X X X X DESIGNS OF CONCRETE STRUCTURES. 95 NOTE. With single spans, fixed at the ends, place' a reinforcement in the upper side of the beam or girder forming a cantilever from the fixed ends extending toward the center. The total area of this reinforcement should be 66.7 per cent of that placed in the lower side as called for in Table I. The distribution of this reinforcement should be as stated in the description of Tables la and 16 for the reinforcement in the upper side of contin- uous girders. When figuring girders of more than one span, having fixed ends, make the following changes in the amount of reinforcement just given. With 2 spans decrease 'the amount by 44.6 per cent. With 3 spans decrease the amount by 36.0 per cent. With 4 spans decrease the amount by 38.3 per cent. With 5 spans decrease the amount by 38.0 per cent. With 6, 7, 8, and 9 spans, decrease the amount by 38.0 per cent. DESCRIPTION OF TABLES la AND Ib. The following tables are inserted to allow for the effect of continuity of beams or girders over one or more supports, and give the proper steel sections to withstand the bending moments given when produced by a uniformly distributed loading 96 HANDBOOK ON REINFORCED CONCRETE. over equal spans. When these conditions do not exist, it remains for the designer to ascertain the bending moments in the different spans, ignoring the effect of continuity, as this is cared for in the results, and to fix upon the size of concrete girder that will care for the largest moment thus found by referring to the table. Opposite the size just determined will be found the reinforcement to adopt for different parts of the girder. Table la is worked out for two spans. Likewise Table Ib is for three spans only, but is applicable to any number with a maximum error of 1 per cent for moments over supports, and that on the safe side. For moments within the spans, the following changes should be allowed in the intermediate spans, the outside spans remaining as in the table. With 4 spans increase the reinforcement in the intermediate spans by 46 per cent. With 5 spans increase the reinforcement in the intermediate spans by 85 per cent. With 6 spans increase the reinforcement in the intermediate spans by 74 per cent. With 7 spans increase the reinforcement in the intermediate spans by 76 per cent. With 8 spans increase the reinforcement in the intermediate spans by 74 per cent. With 9 spans increase the reinforcement in the intermediate spans by 74 per cent. In distributing the reinforcement given in the tables for continuous girders, the following plan may be suggested: DESIGNS OF CONCRETE STRUCTURES. 97 All rods in the underside of the girder should extend from support to support; .3 square inch of steel per square foot section of girder in the upper side of the girder should extend from sup- port to support and lap sufficiently to develop the elastic limit of the section by exposing a sufficient surface to adhesion between the steel and the concrete; one- third of the remaining section in the upper side of the girder, should be one-half the length of the span and center over the support. Another third of the remaining section in the upper side of the girder, should be one-third the length of the span and center over the support. The last third of the remaining section in the upper side of the girder, should be one-fourth the length of the span and center over the support. NOTE. The purpose of the continuity of rods in the upper surface is to care for tension caused by an increase of temperature. The object sought in preparing these tables was to free the designer of the tedious routine in determining the bending moments in the different parts of continuous girders. All spans of the con- tinuous girder should be treated as single spans supported at the ends to determine the maximum moment from which the girder size should be as- certained by reference to the table. It may be unnecessary to state that it is expected that the same size of girder section will be used through- out the length of the continuous girder as deter- mined by the maximum bending moment in the different spans of the girder. 98 HANDBOOK ON REINFORCED CONCRETE. TABLE la. 1 2 3 4 5 6 7 Reinforcement Reinforcement Size of 1 ,, Safe bending moment. over central sup- port. (In upper side of girder.) throughout spans. (In lower side of girder.) beam. Factor of safety = 3.5. Area No. and Area No. and of size of of size of metal. rods. metal. rods. In: In. Ibs. Ft. Ibs. Sq. in. Sq. in. 2.5X6 7,800 650 .47 1-yi" .27 l-is" 2.5X8 15,350 1,280 .52 1-f" .29 1-iV 2.5X10 25,250 2,100 .65 l-yf" .37 1-f* 2.5X12 37,800 3,150 .66 1-tt* .43. 1-H" 3X6 9,380 780 .48 1-f" .27 i-A" 3X8 18,450 1,540 .59 i-H* .33 1-f" 3X10 30,000 2,500 .66 l-ll" .37 1-f" 3X12 45,500 3,790 .78 H" .44 l~tt* 3X14 63,500 5,290 .88 1-lt" .50 i-r 4X8 24,500 2,040 .75 H" .42 i-H- 4X10 40,500 3,380 .86 1-if" .49 i-f r/ 4X12 60,500 5,040 .99 1-1" .56 i-f 4X14 84,500 7,040 1.14 1-1 T&" .64 i-^f" 4X16 112,500 9,380 1.26 1-lf .71 i-l" 5X10 50,650 4,220 1.15 2-|" .65 i_if* 5X12 75,600 6,300 1.32 2- it" .74 i-f 5X14 105,500. 8,790 1.46 2-f .82 ! H* 5X16 140,500 11,710 1.68 2-lf" .95 1-1" 5X18 180,000 15,000 1.86 2-1" 1.05 1-1 A" 5X20 225,500 18,790 2.06 2-lf5" 1.17 i-if 6X12 91,000 7,580 1.53 2-f .86 i-jr 6X14 127,000 10,580 1.78 2-lf" 1.00 i-i" 6X16 168,500 14,040 1.97 2-1" 1.12 1-1 A* 6X18 217,000 18,080 2.19 2-1 A' 1.24 i-if 6X20 270,500 22,540 2.40 2-lf 1.36 2-1" 6X22 332,500 27,710 2.62 2-lf 1.48 2-f 6X24 398,500 33,210 2.84 2-lf 1.61 2-lf DESIGNS OF CONCRETE STRUCTURES. 99 TABLE la. Continued. 1 2 3 4 5 6 7 Reinforcement Reinforcement over central sup- throughout spans. Size of fc)63,rn. Safe bending moment. port. (In upper side of girder.) (In lower side of girder.) Factor of safety = 3.5. Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. 7X14 148,000 12,330 2.14 3-1" .21 l-ll" 7X16 197,000 16,420 2.41 3-M" .36 2-1" 7X18 252,500 21,040 2.62 3- if" .48 2-1" 7X20 315,000 26,250 2.87 3-1" .62 2-lf" 7X22 387,500 32,280 3.11 3-1 A* .76 2-lf" 7X24 464,500 38,710 3.27 3-1 A" .85 2-1" 7X26 547,500 45,630 3.53 3-1 A" 2.00 2-1" 7X28 639,500 53,290 3.77 3-ir 2.14 2-1 iV 8X16 225,000 18,750 2.63 3- if" 1.49 2-|" 8X18 288,500 24,040 2.90 3-1" 1.64 2-M" 8X20 360,500 30,040 3.24 3-1 A" 1.85 2-1" 8X22 442,500 36,880 3.55 3-lJ* 2.01 2-1" 8X24 531,000 44,250 3.82 3-l|" 2.16 2-1 A" 8X26 625,000 52,080 4.09 3-1 A" 2.32 2-l|" 8X28 725,000 60,420 4.32 3-1 A* 2.44 2-1*" 8X30 840,000 70,000 4.65 3-11" 2.63 2-1 A" 8X32 962,000 80,170 4.97 3-1 A" 2.81 2-1 A" 9X18 324,000 27,000 3.38 4- W 1.91 2-1" 9X20 406,000 33,830 3.73 4-1" 2.11 2-1 A" 9X22 498,500 41,540 4.03 4-1" 2.28 2-l|" 9X24 597,000 49,750 4.37 4-1 A" 2.47 2-1*' 9X26 702,500 58,540 4.65 4-1 A" 2.63 3-M" 9X28 800,000 66,660 4.73 3-li" 2.68 3-1" 9X30 946,500 78,870 5.22 3-lf" 2.94 3-1" 9X32 1,082,500 90,210 5.54 3-lf" 3.13 3-1 A" 9X34 1,227,500 102,290 5.87 3-1 A" 3.31 3-1 A" 9X36 1,380,000 115,000 6.16 3-1 A" 3.48 S-lf 10X20 451,000 37,580 4.10 4-r 2.32 3-F 10X22 554,000 46,170 4.43 4-1 A" 2.51 3-lf" 100 HANDBOOK ON REINFORCED CONCRETE. TABLE la. Continued. 1 2 3 4 5 6 7 Reinforcement Reinforcement Safe bending over central sup- port. (In upper throughout spans. (In lower side Size of moment, side of girder.) of girder.) earn. safety =3.5 Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft, Ibs. Sq. in. Sq. in. 10X24 664,000 55,330 4.90 4-li* 2.77 3-1" 10X26 780,000 65,000 5.12 4-li" 2.89 3-1" 10X28 914,000 76,170 5.40 3-lf" 3.05 3-1 A* 10X30 1,050,000 87,500 5.73 3-1 A* 3.24 3-1 A* 10X32 1,200,000 100,000 6.09 3-li" 3.44 3-li" 10X34 1,365,000 113,750 6.71 3- \-\" 3.79 3-11" 10X36 1,532,000 127,670 6.80 3-1 A" 3.85 3-1 A* 10X38 1,702,000 141,830 7.14 3-1 A* 4.03 3-1 A* 10X40 1,905,000 158,750 7.35 3-lf* 4.15 3-1 A* 11X22 610,000 50,830 4.97 5-1" 2.80 3-1" 11X24 729,000 60,750 5.36 5-1 iV' 3.03 3-1" 11X26 858,000 71,500 5.68 5-1 A* 3.21 3-1 A* 11X28 1,002,500 83,540 6.02 4-li" 3.40 3-1 A" 11X30 1,157,000 96,420 6.48 4-1^" 3.66 3-li" 11X32 1,325,000 110,420 6.65 3-li" 3.75 3-11" 11X34 1,500,000 125,000 7.07 3-1 A" 3.96 4-1" 11X36 1,685,000 140,420 7.45 3-lf" 4.20 4-1 rV 11X38 1,871,000 155,920 7.80 3-1 ft* 4.40 4-1 A* 11X40 2,092,000 174,330 8.24 3-1 ft* 4.65 4-11" 11X42 2,312,500 192,710 8.61 3-lf" 4.86 4-11" 11X44 2,540,000 211,670 8.95 3-lf" 5.05 4-11" 12X24 796,000 66,330 5.58 5-1^" 3.15 3-1 A" 12X26 937,000 78,080 6.08 4-li" 3.43 3-1 A* 12X28 1,095,000 91,250 6.51 4-1 A* 3.68 3-11" 12X30 1,262,500 105,210 6.97 4-1 A" 3.93 4-1" 12X32 1,440,000 120,000 7.33 4-lf" 4.14 4-1 A* 12X34 1,640,000 136,670 7.61 4-1 A' 4.30 4-1 A* 12X36 1,841,000 153,420 8.12 3-1 ft* 4.58 4-11" 12X38 2,032,000 169,330 8.42 3-lf" 4.75 4-11" 12 X40, 2,249,000 187,410 8.92 3-lf" 5.03 5-1" DESIGNS OF CONCRETE STRUCTURES 101 TABLE la. Continued. 1 2 3 4 5 6 7 Reinforcement Reinforcement over central sup- throughout spans. Size of Safe bending moment, r* actor of port. (In upper side of girder.) (In lower side of girder.) D63.H1. safety = 3.5. Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. 12X42 2,466,000 205,490 9.35 3-1 If" 5.28 6-1 A* 12X44 2,683,000 223,570 9.85 3-1 ff" 5.56 5-1 A" 12X46 2,900,000 241,670 10.25 3-11" 5.80 5-1 1" 12X48 3,175,000 264,580 10.75 3-11" 6.08 5-ll" 13X26 1,015,000 84,580 6.60 6-1 A' 3.73 5-1" 13X28 1,187,500 98,960 7.05 5-1 A" 3.98 5-ff" 13X30 1,367,500 115,630 7.68 5-lJ" 4.34 5- if" 13X32 1,560,000 130,000 8.08 5-1 ^" 4.57 5-1" 13X34 1,770,000 147,500 8.49 5-1 A* 4.80 5-1" 13X36 1,995,000 166,250 8.92 4-1}" 5.04 5-1" 13X38 2,212,500 184,380 9.19 4-1}" 5.20 5-1 A" 13X40 2,475,000 206,250 9.72 4-1 A" 5.50 6-1 A* 13X42 2,730,000 227,500 10.16 4-lf" 5.75 5-1 J" 13X44 3,010,000 250,830 10.46 3-11" 5.91 5-1 i" 13X46 3,150,000 262,500 11.06 O I lj|// 6.25 5-lJ" 13X48 3,440,000 287,000 11.47 3-1 IS- 6.48 5-1 A* 13X50 3,770,000 314,170 11.98 3-2" 6.75 5-1 A* 13X52 4,062,500 338,540 12.39 3-2^" 6.98 6-1 A* 14X28 1,277,500 106,460 7.62 5-1 4.31 5-M" 14X30 1,472,500 122,710 8.20 5-1 A" 4.63 5-1" 14X32 1,680,000 140,000 8.68 5-lf 4.91 5-1" 14X34 1,910,000 159,170 8.97 4-1}" 5.07 5-1" 14X36 2,145,000 178,750 9.48 4-1 A" 5.36 6-1 A* 14X38 2,375,000 197,920 9.89 4-lf* 5.59 5-1 A" 14X40 2,628,750 219,070 10.47 4-1 1" 5.91 5-l|" 14X42 2,882,500 240,220 10.93 A 1 11 6.18 5-l|" 14X44 3,136,200 261,370 11.42 4-1 ft* 6.46 6-1 A" 14X46 3,390,000 282,500 11.77 3-2" 6.65 6-1 A* 14X48 3,705,000 308,750 12.36 3-2 &" 6.98 s-i A* 14X50 4,050,000 337,500 12,85 3-2 ys" 7.26 5-11" 102 HANDBOOK ON REINFORCED CONCRETE. TABLE la. Continued. 1 2 3 4 5 6 7 Reinforcement Reinforcement Size of Safe bending moment. over central sup- port. (In upper side of girder.) throughout spans. (In lower side of girder.) DOBIu* safety =3.5 Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. 14X52 4,375,000 364,580 13.27 3-2f" 7.50 5-1}" 14X54 4,737,500 394,790 13.72 3-2|" 7.75 5-1}" 14X56 5,110,000 425,830 14.20 3-2 A" 8.02 s-i A* 15X30 1,580,000 131,800 8.57 4-li" 4.84 5-1" 15X32 1,785,000 148,750 8.97 4-14" 5.07 5-1 ^g" 15X34 2,047,500 170,630 9.62 4-1 A* 5.43 5-1 A' 15X36 2,300,000 191,670 10.10 4-lf" 5.71 5- 11" 15X38 2,550,000 212,500 10.54 4-1 1" 5.94 5-1-g" 15X40 2,818,750 234,900 11.19 4-1 tt* 6.32 5-11" 15X42 3,087,500 257,300 11.66 4-1 ft* 6.59 5-1 A* 15X44 3,356,250 279,700 12.18 4-lf" 6.88 5-1 A' 15X46 3,625,000 302,080 12.75 4-1 W 7.21 5-1}" 15X48 3,970,000 330,830 13.27 4-1 }|" 7.50 5-1}" 15X50 4,337,500 361,460 13.84 3- 2 i" 7.82 5-1}" 15X52 4,675,000 389,580 14.23 3-2^" 8.04 5-1 A" 15X54 5,080,000 423,330 14.88 3-2}" 8.41 5-1 A" 15X56 5,475,000 456,250 15.37 3-2}" 8.68 5-lf" 15X58 5,900,000 491,660 15.80 3-2^" 8.93 5-lf" 15X60 6,300,000 525,000 16.23 3-2f" 9.17 5-lf" 16X32 1,923,000 160,250 9.75 5-1 A" 5.51 5-1 A" 16X34 2,180,000 181,670 9.84 5-1 A* 5.56 5-1 A* 16X36 2,457,500 204,790 10.91 5-1 4" 6.17 5-l|* 16X38 2,725,000 227,080 11.35 5-14" 6.42 5-li" 16X40 3,012,500 251,040 11.86 4-lf" 6.70 5-1^" 16X42 3,300,000 275,000 12.38 4-lf" 7.00 5-1 A" 16X44 3,582,500 298,960 12.97 4-1 }f" 7.33 5-1}" 16X46 3,875,000 322,920 13.62 7.70 5-1}" 16X48 4,235,000 352,920 14.14 4-l|" 8.00 5-1 A" 16X50 4,632,500 386,040 14.65 3-2i 8.28 s-i A" 16X52 5,000,000 416,670 15,13 8.53 3-1 W DESIGNS OF CONCRETE STRUCTURES. 103 TABLE la. Continued. 1 2 3 4 5 6 7 Reinforcement Reinforcement Safe bending over central sup- port. (In upper throughout spans. (In lower side Size of moment. side of girder.) of girder.) safety =3.5. Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. 6X54 5,415,000 451,250 15.65 3-2 Y$" 8.83 3- ITS" 6X56 5,850,000 487,500 16.25 3-2f " 9.17 3-l| " 6X58 6,285,000 523,750 16.76 3-2| " 9.46 3-lif" 6X60 6,725,000 560,420 17.34 3-2^ 9.78 3-lrT 6X62 7,200,000 600,000 17.80 3-2^" 10.08 3-1 1 " 6X64 7,685,000 640,420 18.36 3-2* " 10.38 3-l| " 7X34 2,315,000 192,920 10.90 5-1* " 6.15 5-1* * 7X 36 2,605,000 217,080 11.40 5-1*" 6.43 5-1 rV" 7X38 2,895,000 241,250 12.04 5-1 &" 6.80 5-1 iV 7X40 3,237,500 269,480 12.70 5-lf " 7.17 5-li " 7X42 3,575,000 298,000 13.22 5-lfJ 7.46 5-l " 7X44 3,925,000 327,080 13.86 7.82 5-li " 7X46 4,110,000 342,500 14.40 4-lp 8.13 4-1 A" 7X48 4,500,000 375,000 15.00 8.44 4-1* 7X50 4,920,000 410,000 15.60 4-2 * " 8.77 4-1* 7X52 5,315,000 442,930 16.11 4-2 * 9.07 4-1 Tff" 7X54 5,760,000 480,000 16.85 4-2^" 9.48 4-1 TS" 7X56 6,210,000 517,500 17.20 3-2^" 9.67 3- IT!" 7X58 6,685,000 559,080 17.74 3-2^" 9.98 3~1| " 7X60 7,150,000 595,830 18.30 3-2* " 10.35 3-1& " 7X62 7,650,000 637,500 18.88 3-2* " 10.67 3-1 if" 7X64 8,160,000 680,000 19.50 3-2 ]V 11.03 3-1 ii" 7X66 8,710,000 725,830 20.10 3-2f " 11.36 3-2 " 7X68 9,250,000 770,830 20.67 3-2f " 11.70 3-2 * 8X36 2,765,000 230,420 12.10 5-1* " 6.84 5-lfV" 8X38 3,065,000 255,420 12.64 5-lf " 7.13 5-li " 8X40 3,425,000 285,420 13.42 5-1 W 7.57 5-l| " 8X42 3,782,500 315,210 14.04 5-ltt* 7.93 5-iA" 8X44 4,170,000 347,500 14.53 4-1 if" &. 20 4-1 A" 8X46 4,355,000 362,920 15.18 8.56 4-1*" 104 HANDBOOK ON REINFORCED CONCRETE TABLE la. Continued. 1 2 3 4 5 6 7 Reinforcement Reinforcement Size of beam. Safe bending moment. 1* actor of over central sup- port. (In upper side of girder.) throughout spans. (In lower side of girder.) safety =3.5 Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. 18X48 4,760,000 396,670 15.80 4-2 " 8.92 4-1* " 18X50 5,200,000 433,330 16.48 4-2^" 9.30 4-1 ft" 18X52 5,625,000 468,750 17.12 4-2^ " 9.65 4-1 ft" 18X54 6,100,000 508,330 17.75 4-2* " 10.03 4-lf " 18X56 6,575,000 547,920 18.36 4-2* " 10.37 4-lf " 18X58 7,075,000 589,580 19.00 4-2ft" 10.74 4-lii" 18X60 7,565,000 630,420 19.36 s-2ft" 10.95 3-1 if" 18X62 8,100,000 675,000 19.94 3-2f " 11.26 3-1 W 18X64 8,640,000 720,000 20.52 3-2-f " 11.59 3-2 " 18X66 9,230,000 769,170 21.25 12.00 3-2 " 18X68 9,785,000 815,420 21.84 3-2^1" 12.33 3-2ft" 18X70 10,445,000 870,420 22.50 3-2f " 12.72 3-2ft" 18X72 11,040,000 920,000 23.05 3-2H" 13.03 3-2*" 19X38 3,230,000 269,166 13.37 5-1 H" 7.55 5-li " 19X40 3,617,500 301,460 14.10 5 -lii" 7.96 5-1 ft" 19X42 3,985,000 332,080 14.78 5-lf " 8.35 5-1 ft" 19X44 4,395,000 367,080 15.43 5-lf " 8.71 5-lf " 19X46 4,597,500 383,130 16.20 5-llf" 9.15 5-lf " 19X48 5,035,000 419,580 16.77 4-2ft" 9.48 4-1 ft" 19X50 5,495,000 457,920 17.42 4-21 " 9.83 4-lf " 19X52 5,940,000 495,000 18.00 4-2l " 10.16 4-lf " 19X54 6,435,000 536,250 18.73 4-2ft" 10.57 4-lf* 19X56 6,930,000 577,500 19.32 4-2 " 10.90 19X58 7,470,000 622,500 20.05 4-2J " 11.32 4-1^" 19X60 7,990,000 665,830 20.58 4-2 ft" 11.61 4-lf " 19X62 8,560,000 713,330 21.10 3-2^" 11.91 3-2 19X64 9,130,000 760,830 21.75 3-2^" 12.28 3-2ft" 19X66 9,740,000 811,670 22.40 3-2f " 12.65 3-2ft" 19X68 10,350,000 862,500 23.00 3-2 W 13.00 3-21 " 19X70 11,000,000 916,670 23.68 3-2 If" 13.37 3-21 " 19X72 11,650,000 970,830 24.35 3-21 " 13.75 DESIGNS OF CONCRETE STRUCTURES. TABLE la. Continued. 105 1 2 3 4 5 6 7 Reinforcement Reinforcement over central sup- throughout spans. Safe bending port. (In upper (In lower side Size of moment. side of girder.) of girder.) Deani. safety = 3.5. Area No. and Area No. and of size of of size of metal. rods. metal. rods. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. 19X74 12,340,000 1,028,330 25.00 3-2l|" 14.10 3-2 &" 19X76 13,000,000 1,083,330 25.68 3-2H" 14.50 3-2^ " 20X40 3,810,000 317,500 14.80 5-lf " 8.36 5-1 A" 20X42 4,200,000 350,000 15.46 5-lf " 8.73 5-lf " 20X44 4,627,500 385,630 16.20 5-1 If" 9.15 5- If " 20X46 4,837,500 403,130 16.94 5-lf " 9.57 5-!^" 20X48 5,300,000 441,670 17.72 5-1 W 10.01 5-1 &" 20X50 5,785,000 482,080 18.96 5-1 W 10.44 5-4 " 20X52 6,250,000 520,830 19.02 5-1 W 10.76 5-4 " 20X54 6,875,000 572,920 19.71 4-2 " 11.14 4-1 IT 20 X56 7,300,000 608,330 20.26 4-2i " 11.45 4-lf " 20X58 7,860,000 655,000 21.00 4-2^" 11.87 4-lf " 20X60 8,400,000 700,000 21.60 4-2f " 12.20 4-lf " 20X62 9,000,000 750,000 22.32 4-2f " 12.60 4- lH" 20X64 9,630,000 802,500 23.03 4-2^" 13.01 4-1 If" 20X66 10,250,000 854,170 23.71 4-2 TO" 13.40 4-lf " 20X68 10,875,000 906,250 24.15 3-2| " 13.65 3-2^" 20X70 11,600,000 966,670 24.95 3-21T 14.10 3-2^* 20X72 12,250,000 10,20,830 25.60 3-2 W 14.47 3-21 r/ 20X74 12,975,000 1,081,250 26.22 3-3 " 14.82 3-2^ " 20X76 13,700,000 1,141,670 26.86 3-3 " 15.19 3-2^ 20X78 14,460,000 1,205,000 27.66 3-3^" 15.64 3-2^" 20X80 15,240,000 1,270,000 28.37 3-3* " 16.01 3-2^" 106 HANDBOOK ON REINFORCED CONCRETE. KEY TO USING TABLES IA, IB, I, AND II. In cases of continuous girders with 2 spans, use Table la. In cases of continuous girders with 3 spans, use Table Ib. In cases of continuous girders with 4 or more spans, use Table 16, with the modifications given in the description for Tables la and 16. In cases of girders or beams with one span only supported at the ends, when loaded uniformly, and when the span is known, use Table II. In cases of girders or beams with one span only, supported at the ends and receiving concentrated loads, determine the maximum bending moment, and use Table I. In cases of girders or beams fixed at one or both ends, use Tables I and II, modified as stated in the note following Table I. DESIGNS OF CONCRETE STRUCTURES. 107 TABLE 16. 1 2 3 4 5 6 7 8 9 Reinforce- Reinforce- Reinforce- ment over ment, ment, intermediate intermediate outside spans. Size of beam. Safe bending moment. Factor of supports. (In upper side of girder.) span. (In lower side of girder.) (In lower side of girder.) safety 3.5. Area No. and Area No. anc Area No. and of size of of size of of size of metal bars. metal bars. meta bars. In. In. Ibs. Ft. Ibs. Sq. in Sq. in Sq. in 2.5X6 9,700 810 .47 i- H" .12 1-f " .38 1- f ^ 2.5X8 19,100 1,600 .52 i-f " .13 i-t 7 *. .42 2.5X10 31,600 2,620 .65 i-it" .16 .52 1-f " 2.5X12 47,200 3,940 .66 i- it" .19 i- ^" .62 1-it" 3X6 11,700 975 .48 i-f .12 i- 1 " .38 1- f J 3X8 23,050 1,930 .59 i- it" .15 i- ^" .47 3X10 37,500 3,120 .66 i-it" .17 i- &" .53 1- f " 3X12 56,900 4,740 .78 i-l" .19 i- ^" .62 1- it" 3X14 79,400 6,510 .88 i- if" .22 i-i " .70 1-1 " 4X8 30,600 2,550 .75 i-l " .19 i- ^" .60 i- it" 4X10 50,600 4,220 .86 i- if" .21 1-*;; .69 i-l " 4X12 75,600 6,300 .99 1-1 " .25 .79 i- il" 4X14 106,000 8,800 1.14 1-1 A" .29 1 15 .91 1-1 " 4X16 140,500 11,740 1.26 i-ii " .32 1- &" 1.01 1-1 " 5X10 63,300 5,280 1.15 2- f " .29 1- &" .91 1-1 " 5X12 94,500 7,870 1.32 2- it" .33 1-f " 1.06 1-1 A" 5X14 132,000 11,000 1.46 2- 1 " .37 1-f " 1.17 11-1- " 5X16 175,600 14,650 1.68 2- if" .42 i- \\" 1.34 1-1 T 3 / 5X18 225,000 18,750 1.86 2-1 " .47 i- W 1.49 5X20 282,000 23,480 2.06 2-1 TJT" .52 1-f" 1.65 1-1 ^" 6X12 113,600 9,470 1.55 2- 1 " .38 1-f " 1.12 1-1 T 3 ^" 6X14 159,000 13,240 1.78 2- if' .45 1-tt* 1.42 2-1 " 6X16 210,400 17,550 1.97 2-1 " .49 1-f " 1.58 2 } 5 " 6X18 271,500 22,600 2.19 2-1 3^" .55 1-f" 1.75 2- if' 6X20 338,000 28,200 2.40 2-1** .60 -it" 1.92 2-1 " 6X22 415,500 34,690 2.62 2 li- " .65 - it" 2.10 2-1 T&" 6X24 498,500 41,520 2.84 2-l| " .71 -1" 2.27 2-1 iV' 108 HANDBOOK ON REINFORCED CONCRETE. TABLE 16. Continued. 1 2 3 4 5 6 7 8 9 Reinforce- Reinforce- Reinforce- ment over ment, ment, intermediate intermediate outside spans. Size of beam. Safe bending moment. Factor of supports. (In upper side of girder.) span (In lower side of girder.) (In lower side of girder.) cofotir ^ f^ &aieiy o.o. Area No. am Area No. and Area No. and of size of of size of of size of metal. bars. metal bars. metal. bars. In. In. Ibs. Ft, Ibs. Sq. in. Sq. in. Sq. in. 7X14 185,000 15,420 2.14 3-| * .53 I- I" 1.71 2- If" 7X16 246,000 20,550 2.41 3- if" .60 i- W 1.93. 2-1 " 7X18 316,000 26,260 2.62 3- W .66 i-H* 2.10 2-1 rV 7X20 394,000 32,800 2.87 3-1 " .72 i-l " 2.30 2-1* " 7X22 485,000 40,400 3.11 3-1&" .78 i-tf* 2.49 2-11 " 7X24 580,000 48,500 3.27 3-lA" .82 i-if" 2.62 2-1 iV 7X26 685,000 57,100 3.53 3-1&* .88 i-if' 2.82 2-liV 7X28 800,000 66,700 3.77 3-11 " .94 1-1 " 3.02 2-l| * 8X16 281,500 23,480 2.63 3- W .66 1-M" 2.10 2-liV' 8X18 360,600 30,100 2.90 3-1 " .73 1-f " 2.32 2-11 " 8X20 450,500 37,600 3.24 3-liV' .81 i-iT 2.59 3- if 8X22 553,000 46,150 3.55 3-11 " .89 1-1 " 2.84 3-1 " 8X24 664,000 55,400 3.82 3-11 " .96 1-1 " 3.06 3-1 " 8X26 781,000 65,200 4.09 3-lfc- 1.02 i-iiV' 3.27 3-1 ,y 8X28 906,000 75,550 4.32 3-lft* 1.08 i-iA" 3.46 3-11 " 8X30 1,050,000 87,600 4.65 3-1} " 1.14 i-4 " 3.72 3-11 " 8X32 1,202,000 100,800 4.97 3-1 A* 1.24 i-ii " 3.98 3-1^ 9X18 405,000 33,750 3.38 4- W .85 i- W 2.70 3-1 " 9X20 507,000 42,250 3.73 4-1 " .93 1-1 " 2.93 3-1 " 9X22 622,000 52,000 4.03 4-1 " 1.01 1-1 " 3.21 3-iA* 9X24 745,000 62,150 4.37 4-lA" 1.09 i-iA" 3.50 3-11 " 9X26 877,000 73,150 4.65 4-1 h" 1.16 i-ii " 3.72 3-11 " 9X28 1,000,000 83,300 4.73 3-1} " 1.18 2- if" 3.78 3-11 " 9X30 1,185,000 98,500 5.22 3-1 i " 1.31 2-W 4.17 4-liV 9X32 1,353,000 112,800 5.54 3-lf- " 1.39 2-1" 4.43 4-1 rV 9X34 1,535,000 128,000 5.87 3-1Y3 1.47 2-1" 4.70 4-11 " 9X36 1,725,000 143,850 6.16 3-1 A" 1.54 2- I " 4.93 4-11 " 10X20 564,000 47,000 4.10 4-1 " 1.03 2- I " 3.28 3-1 iY 10X22 692,500 57,750 4.43 4-1&" 1.11 2- | " 3. 4 3-lA" DESIGNS OF CONCRETE STRUCTURES. TABLE 16. Continued. 109 1 2 3 4 5 6 7 8 9 Size of beam. Safe be mom Facto safety - nding ent. r of q c Reinforce- ment over intermediate supports. (In upper side of girder.) Reinforce- ment, intermediate span. (In lower side of girder.) Reinforce- ment, outside spans. (In lower side of girder.) >.>. Area No, and Area No. and Area No. and of size of of size of of size of metal. bars. metal. bars. metal. bars. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. Sq. in. 10X24 830,000 69,200 4.90 4-1J " 1.23 *-w 3.92 3-l| " 10X26 975,000 81,250 5.12 4-1 1 " 1.28 2- if' 4.10 3-l| " 10X28 1,142,000 95,200 5.40 3-lf " 1.35 2- if" 4.32 4-1^" 10X30 1,312,000 109,500 5.73 3-1&* 1.44 2- | " 4.58 4-l| " 10X32 1,500,000 125,000 6.09 3-4 " 1.52 2- | * 4.87 4-li " 10X34 1,707,000 142,200 6.71 3-4 " 1.68 2-.il" 5.37 4-1 iV 10X36 1,914,000 159,600 6.80 3-1&* 1.70 2- W 5.45 4-1 h" 10X38 2,127,000 177,400 7.14 3-1 A" 1.79 2-1 " 5.71 4-l| " 10X40 2,380,000 198,500 7.35 3-1 1 " 1.84 2-1 " 5.88 4-li " 11X22 752,000 63,500 4.97 5-1 " 1.24 2- if" 3.98 4-1 " 11X24 910,000 75,800 5.36 5-liV' 1.34 2- if" 4.29 4-1^" 11X26 1,074,000 89,200 5.68 5-lTV' 1.42 2-1 " 4.55 4-1^" 11X28 1,253,000 104^500 6.02 4-11 " 1.51 2-1 " 4.82 4-11 11X30 1,447,000 120,500 6.48 4-1^ " 1.62 2-W 5.18 5-1A" 11X32 1,655,000 138,000 6.65 3-lJ " 1.66 * if* 5.32 5-1^" 11X34 1,875,000 156,000 7.07 3-lA" 1.77 2- it" 5.65 5-li " 11 X36 2,106,000 175,500 7.45 3-lf " 1.87 2-1 " 5.96 5-l| " 11X38 2,340,000 194,600 7.80 3-1 W 1.95 2-1 " 6.25 5-1% " 11X40 2,615,000 217,500 8.24 3-1 W 2.06 2-lA" 6.60 4-iA" 11X42 2,890,000 240,800 8.61 3-l| " 2.15 2-liV' 6.89 4-1 h" 11X44 3,170,000 264,000 8.95 3-lf " 2.24 2-lTV' 7.16 4-l| 12X24 994,000 82,800 5.58 5-1** 1.40 2-|" 4.47 4-lTV' 12X26 1,170,000 97,500 6.08 4-4 " 1.52 2- 1 " 4.87 4-1 \ " 12X28 1,370,000 114,000 6.51 4-ltk" 1.63 2- if' 5.21 5-1^" 12X30 1,578,000 131,500 6.97 4-1A" 1.74 2- W 5.57 5-1 T y 12X32 1 ,800,000 150,000 7.33 4-1 1 " 1.83 2-1 " 5.87 5-4 " 12X34 2,050,000 170,700 7.61 4-l^c" 1.90 2-1 " 6.10 5-1* * 12X36 2,300,000 191,600 8.12 3-1 W 2.03 2-1 " 6.49 5-1 A" 12X38 2,540,000 211,500 8.42 3-1 1 " 2.10 2-1^" 6.73 4-1A" 110 HANDBOOK ON REINFORCED CONCRETE. TABLE Ib. Continued. 1 2 3 4 5 6 7 8 9 Reinforce- Reinforce- Reinforce- ment over ment, ment, intermediate intermediate outside spans. Size of beam. Safe bending moment. Factor of _, r_i. r o C supports. (In upper side of girder.) span. (In lower side of girder.) (In lower side of girder.) saiety >.o. Area No. ant Area No. anc Area No. and of size of of size of of size of metal bars. metal bars. meta! bars. In. In. Ibs. Ft. Ibs. Sq. in Sq. in Sq. in 12X40 2,816,000 234,000 8.92 3-lf' 2.23 2-1A' 7.13 4-lf " 12X42 3,080,000 256,400 9.35 3-1 W 2.34 2-1! ' 7.48 4-11 " 12X44 3,352,000 279,000 9.85 3-1 W 2.46 2-li' 7.88 4-1 A" 12X46 3,620,000 301,700 10.25 3-11 " 2.56 3- if' 8.20 4-1 A* 12X48 3,970,000 332,000 10.75 3-l| " 2.70 3-1 ' 8.60 4-1 \ " 13X26 1,270,000 105,800 6.60 5-lfe" 1.65 2- If" 5.28 5-1 rV 13 X28 1,484,000 124,000 7.05 5-1 A" 1.76 2-1 " 5.65 5-1 iV 13X30 1,710,000 142,500 7.68 5-li " 1.92 2-1 " 6.15 5-4 * 13X32 1,950,000 162,500 8.08 5-1 A* 2.02 2-1 " 6.47 5-11 " 13X34 2,214,000 184,400 8.49 5-1 A" 2.12 2~! A" 6.80 5-11 " 13X36 2,493,000 207,700 8.92 4-l| * 2.23 2-1 A" 7.14 4-lf " 13X38 2,767,000 230,200 9.19 4-4 " 2.40 2-1 1 " 7.36 4-lf " 13X40 3,095,000 258,000 9.72 4-1 A" 2.43 2-lJ " 7.78 4-1 A* 13X42 3,413,000 284,300 10.16 4-lf " 2.54 3- if" 8.14 4-1 T 7 / 13X44 3,765,000 313,800 10.46 3-11 " 2.61 3- if" 8.38 3-1 ^" 13X46 3,940,000 328,000 11.06 3-1 If" 2.77 3-1 " 8.85 3-lf " 13X48 4,300,000 358,600 11.47 3-1 }f" 2.87 3-1 " 9.17 3-lf * 13X50 4,710,000 392,800 11.98 3-2 " 2.99 3-1 " 9.58 3-1 W 13X52 5,085,000 422,500 12.39 3-2^" 3.10 3-iA* 9.92 3-11 " 14X28 1,593,000 133,000 7.62 5-lf " 1.91 2-1 " 6.15 5-11 " 14X30 1,840,000 152,700 8.20 5-1 A" 2.05 2-1 TS" 6.56 5-1 A" 14X32 2,100,000 174,000 8.68 5-lf " 2.17 2-1 A" 6.95 5-1 A" 14X34 2,385,000 198,000 8.97 4-lJ " 2.24 2-1 A" 7.18 4-lf " 14X36 2,680,000 222,400 9.48 4-1 A" 2.37 2~4 " 7.60 4-lf " 14X38 2,970,000 246,000 9.89 4-lf " 2.47 2-lJ " 7.92 4-lui" 14X40 3,282,000 272,400 10.47 4-lf " 2.62 3- if" 8.38 41 7 M 1 16 14X42 3,602,000 299,000 10.93 4-1 W 2.73 3-1 " 8.75 4-1 \ " 14 X44 3,920,000 324,600 11.42 4-1 W 2.86 3-1 " 9.14 4-1 A" 14X46 4,238,000 349,000 11.77 3-2 * 2.94 3-1 " 9.43 3-lif" DESIGNS OF CONCRETE STRUCTURES. TABLE I&. Continued. HI 1 1 Reinforce- Reinforce- Reinforce- ment over intermediate ment, intermediate ment, outside spans. Size of beam. Safe bending moment. Factor of supports. (In upper side of girder.) span. (In lower side of girder.) (In lower side of girder.) satety == o.5. Area No. anc Area No. anc Area No. and of size of of size of of size of metal. bars. metal bars. metal bars. In. In. Ibs. Ft. Ibs. Sq. in Sq. in Sq. in 14X48 4,625,000 381,200 12.36 3-2*' 3.09 3-1*' 9.89 3-1 if" 14X50 5,055,000 417,000 12.85 3-2** 3.21 3-1*' 10.29 3-l| " 14X52 5,465,000 450,100 13.27 3-2* " 3.32 3-1*' 10.61 3-l| " 14X54 5,918,000 487,500 13.72 3-2| " 3.43 3-1*' 10.99 3-i if" 14X56 6,385,000 526,500 14.20 3-2*" 3.55 3-1*' 11.37 3-2 " 15X30 1,975,000 165,000 8.57 4-11 " 2.14 3-1 ' 6.86 4-1*" 15X32 2,230,000 186,000 8.97 4-11 " 2.24 3-f ' 7.18 4-1 1 " 15X34 2,560,000 213,500 9.62 4-1*" 2.41 3- if' 7.70 4-1 1 " 15X36 2,872,000 239,600 10.10 4-lf " 2.53 3- ir 8.08 4-1*" 15X38 3,186,000 266,000 10.54 4-lf * 2.63 3- if' 8.40 4-1^ " 15X40 3,520,000 294,000 11.19 4-1 W 2.80 3-1 ' 8.95 4-1* 15X42 3,860,000 322,000 11.66 4-1 W 2.92 3-1 ' 9.32 4-1*" 15X44 4,195,000 350,000 12.18 4-lf >' 3.05 3-1 ' 9.74 4-1*" 15X46 4,527,000 378,000 12.75 4-1 if" 3.19 3-1*' 10.20 4-lf " 15X48 4,960,000 414,000 13.27 4-llf' 3.32 3-1*' 10.60 4-lH" 15X50 5,420,000 452,000 13.84 3-2J " 3.46 3-1* ' 11.06 3-1 if" 15X52 5,845,000 485,000 14.23 30 3 M ~ TG" 3.56 3-1* ^ 11.37 3-2 " 15X54 6,350,000 529,500 14.88 3-2J " 3.72 11.89 3-2 " 15X56 6,849,000 570,500 15.37 3-2^ " 3.84 4-1 " 12.29 3-2*" 15X58 7,370,000 615,000 15.80 3-2JL" 3.95 4-1 " 12.63 3-2*" 15X60 7,872,000 656,000 16.23 3-2f " 4.06 4-1 " 12.97 3-2J " 16X32 2,402,000 200,000 9.75 5-1*" 2.44 3- W 7.80 5-1*" 16X34 2,724,000 226,800 9.84 5-1*" 2.46 3- if " 7.87 5-1*" 16X36 3,070,000 256,000 10.91 5-11 " 2.73 3-1 " 8.73 5-l| " 16X28 3,402,000 283,300 11.35 5-1 1 " 2.84 3-1 " 9.08 5-lf " 16X40 3,762,000 313,500 11.86 4-lf " 2.97 3-1 " 9.48 4-1 fa" 16X42 4,125,000 343,400 12.38 4-lf * 3.10 3-1*" 9.90 4-lf " 16X44 4,480,000 373,500 12.97 4-1 H^ 3.24 3-1*" 0.10 4-lf * 16X46 4,850,000 403,000 13.62 3.41 3-1*" 0.60 4-lf " 112 HANDBOOK ON REINFORCED CONCRETE. TABLE 16. Continued. 1 2 3 4 5 6 7 8 9 Reinforce- Reinforce- Reinforce- ment over ment, ment, intermediate intermediate outside spans Size of beam. Safe bending moment. Factor of ,ety- supports. (In upper side of girder.) span. (In lower side of girder.) (In lower, side of girder.) Area No. am Area No. an Area No. and of size of of size oi of size of metal. bars. metal bars. meta bars. In. In. Ibs. Ft. Ibs. Sq. in Sq. in Sq. in 16X48 5,290,000 440,200 14.14 4-lf 3.54 3-11 11.00 4-1 W 16X50 5,790,000 482,000 14.65 3-21' 3.66 3-11 11.70 3-2 " 16X52 6,250,000 520,500 15.13 3-21 f 3.78 4-1 12.1 3-2 " 16X54 6,770,000 564,000 15.65 3-2 iV 3.91 4-1 ' 12.5 3-2^" 16X56 7,310,000 609,500 16.25 3-2| ' 4.06 4-1 ' 13.0 3-2^" 16X58 7,850,000 654,900 16. 7f 3-2| ' 4.19 4-1 &' 13.4 3-21 // 16X60 8,400,000 700,000 17.34 4.34 4-liV 13.86 3-21 " 16X62 9,000,000 750,000 17.80 3-2 ^j' 4.45 4-1 TS' 14.2 3-2^" 16X64 9,600,000 800,000 18.36 3-21 / 4.59 4-11 " 14.67 3-2 7l V' 17X34 2,886,000 241,000 10.90 5-1* ' 2.73 3-1 " 8.72 5-lf " 17X36 3,258,000 271,500 11.40 5-11 / 2.85 3-1 " 9.12 5-lf " 17X38 3,620,000 301,400 12.04 5-1 TS' 3.01 3-1 " 9.62 5-1 J^" 17X40 4,040,000 336,500 12.70 5-lf " 3.18 3-1 TS" 10.15 5-lJ^" 17X42 4,470,000 372,500 13.22 5-lf * 3.31 3-1 TS" 10.50 5-1* " 17X44 4,900,000 408,600 13.86 5-1 W 3.47 3-1 T&" 11.09 5-H " 17X46 5,130,000 427,500 14.40 4-1 W 3.60 3-11 " 11.51 4-1 f " 17X48 5,620,000 468,500 15.00 4-1 If" 3.75 3-1 i " 12.00 4-lf " 17X50 6,140,000 512,200 15.60 4-2 " 3.90 4-1 " 12.47 4-lif* 17 X52 6,635,000 554,000 16.11 4-2 " 4.03 4-1 " 12.88 4-lyi'' 17X54 7,200,000 600,000 16.85 4-2^" 4.21 4-1 ^" 13.48 4-l| " 17X56 7,750,000 646,000 17.20 3-2^" 4.30 4-1 ^" 13.75 3-21 // 17 X58 8,350,000 698,500 17.74 3-2f G " 4.44 4-1 TS" 14.20 3-2^" 17X60 8,925,000 744,500 18.30 3-2^ " 4.58 4-1 1 " 14.63 3- 2l 3 6 " 17X62 9,550,000 796,000 18.88 3-2^ " 4.72 4-11 15.10 3-2^ " 17X64 10,200,000 850,000 19 50 3-2^" 4.88 4-1 1 " 15.60 3-2 A* 17X66 10,900,000 907,500 20.10 3-2 A" 5.03 4-1 ^" 16.08 3-2f " 17X68 11,560,000 962,500 20.67 3-2f " 5.17 *-!&* 16.53 3-2f " 18X36 3,452,000 288,000 12.10 5-11 // 3.03 3-1 " 9.68 5-1 T y 18X38 3,828,000 319,200 12.64 5-lf " 3.16 3-1 j^" 10.11 5-1^" DESIGNS OF CONCRETE STRUCTURES. 113 TABLE 16. Continued. 1 2 3 4 5 6 7 8 9 Reinforce- Reinforce- Reinforce- ment over ment, ment, intermediate intermediate outside spans. Size of beam. Safe bending moment. Factor of safety 3 5 supports. (In upper side of girder.) span. (In lower side of girder.) (In lower side of girder.) Area No. am Area No. am Area No. and of size of of size ol of size of metal. bars. metal bars. metal. bars. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in Sq. in 18X40 4,275,000 356,700 13.42 5-1 W 3.36 3-1* 10.74 5-1** 18X42 4,725,000 394,000 14.04 5-1 it' 3.51 3-1* 11.23 5-lj " 18X44 5,205,000 434,500 14.53 4-ltf' 3.63 3-1* 11.62 4-1 f " 18X46 5,445,000 453,500 15.18 4-1 le' 3.80 3-1* 12.16 4. If " 18X48 5,945,000 495,500 15.80 4-2 ' 3.95 4-1 ' 12.65 4-1 W 18X50 6,500,000 542,200 16.48 4-2x6-' 4.12 4-1 115 13.20 4-1JT 18X52 7,028,000 586,000 17.12 4-2* ' 4.28 IHF 13.70 18X54 7,620,000 636,000 17.75 4-2*' 4.44 4 ITT 14.20 4-lif" 18X56 8,210,000 685,000 18.36 4-2*' 4.59 4-1*' 14.69 4-iif" 18X58 8,830,000 737,000 19.00 4-2^-' 4.75 4-1*' 15.20 4-2 " 18X60 9,450,000 788,000 19.36 3-2&' 4.84 4-1*' 15.50 3 ~ 2 yC 18X62 10,130,000 843,500 19.94 3-2f ' 4.99 4-1* ' 15.95 18X64 10,800,000 900,000 20.52 3-2f ' 5.13 4-1 T&' 16.40 S-2f* 18X66 11,550,000 961,000 21 .'25 3-2 i*' 5.31 4-liV 17.00 3-2 3^" 18X68 12,230,000 1,020,000 21.84 3-2.T*' 5.46 4-1 1^ 17.46 3-2 le " 18X70 13,040,000 1,089,000 22.50 3-2f " 5.63 4-1*' 18.00 3-2^ " 18X72 13,800,000 1,150,000 23.05 3-2H" 5.76 4-1* " 18.43 3-2J " 19X38 4,030,000 336,200 13.37 6-lft* 3.34 3-iA* 10.70 5-l| " 19X40 4,520,000 376,900 14.10 5-1 1^" 3.53 3-1* " 11.28 5-1 &" 19X42 4,980,000 415,000 14.78 5-lf " 3.70 3-1* " 11.82 5-1^" 19X44 5,495,000 458,800 15.43 5-lf " 3.86 4-1 " 12.33 5-lf " 19X46 5,745,000 478,700 16.20 5-1 W 4.05 4-1 " 12.94 5-lf " 19X48 6,291,000 524,800 16.77 4-2&" 4.19 4-1 re" 13.40 4-1* ' 19X50 6,855,000 571,000 17.42 4-2* " 4.36 4-1 A" 13.94 4-4 " 19X52 7,430,000 618,400 18.00 4-2* " 4.50 4-1 re" 14.40 4-1 if" 19X54 8,038,000 670,000 18.73 4-2^" 4.68 4-1 " 14.97 A_'I 15^ 19X56 8,655,000 722,000 19.32 4-2 " 4.83 4-1* " 15.45 4-2 '" 19X58 9,325,000 777,700 20.05 4-2 " 5.01 4-1* " 16.03 4-2 " 19X60 9.978,000 832,500 20.58 4-2ft* 5.15 5-1 A* 16.46 4-2 A* 19X62 10,700,000 892,000 21.10 3-2is" 5.23 5-1 lV 16.88 3-2^" 114 HANDBOOK ON REINFORCED CONCRETE. TABLE 16. Continued. 1 2 3 4 5 6 7 8 9 Reinforce- Reinforce- Reinforce- ment over ment, ment, intermediate intermediate outside spans. Size of beam. Safe bending moment. Factor of supports. (In upper side of girder.) span. (In lower side of girder.) (In lower side of girder.) sfifcty 3.5, Area No. and Area No. am' Area No. and of size of of size of of size of metal. bars. metal. bars. metal . bars. In. In. Ibs. Ft. Ibs. Sq. in. Sq. in. Sq. in 19X64 11,420,000 950,000 21 75 3-2H" 5.44 5-1 h" 17.40 3-2iV' 19X66 12,180,000 1,015,000 22.40 3-2f " 5.60 5-1 iV' 17.90 3-2^ " 19X68 12,940,000 1,088,000 23.00 3-2H" 5.75 5-11- " 18.40 3-2^ " 19X70 13,750,000 1,145,000 23.68 3-2 fi" 5.92 5-4 " 18.94 3-2JL" 19X72 14,565,000 1,213,000 24.35 3-21 " 6.09 5-i i " 19.46 3-2&* 19X74 15,420,000 1,286,000 25.00 3-2 ft" 6.25 5-l| " 20.00 3-2f " 19X76 16,245,000 1,353,500 25.68 3-2 If" 6.42 5-1 b" 20.53 3-2| " 20X40 4,770,000 396,800 14.80 5-lf " 3.70 4-1 " 11.85 5-1^ 20X42 5,250,000 437,500 15.46 5-1 f " 3.87 4-1 " 12.37 5-lf " 20X44 5,795,000 482,000 16.20 5-1 W 4.05 4-1 " 12.97 5-lf " 20 X46 6,050,000 504,700 16.94 5-11 " 4.24 4-llV' 13.56 5-1 W 20X48 6,625,000 552,000 17.72 5-1 W 4.43 4-1 A" 14.19 5-1 W 20X50 7,235,000 602,800 18.96 5-1 jf 4.61 4-4 " 14.77 5-lf " 20X52 7,820,000 651,200 19 02 5-1 ir 4.76 4-4 " 15.22 4-2 " 20X54 8,600,000 717,000 19.71 4-2^ " 4.93 4-li " 15.79 4-2 " 20X56 9,126,000 761,000 20.26 4 -2| " 5.07 5-1 " 16.24 4-2^" 20X58 9,828,000 819,200 21.00 4-2&* 5.25 5-lA" 16.81 4-2 T y 20X60 10,500,000 875,000 21.60 4-2| " 5 40 5-liV' 17.30 4-21 " 20X62 11,250,000 937,700 22.32 4-2f " 5.58 5-1A" 17.88 4-21 " 20X64 12,040,000 1,003,000 23.03 4-2^" 5. 70 5-li " 18.44 4-2A* 20X66 12,830,000 1,067,000 23.71 4-2^" 5.93 5-11 " 19.00 3-2^ 20X68 13,600,000 1,145,000 24.15 3-21" 6.04 5-l| " 19.34 3-2A* 20X70 14,510,000 1,208,000 24.95 3-2 W 6.24 5-11 " 19.98 3-2f " 20X72 15,340,000 1,278,000 25.60 3-2M" 6.40 5-1^ 20.50 3-2f " 20 X74 16,250,000 1,353,000 26.22 3-3 " 6.56 &-iA* 21.00 3-2W 20X76 17,140,000 1,428,000 26.86 3-3 " 6.72 5-1 A" 21 50 3-2H" 20X78 18,100,000 1,508,000 27.66 3-3A" 6.92 5-1 -h" 22.14 3-2f " 20X80 19,090,000 1,588,000 28.37 3-3i " 7.09 5-1}- " 22.71 3-2f " DESIGNS OF CONCRETE STRUCTURES. 115 DESCRIPTION OF TABLE II. This table is inserted to be used in a more specific way than Table I, in cases of uniform loading where the total live load in tons uniformly distributed along the beam or girder is known, as well as the span in feet. Only a sufficient number of sizes are here given to cover the ordinary load- ing met with in practice, and such sizes are se- lected as are capable of withstanding the severest loading for a given amount of material in other words, the most economical sizes. It may happen in practice that certain local conditions, such as want of head-room, etc., may enter the case to an extent to prohibit the use of certain sizes here given. For such cases Table I, which is more general in scope, may be resorted to. Then again, in certain particular cases, neither of the two tables may apply. In such instances, which can Jiappen only seldom, the designer may well afford to spend his time to meet the special requirements. The table in itself needs little, if any, explana- tion. Column 1 gives the span in feet; column 2 gives the gross load in tons uniformly distributed along the span, given in column 1, that the size, designated above, will safely carry with a factor of safety of 3.5. Column 3, in a like manner, gives the net load after deducting the weight of the beam itself. Only one other thing needs mentioning. It may be noticed that opposite two different spans of 116 HANDBOOK ON REINFORCED CONCRETE. each size, the corresponding loading is under- scored. This is to show that all spans lying be- tween the underscoring are the proper ones to use whenever possible, for a cantilever loading only, in order to be certain that the shearing stress brought to bear upon the section will not be ex- cessive. (Table III takes into account the design to resist various shearing values.) It should be noted that the loading for all spans above the higher limit, designated by the underscoring, can safely be used with a cantilever loading, but less economically, because, for the sizes of shear bars designated in Table III, there will be supplied more metal than is necessary to withstand the shear, allowing the same factor of safety of 3.5. In other words, above this limit, we are designing safely, but not as economically, as possible. At the same time, other sizes for the particular span may be selected, which will be safe as well as economical. On the other hand, it is not safe to use the loading for spans below the limit desig- nated by the underscoring, without increasing the area of the shear bars over the largest size given in Table III. In all cases, for loadings with sup- ported or fixed ends, the tables apply safely. DESIGNS OF CONCRETE STRUCTURES. 117 TABLE II. Beams and Girders (Single Spans Supported at Ends). 24" > ( 6" zy: <8" 2J" X 10" 2*"X 12" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 3 87 85 4 5 .65 .52 .62 .48 1.28 1.02 1.24 .97 2.10 1.68 2.05 1.62 2.52 2.44 6 .43 .38 .85 .79 1.40 1.32 2.10 2.01 7 .37 .32 .73 .66 1.20 1.11 1.80 1.69 8 9 .32 .26 .64 .51 .56 .49 1.05 .93 .95 .82 1.58 1.40 1.46 1.27 10 11 .51 .42 .84 76 .71 62 1.26 1 14 1.11 .97 12 .70 .55 1.05 .87 13 65 .49 .07 .77 14 .90 .69 15 84 .62 3"X 12" 3"X 14" 4"> C 14" 4"X 16" 5 3 03 2 94 g 2 53 2 42 3 53 3 40 4 69 4 52 7 2.16 2.03 3.08 2.93 4.02 3.82 5.36 5.13 8 1.90 1.75 2.65 2.47 3.52 3.29 4.69 4.43 9 10 11 12 1.69 1.52 1.38 1.26 1.52 1.33 1.17 1.03 2.35 2.12 1.92 1.81 2.15 1.90 1.68 1.55 3.13 2.82 2.56 2.35 2.87 2.53 2.24 2.00 4.17 3.75 3.41 3.13 3.87 3.42 3.05 2.73 118 HANDBOOK ON REINFORCED CONCRETE. TABLE II. Beams and Girders. Continued. 3" XI 2" 3"X 14" 4"X 14 4"> ;16" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 13 1.17 .93 1.63 1.34 2.16 1.78 2.89 2.46 14 1.08 .82 1.51 1.20 2.01 1.60 2.68 2.22 15 1.01 .73 1.41 1.08 1.88 1.44 2.50 2.00 16 1.32 .97 1.76 1.29 2.35 1.82 17 1 24 87 1 66 1 17 2 21 1 65 18 1.18 .79 1.56 1.04 2.09 1.49 19 1 98 1 35 20 1.88 1.22 5"X 16" 5"X 18" 5"X 20" 6"X 20" 7 6.69 6.40 8 5.86 5.53 7.50 7.12 9.40 8.98 11.27 10.77 9 5.20 4.82 6.47 6.05 8.34 7.87 10.04 9.48 10 4.68 4.26 6.00 5.53 7.52 7.00 9.02 8.39 11 4.26 3.80 5.46 4.94 6.84 6.26 8.21 7.52 12 3.95 3.45 5.01 4.45 6.26 5.63 7.52 6.77 13 3.61 3.07 4.62 4.01 5.78 5.10 6.95 6.13 14 3.35 2.77 4.30 3.65 5.37 4.64 6.45 5.51 15 3.13 2.50 4.00 3.30 5.01 4.23 6.02 5.08 16 2.93 2.26 3.76 3.01 4.70 3.86 5.64 4.64 17 2.76 2.05 3.53 2.73 4.42 3.58 5.31 4.25 18 2.61 1.86 3.34 2.50 4.18 3.24 5.02 3.89 19 2.47 1.68 3.16 2.27 3.96 2.97 4.75 3.56 20 2.34 1.51 3.00 2.06 3.76 2.71 4.52 3.27 21 2 86 1 88 3 58 2 48 4 30 2 98 22 2.78 1.71 3.41 2.26 4.10 2.72 23 2.61 1.48 3.27 2.07 3.93 2.49 24 3 13 1.87 3.76 2.26 25 3.00 1.69 3.61 2.04 DESIGNS OF CONCRETE STRUCTURES. 119 TABLE II. Beams and Girders. Continued. 6"X 22" 6"X 24" 7"X 24" 7"X 26" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 9 12.30 11.78 10 11.08 10.39 13.37 12.62 15.48 14.62 18.25 17.30 11 10.07 9.31 12.16 11.33 14.08 13.12 16.60 15.56 12 9.22 8.39 11.15 10.25 12.90 11.85 15.20 14.06 13 8.52 7.62 10.30 9.32 11.90 10.76 14.04 12.81 14 7.90 6.93 9.55 8.50 11.05 9.83 13.04 11.71 15 7.38 6.34 8.91 7.78 10.32 9.31 12.17 10.75 16 6.92 5.81 8.37 7.17 9.67 8.27 11.41 9.89 17 6.52 5.35 7.87 6.59 9.10 7.61 10.73 9.12 18 6.15 4.91 7.43 6.08 8.60 7.02 10.14 8.43 19 5.83 4.52 7.04 5.61 8.13 6.47 9.62 7.75 20 5.54 4.16 6.68 5.18 7.73 5.98 9.12 7.22 21 5.27 3.82 6.38 4.80 7.38 5.54 8.70 6.71 22 5.03 3.51 6.08 4.43 7.03 5.10 8.30 6.21 23 4.82 3.23 5.82 4.09 6.73 4.72 7.94 5.76 24 4.61 2.95 5.58 3.78 6.45 4.35 7.61 5.33 25 4.43 2.70 5.35 3.47 6.19 4.00 7.30 4.92 26 4.26 2.46 5.14 3.19 5.97 3.50 7.02 4.55 27 4.10 2.23 4.95 2.92 5.73 3.37 6.77 4.21 28 4.78 2.68 5.53 3.08 6.52 3.86 29 4 61 2 43 5 34 2 80 6.30 3 54 30 4 46 2 20 5.16 2.53 6.08 3.13 31 5 90 2 96 32 5.70 2.66 120 HANDBOOK ON REINFORCED CONCRETE. TABLE II. Beams and Girders. Continued. 7"X 28" 8"X 28" 8"X 30" 8"X 32" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. a 11 19 40 18 28 21 95 20 66 12 17 76 16 53 20 10 18 70 23 35' 21 85 13 16.40 15.07 18.57 17.05 21.55 19.93 24.62 22.88 14 15.20 13.77 17.26 16.63 20.00 18.25 22.85 20.98 15 14.20 12.67 16.10 14.45 18.67 16.80 21.30 19.30 16 13.32 11.69 15.10 13.23 17.50 15.50 20.00 17.86 17 12.54 10.81 14.20 12.22 16.46 14.34 18.82 16.55 18 11.84 10.01 13.42 11.32 15.56 13.31 17.78 15.38 19 11.22 9.28 12.71 10.49 14.75 12.37 16.86 14.32 20 10.65 8.61 12.08 9.74 14.00 11.50 16.00 13.33 21 10.16 8.02 11.50 9.05 13.33 10.71 15.25 12.45 22 9.68 7.44 10.97 8.40 12.74 9.99 14.56 11.62 23 9.27 6.93 10.50 7.81 12.17 9.30 13.92 10.85 24 8.88 6.44 10.06 7.26 11.68 8.68 13.34 10.14 25 8.52 5.97 9.66 6.74 11.20 8.08 12.80 9.46 26 8.20 5.55 9.28 6.24 10.77 7.52 12.30 8.83 27 7.90 5.15 8.95 5.80 10.37 7.00 11.87 8.27 28 7.62 4.77 8.63 5.36 10.00 6.50 11.44 7.70 29 7.35 4.39 8.33 4.94 9.65 6.03 11.04 7.17 30 7.10 4.04 8.06 4.56 9.34 5.59 10.68 6.68 31 6.88 3.72 7.78 4.16 9.04 5.16 10.32 6.19 32 6.66 3.40 7.55 3.81 8.75 4.75 10.00 5.73 33 6.46 3.10 7.32 3.36 8.48 4.36 9.70 5.30 34 6.27 2.80 7.10 3.13 8.22 3.97 9.41 4.87 35 6.10 2.53 6.90 2.81 7.99 3.62 9.15 4.48 36 7 78 3 28 8.90 4.10 37 7.54 2.92 8.67 3.74 38 8 43 3.36 39 8.21 3.01 40 8 00 2.67 DESIGNS OF CONCRETE STRUCTURES. 121 TABLE II. Beams and Girders. Continued. 1 9" X 32" 9" X 34" 9" X 36" 2 3 2 3 2 3 2 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 ' 32 33 34 35 36 37 38 39 40 41 42 43 44 45 27.80 25.80 24.08 22.55 21.25 20.05 19.00 18.08 17.20 16.40 15.70 15.08 14.45 13.88 13.37 12.90 12.45 12.03 11.54 11.29 10.94 10.52 10.31 10.04 9.76 9.51 9.25 9.02 25.85 23.70 21.83 20.15 18.70 29.30 27.27 25.55 24.04 22.70 21.52 20.43 19.50 18.59 17.78 17.03 16.36 15.74 15.15 14.52 14.10 13.63 13.20 12.78 12.39 12.04 11.69 11.36 11.06 10.76 10.49 10.23 9.98 9.74 26.97 24.88 23.00 21.33 19.83 30.68 28.72 27.08 25.58 24.22 23.02 21.94 20.92 20.00 19.17 18.40 17.71 17.04 16.45 15.87 15.35 14.84 14.40 13.94 13.54 13.15 12.80 12.44 12.12 11.80 11.50 11.22 10.96 10.70 10.47 10.24 28 . 15 26.02 24.21 22.54 21.01 17.30 16.15 15.08 14.05 13.10 12.25 11.48 10.70 9.98 9.32 8.70 8.10 18.49 17.24 16.15 15.08 14.11 13.20 12.37 11.59 10.85 10.06 9.48 8.86 19.64 18.40 17.21 16.12 15.12 14.18 13.32 12.49 11.73 10.98 10.29 9.61 9.00 7.53 6.89 6.49 5.99 5.42 5.06 4.64 4.21 3.71 3.40 3.02 8.26 7.68 7.13 6.62 6.11 5.62 5.16 4.71 4.27 3.86 3.45 3.04 8.37 7.80 7.25 6.73 6.20 5.71 5.22 4.85 4.30 3.88 3.45 3.05 2.64 122 HANDBOOK ON REINFORCED CONCRETE. TABLE II. Beams and Girders. Continued. 10" > (36" 10" > ;38" 10" K40" 11" > ;40" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 16 31.90 28 90 35.45 32.28 18 28.35 24.97 31.52 27.66 35.30 31.56 38.75 34.63 20 25.50 21.75 28.34 24.28 31.75 27.59 34.83 30.25 22 23.20 19.07 25.80 21.45 28.88 24.30 31.70 26.66 24 21.27 17.77 23.65 18.90 26.48 21.49 29.05 23.55 26 19.64 14.77 21.84 16.69 24.46 18.55 26.82 20.67 28 18.24 12.99 20.28 14.73 22.70 16.87 24.92 17.52 30 17.00 11.36 18.90 12.95 21.18 14.94 23.24 16.37 32 15.94 9.94 17.74 11.41 19.86 13.21 21.80 14.48 34 15.00 8.64 16.70 9.97 18.70 11.63 20.50 12.72 36 14.18 7.41 15.77 8.65 17.56 10.07 19.39 11.15 38 13.44 6.31 14.94 7.42 16.72 8.82 18.35 9.65 40 12.76 5.26 14.20 6.28 15.90 7.58 17.40 8.25 42 12.16 4.28 13.50 5.19 15.13 6.40 16.60 7.00 44 11.60 3.35 12.90 4.20 14.44 5.29 15.85 5.79 46 12.35 3.25 13.81 4.26 15.16 4.54 48 11 83 2 33 13 24 3 27 14 54 3.56 50 12.70 2.30 13.95 2.51 u*> 42" 11" X 44" 12" > <44" 12" X 46" 18 42 80 38 46 47 05 42 46 49 70 44 85 20 38.50 33.68 42.35 37.30 44.75 39.25 48.30 42.55 22 35.02 29.72 38.50 32.95 40.70 34.65 43.86 37.53 24 32.10 26.32 35.27 29.22 37.30 30.70 40.25 33.35 26 29.64 23.38 32.58 26.03 34.47 27.32 37.10 29.62 28 27.54 20.79 30.22 23.17 32.00 24.30 34.52 26.47 30 25.70 18.47 28.22 20.65 29.82 21.57 32.20 23.58 32 24.10 16.40 26.44 18.37 28.00 19.20 30.25 21.05 DESIGNS OF CONCRETE STRUCTURES. 123 TABLE II. Beams and Girders. Continued. 11" X 42" 11" > ,44" 12") < 44" 12" > <46" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 34 22.67 14.47 24.90 16.33 26.33 16.98 28.40 18.63 36 21.41 12.83 23.50 14.43 24.88 14.98 26.80 16.45 38 20.28 11.13 22.28 12.71 23.53 12.94 25.40 14.46 40 19.27 9.64 21.15 11.05 22.36 11.36 24.15 13.65 42 18.35 8.21 20.16 9.56 21.32 9.77 23.00 10.92 44 17.50 6.90 19.24 8.14 20.34 8.24 21.93 9.28 46 16.75 5.65 18.40 6.80 19.46 6.82 20.98 7.75 48 16.06 4.47 17.63 5.53 18.65 5.45 20.10 6.20 50 15.43 3.27 16.93 4.30 17.87 4.12 19.30 4.90 52 14.83 2.27 16.27 3.15 17.21 2.91 18.58 3.63 54 15 67 3 03 16 60 1 75 17 89 2 36 56 17 26 1 16 58 16.76 .06 12" X 48" 13" X 48" 13") <50" 13" X 52" 2Q 53 00 47 00 55 30 48 80 22 48.20 41.50 50.28 43.13 57.25 49.80 61.50 53.76 24 44.20 37.00 46.20 38.40 52.45 44.30 56.40 47.96 26 40.77 32.97 42.55 34.10 48.45 39.60 52.05 42.91 28 37.87 29.47 39.54 30.44 45.00 35.52 48.30 38.46 30 35.30 26.30 36.90 27.15 42.00 31.85 45.15 34.60 32 33.12 23.50 34.60 24.20 39.33 28.49 42.30 31.05 34 31.17 20.97 32.57 21.52 37.00 25.48 39.80 27.85 36 29.42 18.62 30.78 19.08 34.96 22.76 37.60 24.95 38 27.90 16.50 29.13 16.78 33.12 20.26 35.60 22.25 40 26.50 14.50 27.70 14.70 31.48 17.93 33.87 19.80 42 25.20 12.60 26.35 12.70 29.95 15.71 32.22 17.45 44 24.08 10.88 25.16 11.86 28.60 13.50 30.80 15.33 46 23.05 9.25 24.07 9.12 27.36 11.78 29.44 13.28 OF THE: *- .-<- i-r\/ 124 HANDBOOK ON REINFORCED CONCRETE. TABLE II. Beams and Girders. Continued. 12" > ( 48" 13" X 48" 13" X 50~ 13" X 52" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 48 22.10 7.70 23.06 7.46 26.20 9 95 28.20 11.33 50 21.20 6.20 22.15 5.90 25.18 8.24 27.10 9.54 52 20.38 4.78 21.30 4.40 24.20 6.60 26.06 7.77 54 19.63 3.43 20.53 2.98 23.30 5.00 25.10 6.10 56 18.94 2.14 19.76 1.56 22.47 3.51 24.20 4.54 58 60 18.28 17.67 .88 19.08 18.47 .33 21.72 21.00 2.08 .70 23.34 22.58 2.94 1.48 62 20 30 21.85 14" X 52" 14" > (54" 14" <56" 15" > : 56" 22 66.30 57.96 24 60.80 51 .70 65.90 56.47 71.20 61.40 76.00 65.47 26 56.20 46.36 60.80 50.57 65.70 55.08 70.20 58.80 28 52.20 41.60 56.50 45.50 61.00 49.55 65.20 52.92 30 48.70 37.33 52.75 40.90 57.00 44.74 60.80 47.65 32 45.65 33.53 49.75 37.18 53.35 40.27 57.03 43.00 34 42.95 30.08 46.50 33.14 50.23 36.30 53.72 38.82 36 40.60 26.98 44.00 29.85 47 . 50 32.80 50.75 34.95 38 38.43 24.03 41.65 26.72 44.98 29.45 48.00 31.34 40 36.50 21.36 39.52 23.82 42.70 26.35 45.65 28.61 42 34.75 19.85 37.65 21.15 40.70 23.54 43.50 25.10 44 33.20 16.53 35.95 18.67 38.80 20.80 41.50 22.20 46 31.73 14.33 34.40 16.35 37.13 18.30 39.70 19.52 48 30.40 12.22 32.95 14.10 35.60 16.00 38.00 17.95 50 29.22 10.29 31.65 12.01 34.18 13.76 36.50 14.58 52 28.08 8.41 30.40 10.00 32.82 11.56 35.10 12.22 54 27.06 6.64 29.28 8.08 31.60 9.52 33.80 10.12 56 26.08 4.88 28.26 6.26 30.50 7.60 32.60 8.05 58 25.18 3.23 27.28 4.48 29.42 5.70 31.50 6.08 60 24.32 1.62 26.37 2.72 28.45 3.90 30.43 4.13 62 23.53 .07 25.50 1.15 27.55 2.25 29.45 2.25 64 24.70 26.70 .55 28.53 .45 DESIGNS OF CONCRETE STRUCTURES. 125 TABLE II. Beams and Girders. Continued. 15" X 58" 15" X 60" 16" X 60" 16" X 62" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net.' 24 82 00 71 13 26 75.80 64.03 80.80 68.62 86.20 73.20 92.40 78.98 28 70.30 57.63 75.00 61.89 80.00 66.00 85.80 71.34 30 65.60 52.00 70.00 53.94 74.75 59.75 80.10 64.60 32 61.50 47.00 65.70 50.70 70.05 54.05 75.10 58.58 34 57.90 42.50 61.77 45.83 66.00 49.00 70.70 53.15 36 54.70 38.40 58.40 41.54 62.30 44.30 66.75 48.15 38 51.80 34.60 55.25 37.45 59.00 40.00 63.20 43.57 40 49.25 31.15 52.50 33.76 56.00 36.00 60.00 39.35 42 46.80 27.80 50.00 30.32 53.30 32.30 57.20 35.50 44 44.75 24.85 47.75 27.13 51.00 29.00 54.65 31.95 46 42.78 21.95 45.70 24.15 48.75 25.75 52.30 28.55 48 41.00 19.38 43.75 21.27 46.70 22.70 50.00 25.20 50 39.40 16.78 42.00 18.58 44.90 19.90 48.00 22.20 52 37.90 14.35 40.40 16.02 43.15 17.15 46.25 19.41 54 36.44 11.99 38.90 13.60 41.50 14.50 44.50 16.60 56 35.20 10.82 37.50 11.25 40.00 12.00 42.90 14.00 58 33.95 7.70 36.20 9.00 38.70 9.70 41.45 11.50 60 32.80 5.60 35.00 6.90 37.40 7.40 40.00 9.00 62 31.74 3.66 33.90 4.87 36.20 5.20 38.80 6.80 64 30.78 1.78 32.86 2.86 35 08 3.08 37.55 4.50 66 29.85 31.80 .85 34.00 1.00 36.40 2.30 68 30.92 33.00 35.40 .40 16" X 64" 17" X 64" 17" X 66" 17" X 68" 28 91.70 76.78 97.20 81.36 103.70 87.40 110.30 93.50 30 85.50 69.50 90.75 73.80 96.80 79.30 103.00 85.00 32 80.25 63.20 85.00 66.90 90.75 72.11 96.50 77.30 34 75.50 57.40 80.00 60.80 85.30 65.50 90.80 70.40 36 71.30 52.10 75.60 55.26 80.70 59.70 85.75 64.15 126 HANDBOOK ON REINFORCED CONCRETE. TABLE II. Beams and Girders. Continued. 16" > ( 64" 17" > ; 64" 17" ) < 66" 17" > < 68" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 38 67.60 47.34 71.60 50.12 76.45 54.30 81.30 58.50 40 64.20 42 . 88 68.00 45.40 72.60 49.30 77.10 53.10 42 61.00 38.60 64.75 41.02 69.15 44.65 73.50 48.30 44 58.30 34.86 61.80 36.92 66.00 40.38 70.20 43.80 46 55.75 31.25 59.15 33.15 63.10 36.30 67.10 39.50 48 53.50 27.90 56.70 29.58 60.50 32.50 64.30 35.50 50 51.35 24.70 54.35 26.30 58.20 29.10 61.75 31.75 52 49.30 21.60 52.30 22.90 55.80 25.50 59.35 28.15 54 47.55 18.80 50.40 19.90 53.80 22.34 57.20 24.80 56 45.80 15.97 48.50 16.85 51.80 19.20 55.15 21.55 58 44.25 13.33 46.85 14.10 50.05 16.25 53.25 17.45 60 42.75 10.75 45 . 35 11.45 48.35 12.35 51.50 15.50 62 41.45 8.41 43.85 8.85 46.80 9.68 49.80 12.60 64 40.15 6.05 42.50 6.30 45.40 8.10 48.25 9.85 66 38.90 3.70 41.20 3.90 44.00 5.57 46.75 7.15 68 37.75 1.51 40.00 1.60 42.70 3.10 45.40 4.60 70 36.70 38.90 41.50 .75 44.15 3.15 72 40.30 42.90 18" X 68" 18" X 70" 18" X 72" 19" X 72" 28 116 50 98 65 30 108.90 89.76 116.50 96.80 122.80 102.53 129.50 118.05 32 102.00 81.60 109.00 88.00 115.00 93.40 121.50 98.62 34 96.00 74.30 102.50 80.20 108.40 85.45 114.30 90.00 36 90.75 67.75 96.90 73.28 102.50 78.20 108.00 82.28 38 85.90 61.68 91.75 66.82 96.90 71.25 102 . 40 75.22 40 81.60 56.10 87.10 52.85 92.00 65.00 97.10 68.50 42 77.70 50.90 83.00 55.40 87.60 59 . 25 92.50 62.50 44 74.20 46.15 79.20 50.30 83 . 75 54 . 05 88.30 56.35 46 71.00 41.84 75.80 45.60 80.20 49.15 84.50 51 64 48 68.00 37.40 72.60 41.10 76 80 44.40 81.00 46.70 DESIGNS OF CONCRETE STRUCTURES. 127 TABLE II. Beams and Girders. Continued. 18" > : 68" 18" ; < 70" 18" >< 72" 19" > ( 72" 1 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 50 65.20 33.30 69.70 36.90 73.70 39.94 77.75 42.00 52 62.75 29.57 67.00 32.90 70.80 35 . 70 74.80 37.00 54 60.50 26.08 64.70 29.25 68.20 31.72 72.00 33.40 56 58.25 24.55 62.25 25.47 65 80 28.00 69.40 29.64 58 56.30 19.30 60.00 21.92 63.50 24.30 67.00 25.50 60 54.50 16.25 58.10 18.60 61.30 20.80 64.75 21.85 62 52.65 13.15 56.30 15.60 59.35 17.50 62.70 18.40 64 51.00 10.22 54.50 12.50 57.50 14.30 60.75 15.00 66 49.40 8.30 52.80 9.50 55.90 11.40 58.90 11.70 68 48.00 4.65 51.25 6.55 54.20 8.30 57.20 8.55 70 46.55 1.88 49.80 3.80 52.70 5.45 55.50 5.50 72 45.30 48.50 1.25 51.20 2.60 54.00 2.52 74 49.75 52.50 19" > C74" 19" > C76" 20") < 76" 20" X 78" 30 137.00 114.94 32 128.60 105.10 135.20 111.02 142.70 117.30 150.70 124.70 34 121.00 96.00 127.40 101.72 134.20 107.25 141.80 114.20 36 114.40 87.95 120.40 93.20 127.70 99.15 134.00 104.80 38 108.40 80.50 114.00 85.30 120.00 89.88 126.80 95.95 40 103 . 00 73.60 108.20 78.00 114.20 82.50 120.50 88.00 42 98.00 67.12 103.00 71.30 108.70 75.40 115.00 80.90 44 93.50 61.15 98.50 65.30 103.70 68.82 109 . 50 73.75 46 89.50 55.70 94.00 59.45 99.20 62.75 104.90 67.50 48 85.80 50.50 90.25 54.00 95.10 56.05 100 . 50 61.50 50 82.25 45.50 86.70 48.95 91.25 51.65 96.40 55.80 52 79.20 41.00 83.25 43.98 87.80 46.55 92.80 50.55 54 76.25 36.55 80.20 39.45 84.50 41.75 89.25 45.35 56 73 . 50 32.30 77.30 35.05 81.50 37.15 86.10 40.60 58 71.00 28.40 74.70 30.95 78.70 32.70 83.10 36.00 60 68.50 24.40 72.20 26.92 76.00 28.50 80.30 31.55 62 66.30 20.75 69.80 22.92 73.70 24.55 77.80 26.45 128 HANDBOOK ON REINFORCED CONCRETE. TABLE II. Beams and Girders. Continued. 1 19" X 74" 19" X 76" 20" X 76" 20" X 78" 2 3 2 3 2 3 2 3 Span. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. Load Gross. Load Net. 64 66 68 70 72 74 76 78 64.25 62.30 60.60 58.75 57.20 55.70 54.20 17.25 13.80 10.60 7.25 4.25 1.30 67.75 65.70 63.75 61.80 60.20 58.50 57.00 19.45 15.90 12.40 8.90 5.80 2.60 71.30 69.20 67.20 65.20 63.30 61.70 60.00 20.55 16.92 13.30 9.70 6.30 3.00 75.25 73.00 70.90 68.80 67.00 65.20 63.40 61.80 23.25 19.40 15.65 11.90 8.50 5.05 1.70 20" X 80" 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 149.20 141.00 133.50 127.00 120.80 115.60 110.40 105.60 101.50 97.50 94.00 90.50 87.50 84.60 81.80 79.20 76.80 74.60 72.50 70.50 68.50 66.75 65.00 120.90 111.00 101.90 93.70 85.80 79.00 72.10 65.60 59.90 54.20 49.00 43.90 39.20 34.60 30.20 25.90 21.80 18.00 14.20 10.50 6.90 3.45 DESIGNS OF CONCRETE STRUCTURES. 129 DESCRIPTION OP TABLE III. Table III is given to show how much shearing force the same size of beams, figured to resist bending in Table I, will resist. Suppose a certain size has been selected from Tables I or II to with- stand the maximum bending moment in the case at hand. Of course we know the maximum shear- ing force in this particular case, for this had to be determined before obtaining the maximum bend- ing moment. Hence, by referring to Table III, and opposite the size already selected, ascertain under which of the three columns, 5, 6, or 7, the SKETCH 1. shearing force in question falls. As you will note by the titles of these columns, column 5 is figured to use shear bars with an aggregate area of cross- section of .19 square inches, column 6 with an area of .28 square inches; likewise column 7 of .38 square inches area. These shear bars are found upon the market of various designs. Very commonly they are in the form of a U-shaped bar lettered "a" in Sketch 1, which may be inserted vertically to the horizontal axis of the beams, or inclined at an angle, prop- 130 HANDBOOK ON REINFORCED CONCRETE. erly 60 degrees, with the vertical axis, and in the direction at right angles to the lines of shear cracks, which develop when a beam is SKETCH 2. tested to destruction, as may be seen in cuts of two tests shown in another section on page 45. These may be met with in the rolled and stamped section shown in Sketch 2 and inserted in the beam as shown in Sketch 3. These are two of several patented shapes, which are used to resist longitudinal shear. Instead of making the tables apply to any of these special shapes, the writer 15-2 SKETCH 3 SKETCH 4. has taken a general case, shown in Sketch 4, to which results any of the patented shapes may be applied. By the aggregate area of shear bars just men- tioned, is meant the combined area of the cross- sections of bars lettered "b" in Sketch 4. Bars DESIGNS OF CONCRETE STRUCTURES. 131 "b" should be placed at an angle of 60 degrees, about with the vertical. In the tables, column 1 gives the size of beams; column 2 gives the total area of the size opposite which it appears; column 3 gives the area of concrete, and 4 the steel area, making up the total area under column 2. VERTICAL SHEAR. In obtaining the values under column 5, it was reasoned that the maxi- mum shearing force, which always happens at a support, causes a given strain upon the section at that point, which strain is uniform at all points of the section, through the steel, as well as through the concrete. The value of this strain was so fixed that the stress per square inch caused thereby, throughout the concrete section, was very moderate, which always happens with a concen- trated load in the middle of the span of a beam supported at both ends. The strain just referred to was fixed at .0000167 inches, which, with a modulus of elasticity of 3,000,000, gives a working stress of a 1-1^-3 or a 1-2-4 concrete, 50 pounds per square inch, and a factor of safety of 7, calling the ultimate shearing stress 350 pounds per square inch. Column 6 was figured allowing the working strain and the stress caused thereby to be mod- erate, and is adapted to meet the ordinary cases of a beam uniformly loaded and supported at the ends. The working stress was fixed at .000025 inches, which in a like manner means a working 132 HANDBOOK ON REINFORCED CONCRETE. stress of 75 pounds per square inch, or a factor of safety of 5.25. In a like manner column 7 was figured to be adapted to general cases of cantilever loading, where the maximum shearing force, for a given maximum bending moment, is greatest. In this case the strain was limited to .0000333 inches, giv- ing a corresponding working stress of 100 pounds per square inch, and a factor of safety of 3.5. Hence it may be seen that column 5 is generally applicable to cases of concentrated central loads upon beams supported at both ends; column 6 to cases of uniform loading upon beams similarly supported; and column 7 to cases of cantilever loading. This adaptation holds only in a general way, and will not apply to all cases, one of which was mentioned under Table II. To obtain any shearing force under column 5, the area of the concrete in square inches given under column 3 was multiplied by 50 pounds per square inch, to which force in pounds, was added the product of multiplying the area of steel in square inches under column 4 by 500 pounds per square inch, since by applying a given strain to both concrete and steel, there is caused ten times the stress in the steel as there is in the concrete. In a like manner the values under columns 6 and 7 were obtained by using 75 and 100 pounds per square inch allowable stress for the concrete, and the proportionate stresses of 750 and 1,000 pounds per square inch for the area of steel respectively. DESIGNS OF CONCRETE STRUCTURES. 133 LONGITUDINAL SHEAR. It is a well recognized fact that, in elastic beams undergoing vertical shearing, there is caused a corresponding longi- tudinal shear which is greatest at the neutral axis of the section in question, and decreases at any axis approaching either the top or bottom of the section. In rectangular shapes, the intensity of stress at the neutral axis equals 3 X the total vertical shearing force divided by 2 X the breadth of the beam X the depth of the beam, or, in the characteristic form, * Intensity of stress = 2 on, By applying this to the values of shearing force given under columns 5, 6, or 7, for the breadth and depth of beam given under column 1, we obtain for an intensity of longitudinal shearing stress per square inch of 90 pounds for column 5, 135 pounds for column 6, and 180 pounds for column 7. By comparing these values with the corresponding ones used as working vertical shear- ing stress per square inch, namely, 50 pounds, 75 pounds, and 100 pounds, you will notice that a given vertical shearing stress causes a longitudinal shearing stress of a magnitude of f of itself. Hence, without inserting a steel member to reduce the stress and help out the concrete at the neutral axis of the sections near the supports, we are reducing our working factors of safety by 45 per cent in each case. In other words, instead of 134 HANDBOOK ON REINFORCED CONCRETE. having factors of 7, 5.25, and 3.5, as we had for the three particular cases in vertical shear, we have corresponding ones of but 3.9, 2.92, and 1.95, which are not ample, and if they were, w r ould be unsatisfactory to use, since the general design would be weaker in some places than others. To relieve the concrete at this point, we have only to insert a rod of an area of ^ of that of the concrete in the layer where the width of the layer is the side of the rod, and the length is the width of the beam. See rod (7, Sketch 4, which is the rod just mentioned, and the shaded section, which repre- sents the concrete. The rod should be ^ 8 , be- cause we have to relieve the stress in the concrete by 45 per cent, and the effect of a given area of steel is ten times that of a like area of concrete. By combining these two ratios, we get $ X = T V This means for a 5-inch wide beam, that rod C should be } inch square; for a 10-inch wide beam, J inch square; and for a 20-inch wide beam, 1 inch square. All intervening sizes may be graded accordingly. As this rod C is not required at the middle of the span, and is most needed at the ends, it may not be continuous, but used at the ends only, and extend sufficiently toward the center to satisfy the designer that the longitudinal shearing stress beyond the limits of the rod is not excessive. It has already been stated that a given vertical shearing stress causes a longitudinal shearing stress of | of itself. Hence in Sketch 5 ; if we lay SUPPORT SIDE ELEVATION OF BEAM DESIGNS OF CONCRETE STRUCTURES. 135 off to any scale, ab in a vertical line and equal to five parts, and be to the same scale ^equal to nine parts, and at right angles to ab, then will the line ac give the magnitude of the resultant when di- vided into the same units that the other two forces were laid out to, and also the direction of action of this resultant. The mag- nitude, as will be noted, becomes 2.1 times the ver- tical shearing stress, and the direction of action is inclined to the vertical at an angle bac, the tangent of which is 1.8, which denotes an angle of 61 degrees. It has been remarked that the shear-cracks, when a beam is tested to destruction, occur along lines making an angle of about 60 degrees with the vertical. The above demonstration goes to show why such is the case. It might have been argued, upon first thought, that putting in bar c, Sketch 3, could have no effect upon the longitudinal shear and would in no wise help out the concrete tending to shear in a plane parallel with itself, but upon referring to Sketch 4, we see that rod c will cut the resultant line of force ac at an angle of 29 degrees and, consequently can offer a component to react against the resultant ac. The rods marked "b" in Sketch 4 will be suf- ficient to help out the concrete at all axes except the neutral axis, for the aggregate areas of these 136 HANDBOOK ON REINFORCED CONCRETE. rods will, when .19 square inch area, and the width of beam 20 inches, which is the limit of the table, reduce the longitudinal shearing stress by 10 per cent, which stress reduces in magnitude greatly as the top or bottom layers are approached. Ten per cent increase over the factor of safety of 3.9 gives 4.3 at a layer just above or below the neutral axis, which is ample. Again, with an aggregate ' area of .38 square inches for rods "b," and with a width of beam of 20 inches, the shear- ing stress would be reduced 19 per cent, and the factor of safety at a layer just either side of the neutral axis would be 2.3 at the very least, and undoubtedly much more, which may be ascer- tained by applying the formulae for longitudinal shearing stress at that layer. In distributing the shear bars along the length of a beam or girder the following suggestion is offered. Since the shearing stress per square inch varies uniformly from zero at the free end of a cantilever, or at the center between the supports or fixed ends of a beam, to a maximum at the sup- ports or fixed ends, the spacing of bars should vary inversely and uniformly. Because this varia- tion is uniform, it may be represented by the rela- tionship of the odd numbers 1, 3, 5, 7, etc., to each other. With a uniformly distributed load- ing along the length of the beam or girder, the shearing stress per square inch varies as the length of a cantilever beam called "Z," and as the half length also called "Z," of a beam supported or DESIGNS OF CONCRETE STUCTURES. 137 fixed at the ends. Likewise the shearing stress varies indirectly as the depth of the beam desig- nated "d." Hence the shearing stress varies as the ratio of -,. This value increases when ap- proaching the supports and since, as stated before, the spacing of bars decreases, this latter may be represented by the inverse ratio or -j - Accord- ingly it is suggested to call this ratio a fraction of a foot, then express its value in inches, thus giving the location of the first pair of bars from the sup- ports or fixed ends. The location of the next pair, in a like manner, is three times this constant from the first pair; likewise the third pair are distant five times this constant from the second pair and so on, receding from the support. NOTE. In dealing with continuous girders, the values of the safe shearing forces given in columns 5, 6, and 7 of Table III, should be modified as follows : With '2 spans decrease the values given by 12.5 per cent. With 3 spans decrease the values given by 11.0 per cent. With 4 spans decrease the values given by 11.5 per cent. With 5, 6, 7, and 8 spans, decrease the values given by 11,3 per cent. 138 HANDBOOK ON REINFORCED CONCRETE. TABLE III. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars 0.28 in. Area of shear bars 0.38 in. 2.5X6 15 14.53 .47 .48 .72 .96 2.5X8 20 19.48 .52 .62 .93 1.24 2.5X10 25 24.35 .65 .77 1.16 1.54 2.5X12 30 29.43 .66 .90 1.35 1.80 3X6 18 17.52 .48 .56 .84 1.12 3X8 24 23.41 .59 .73 1.10 1.47 3X10 30 29.34 .66 .90 1.35 1.80 3X12 36 35.22 .78 1.08 1.59 2.15 3X14 42 41.12 .88 1.25 1.87 2.50 4X8 32 31.25 .75 .97 1.45 1.94 4X10 40 39.14 .86 1.19 1.79 2.39 4X12 48 47.01 .99 1.43 2.14 2.85 4X14 56 54.86 1.14 1.66 2.49 3.31 4X16 64 62.74 1.26 1.86 2.79 3.77 5X10 50 48.85 1.15 1.51 2.26 3.02 5X12 60 58.68 1.32 1.80 2.70 3.60 5X14 70 68.54 1.46 2.08 3.12 4.16 5X16 80 78.32 1.68 2.38 3.32 4.76 5X18 90 88.14 1.86 2.67 4.00 5.34 5X20 100 97.94 2.06 2.97 4.50 5.93 6X12 72 70.47 1.53 2.14 3.22 4.29 6X14 84 82.22 1.78 2.50 3.75 5.00 6X16 96 94.03 1.97 2.84 4.26 5.69 6X18 108 105.81 2.19 3.20 4.79 6.39 6X20 120 117.60 2.40 3.54 5.31 7.08 6X22 132 129.38 2.62 3.89 5.81 7.78 6X24 144 141.16 2.84 4.24 6.36 8.48 7X14 98 95.86 2.14 2.94 4.41 5.87 7X16 112 109.59 2.41 3.34 5.02 6.69 7X18 126 123 . 38 2.62 3.73 5.60 7.48 DESIGNS OF CONCRETE STRUCTURES. 139 TABLE III. Continued. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars 0.28 in. Area of shear bars 0.38 in. 7X20 140 137.13 2.87 4.14 6.22 8.29 7X22 154 150.89 3.11 4.55 6.83 9.10 7X24 168 164.73 3.27 4.93 7.40 9.87 7X26 182 178.47 3.53 5.34 8.02 10.69 7X28 196 192.23 3.77 5.74 8.63 11.50 8X16 128 125.37 2.63 3.79 5.68 7.57 8X18 144 141.10 2.90 4.25 6.37 8.51 8X20 160 156.76 3.24 4.93 7.09 9.46 8X22 176 172.45 3.55 5.19 7.78 10.40 8X24 192 188 . 18 3.82 5.67 8.50 11.32 8X26 208 203.91 4.09 6.11 9.18 12.24 8X28 224 219.68 4.32 6.56 9.85 13.15 8X30 240 235 . 35 4.65 7.04 10.57 14.09 8X32 256 251.03 4.97 7.52 11.26 15.04 9X18 162 158.62 3.38 4.81 7.20 9.62 9X20 180 176.27 3.73 5.34 8.02 10.68 9X22 198 193.97 4.03 5.85 8.79 11.71 9X24 216 211.63 4.37 6.38 9.57 12.77 9X26 234 229.35 4.65 6.94 10.84 13.79 9X28 252 247.27 4.73 7.36 11.05 14.73 9X30 270 264.78 5.22 7.93 11.89 15.85 9X32 288 282.46 5.54 8.44 12.68 16.89 9X34 306 300.13 5.87 8.97 13.45 17.94 9X36 324 317.84 6.16 9.48 14.21 18.97 10X20 200 195.90 4.10 5.92 8.89 11.85 10X22 220 215.57 4.43 6.49 9.73 12.99 10X24 240 235.10 4.90 7.10 10.66 14.21 10X26 260 254.88 5.12 7.66 11.47 15.31 10X28 280 274.60 5.40 8.23 12.33 16.43 10X30 300 294 . 27 5.73 8.78 13.20 17.58 10X32 320 313.91 6.09 9.38 14.04 18.74 10X34 340 333.29 6.71 10.00 15.01 20.02 140 HANDBOOK ON REINFORCED CONCRETE. TABLE III. Continued. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars 0.28 in. Area of shear bars 0.38 in. 10X36 360 353 . 20 6.80 10.53 15.80 21.06 10X38 380 372.86 7.14 11.10 16.63 22.21 10X40 400 392 . 47 7.53 11.68 17.53 23.39 11X22 242 237.03 4.97 7.17 10.76 14.34 11X24 264 258 . 64 5.36 7.79 11.71 15.61 11X26 286 280 . 32 5.68 8.43 12.64 16.86 11X28 308 301.98 6.02 9.05 13.56 18.11 11X30 330 323.52 6.48 9.70 14.53 19.42 11X32 352 345.35 6.65 10.29 15.45 20.59 11X34 374 366.93 7.07 10.94 16.40 21.88 11X36 396 388.55 7.45 11.58 17.37 23.15 11 X38 418 410.20 7.80 12.20 18.33 24.40 11X40 440 431.76 8.24 12.86 19.29 25.71 11X42 462 453.39 8.61 13.48 20.23 26.98 11X44 484 475.05 8.95 14.09 20.91 28.23 12X24 288 282.42 5.58 8.46 12.69 16.91 12X26 312 305.92 6.08 9.17 13.79 18.34 12X28 336 329.49 6.51 9.86 14.79 19.73 12X30 360 353 . 03 6.97 10.57 15.86 21.14 12X32 384 376 . 67 7.33 11.26 16.88 22.50 12X34 408 400 . 39 7.61 11.90 17.86 23.83 12X36 432 423.88 8.12 12.63 18.94 25.26 12X38 456 447.58 8.42 13.31 19.96 26.59 12X40 480 471.08 8.92 13.98 20.99 28.02 12X42 504 494 . 65 9.35 14.69 22.03 29.41 12X^4 528 518.15 9.85 15.41 23.14 30.84 12X46 552 541.75 10.25 16.12 24.14 32.22 12X48 576 565.25 10.75 16.84 25.23 33.64 13X26 338 331.40 6.60 9.95 14.90 19 87 13X28 364 356.95 7.05 10.67 16.00 21.38 13X30 390 382 . 32 7.68 11.47 17.23 22.96 13X32 416 407.92 8.08 12.22 18.33 24.44 DESIGNS OF CONCRETE STRUCTURES. 141 TABLE III. Continued. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars 0.28 in. Area of shear bars 0.38 in. 13X34 442 433.51 8.49 12.95 19.43 25.92 13X36 468 459.08 8.92 13.70 20.55 27.42 13X38 494 484.81 9.19 14.40 21.60 28.84 13X40 520 510.28 9.72 15.20 22.80 30.38 13X42 546 535 . 84 10.16 15.94 23.91 31.87 13X44 572 561.54 10.46 16.65 24.97 33.31 13X46 598 586.94 11.06 17.94 26.15 34.88 13X48 624 612.53 11.47 18.17 27.30 36.36 13X50 650 638.02 11.98 18.95 28.39 37.89 13X52 676 663.61 12.39 19.69 29.27 39.38 14X28 392 384.38 7.62 11.50 17.27 23.03 14X30 420 411.80 8.20 12.35 18.48 24.69 14X32 448 439.32 8.68 13.15 19.72 26.32 14X34 476 467.03 8.97 13.91 20.86 27.84 14X36 504 494 . 52 9.48 14.72 22.08 29.47 14X38 532 522.11 9.89 15.50 23.25 31.05 14X40 560 549 53 10.47 16.37 24.54 32.71 14X42 588 577.07 10.93 17.14 25.73 34.32 14X44 616 604 . 58 11.42 17.98 26.91 35.94 14X46 644 632 . 23 11.77 18.74 28.11 37.50 14X48 672 659.64 12.36 19.56 29.37 39.16 14X50 700 687 . 15 12.85 20.37 30.57 40.78 14X52 728 714.73 13.27 21.17 31.73 42.37 14X54 756 742 . 28 13.72 21.95 32.92 43.98 14X56 785 770 . 80 14.20 22.85 34.23 45.64 15X30 450 441.43 8.57 13.18 19.76 26.36 15X32 480 471.03 8.97 13.99 21.02 28.04 15X34 510 500.38 9.62 14.91 22.36 29.83 15X36 540 529.90 10.10 15.78 23.64 31.55 15X38 570 559.46 10.54 16.61 24.93 33.25 15X40 600 588.81 11.19 17.50 26.29 35.04 15X42 630 618.34 11.66 18.36 27.55 36.75 15X44 660 647.82 12.18 19.23 28.81 38.48 142 HANDBOOK ON REINFORCED CONCRETE. TABLE III. Continued. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars 0.28 in. Area of shear bars 0.38 in. 15X46 690 677 . 25 12.75 20.09 30.15 40.24 15X48 720 706.71 13.27 20 . 97 31.48 41.97 15X50 750 736.16 13.84 21.86 32.79 43.73 15X52 780 765 . 77 14.23 22.71 34.09 45.41 15X54 810 795.12 14.88 23.61 35.43 47.20 15X56 840 824.63 15.37 24.44 36.67 48.92 15X58 870 854 . 20 15.80 25.30 37.93 50.61 15X60 900 883 . 77 16.23 26.15 39.21 52.31 16X32 512 502 . 25 9.75 14.99 22.50 29.99 16X34 544 534.16 9.84 15.81 23.69 31.63 16X36 576 565 . 09 10.91 16.87 25.29 33.71 16X38 603 596.65 11.35 17.74 26.63 35.51 16X40 640 628 . 14 11.86 18.67 27.97 37.34 16X42 672 659 . 62 12.38 19.57 29.37 39.17 16X44 704 691.03 12.97 20.52 30.64 41.04 16X46 736 722 . 38 13.62 21.45 32.19 42.93 16X48 768 753.86 14.14 22.34 33.54 44.77 16X50 800 785.35 14.65 23.31 34.95 46.59 16X52 832 816.87 15.13 24.19 36.27 48.41 16X54 864 848 . 35 15.65 25.11 37.37 50.25 16X56 896 879.75 16.25 26.04 39.06 52.12 16X58 928 911.24 16.76 26.94 40.42 53.94 16X60 960 942.96 17.04 27.83 41.77 55.67 16X62 992 974 . 20 17.80 28.82 43.18 57.61 16X64 1024 1005.64 18.36 29.72 44.64 59.46 17X34 578 567 . 10 10.90 16.88 25.35 33.81 17X38 612 600 . 60 11.40 17.85 26.79 35.73 17X38 646 633.96 12.04 18.86 28.26 37.72 17X40 680 667 . 30 12.70 19.88 29.76 39.72 17X42 714 700 . 78 13.22 20.80 31.21 41.65 17X44 748 734.19 13.86 21.82 32.70 43.64 17X46 782 767 . 60 14.40 22.79 34.15 45.58 17X48 816 801.00 15.00 23.75 35.66 47.55 DESIGNS OF CONCRETE STRUCTURES. 143 TABLE III. Continued. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars 0.28 in. Area of shear bars 0.38 in. 17X50 850 834.40 15.60 24.75 37.11 49.52 17X52 884 867.89 16.11 25.75 38.57 51.45 17X54 928 911.15 16.85 26.97 39.03 53.98 17X56 962 944.80 17.20 27.90 41.82 55.84 17X58 996 978.26 17.74 28.90 43.33 57.79 17X60 1030 1011.70 18.30 29.84 44.80 59.74 17X62 1064 1045.12 18.88 30.86 46.31 61.70 17X64 1098 1078.50 19.50 31.83 49.70 63.68 17X66 1132 1111.90 20.10 32.80 49.43 65.65 17X68 1166 1145.33 20.67 33.80 50.75 67.60 18X36 648 635.90 12.10 18.92 28.39 37.85 18X38 684 761.36 12.64 19.96 29.89 39-89 18X40 720 706.58 13.42 21.01 31.54 42.04 18X42 756 741.96 14.04 22.05 33.07 44.12 18X44 792 777.47 14.53 23.04 34.58 46.14 18X46 828 812.82 15.18 24.10 35.81 48.23 18X48 864 848 . 20 15.80 25.15 37.68 50.31 18X50 900 883.52 16.48 26.22 39.28 52.42 18X52 936 918.88 17.12 27.27 40.85 54.51 18X54 972 954 . 25 17.75 28.32 42.41 56.59 18X56 1008 989 . 64 18.36 29.34 44.00 58.66 18X58 1044 1025.00 19.00 30.38 45. sr 60.75 18X60 1080 1060.64 19.36 31.34 47.00 62.71 18X62 1116 1096.06 19.94 32.38 48.58 ' 64.78 18X64 1152 1131.48 20.52 33.40 50.17 66.55 18X66 1188 1166.75 21.25 34.43 51.66 68.98 18X68 1224 1202.16 21.84 35.47 53.24 71.03 18X70 1260 1237.50 22.50 36.53 54.82 73.13 18X72 1296 1262.95 23.05 37.34 55.92 74.67 19X38 722 708.63 13.37 21.04 31.59 42.12 19X40 760 745.90 14.10 22.18 33.26 44.35 19X42 798 783 . 22 14.78 23.26 34.93 46.55 19X44 836 820 . 57 15.43 24.35 36.54 48.75 19X46 874 857 . 77 16 23 25.45 38.23 51.01 19X48 912 895 . 23 16.77 26.58 39.87 53.15 144 HANDBOOK ON REINFORCED CONCRETE. TABLE III. Continued. 1 2 3 4 5 6 7 Size of beam. Area of beam. Area of concrete. Area of steel. Shearing force in tons. Area of shear bars 0.19 in. Area of shear bars . 28 in. Area of shear bars 0.38 in. 19X50 950 932 . 58 17.42 27.66 41.53 55 . 34 19X52 988 970.00 18.00 28.75 43.13 57.50 19X54 1026 1007.27 18.73 29.82 44.76 59.73 19X56 1064 1044.68 19.32 30.93 46.38 61.90 19X58 1102 1081.95 20.05 32.07 48.08 64.13 19X60 1140 1119.42 20.58 33.09 49.62 66.26 19X62 1178 1146.90 21.10 34.15 50.88 67.90 19X64 1216 1194.25 21.75 35.32 52.92 70.59 19X66 1254 1231.60 22 .40 36.36 54.55 72.28 19X68 1292 1269.00 23.00 37.35 55.95 74.95 19X70 1330 1306 . 32 23.68 38.55 51.27 77.16 19X72 1368 1333.65 24.35 39.39 59.08 78.86 19X74 1406 1381.00 25.00 40.75 61.23 81.55 19X76 1444 1418.32 25.68 41.90 62.83 83.76 20X40 800 785.20 14.80 23.35 35.03 46.66 20X42 840 824.54 15.46 24.48 36.72 48.96 20X44 880 863.80 16.20 25.39 38.08 51.29 20X46 920 903.06 16.94 26.79 40.22 53.63 20X48 960 942 . 28 17.72 28.48 41.95 55.98 20X50 1000 981.04 18.96 29.24 43.87 58.53 20X52 1040 1020.98 19.02 30.25 45.38 60.56 20X54 1080 1060 . 29 19.71 31.43 47.14 62.87 20X56 1120 1099.74 20.26 32.56 48.83 65.12 20X58 1160 1139.00 21.00 33.70 50.50 67.45 20X60 1200 1178.40 21.60 34.83 52.25 69.72 20X62 1240 1217.68 22.32 35.98 53.99 72.05 20X64 1280 1256.97 23.03 37.14 55.64 74 37 20X66 1320 1296.29 23.71 38.33 57.44 76.67 20X68 1360 1335.85 24.15 39 44 59.16 78.87 20X70 1400 1375.05 24.95 40.62 60.91 81.23 20X72 1440 1414.40 25.60 41.77 62.60 83.52 20X74 1480 1453.78 26.22 42.85 64.33 85.80 20X76 1520 1493.14 26.86 44.00 66.08 88.09 20X78 1560 1532.34 27.66 45.26 67.92 90.45 20X80 1600 1571.63 28.37 46.33 69.53 92.77 DESIGNS OF CONCRETE STRUCTURES. 145 DESCRIPTION OF TABLE IV. This table is worked out for the same cases as was Table II, up to, and including beams 13 inches wide, with the purpose of satisfying the designer that no fear need be felt that the design be weak in resisting deflection. Like designing with steel shapes, little or no attention need be exercised in this regard, unless, in cases where it is expressly desired to obtain and retain a floor strictly level. It was thought that it was unnecessary to carry out the table further, as it may readily be seen that allowing a deflection of -g-J-g- of the span, the load causing this deflection, which is expressed in tons uniformly distributed, will be twice as large as will the beam carry with a factor of safety of 3.5, as shown in Table II. In assigning an allowable deflection of -g-J-j- of the span, when working up the table, the writer had two things in mind: first, that this is a very moderate amount, and may well be allowed for floors carrying machinery which has to be main- tained level, and in line, and for floors, from the underside of the beams of which is hung shafting; second, for the reason that, at about this deflec- tion, hair cracks begin to appear upon the under- side of the beam or girder extending up to the tension members through the non-reinforced pro- tection for the steel. These cracks are of the very slightest importance when considered as af- fecting the strength of the beam or girder, and 146 HANDBOOK ON REINFORCED CONCRETE. the only objections that can be offered against their existence are the unsightly appearance they offer, and that they render the steel protection less durable as a fire resisting medium. This latter, however, is a matter of great importance, and should be kept well in mind during the design. The table itself needs no other explanation NOTE. Make the following modifications in the values given for safe uniformly distributed loads given under Table IV when applying them to continuous girders : With 2 spans increase the values by 44.6 per cent. With 3 spans increase the values by 36.0 per cent. With 4 spans increase the values by 38.3 per cent. With 5 spans increase the values by 38.0 per cent. With 6, 7, 8, and 9 spans, increase the values by 38.0 per cent. DESIGNS OF CONCRETE STRUCTURES. 147 TABLE IV. Uniformly Distributed Load in Tons, Allowing a Safe Deflection of -%^-Q of Span, for the Following Sizes. Span. 2.5X6 2.5X8 12.5X10 2.5X12 3X 12 3X 14 4X14 4X16 5 1.28 3.36 6.85 12.20 14.40 6 .89 2.34 4.76 8.48 10.00 16.40 21.18 7 .65 1.72 3.50 6.23 7.36 12.05 15.55 23.70 8 .50 1.32 2.68 4.78 5.75 9.23 12.18 18.15 9 .40 1.04 2.12 3.77 4.45 7.04 9.40 14.35 10 .84 1.72 3.05 3.61 5.90 7.62 11.63 11 1.42 2.53 2.98 4.88 6.30 9.60 12 1.14 2.03 2.50 4.10 5.29 8.07 13 1.02 1.81 2.14 3.50 4.51 6.88 14 1.56 1.84 3.02 3.89 5.93 15 1.36 1.60 2.63 3.39 5.16 16 2.31 2.98 4.54 17 2.04 2.64 4.02 18 1.82 2.35 3.59 19 3.23 20 2.91 Span. 5X16 5X18 5X 20 6X 20 6X 22 6X 24 7X 24 7X 26 7 31.15 8 23.85 33.50 48.10 56.35 9 18.90 26.50 37.15 44.50 50.60 10 15.30 21.40 30.10 36.05 41.00 62.50 76.00 11 12.60 17.70 24.90 29.78 33.88 52.50 62.75 80.20 12 10.60 14.90 20.90 25.10 28.50 44.10 52.75 67.35 13 9.05 12.70 17.80 21.38 24.30 37.63 45.00 57.50 14 7.79 10.90 15.35 18.38 20.88 32.40 38.75 49.50 15 6.55 9.52 13.40 16.05 18.23 28.25 33.75 43.13 16 6.00 8.38 11.75 14.10 16.00 24.83 29.70 37.90 17 5.28 7.40 10.40 12.50 14.20 22.55 26.25 33.55 18 4.72 6.62 9.29 11.15 12.68 19.60 23.4-> 29.93 19 4.24 5.94 8.34 10.00 11.38 17.63 21.05 26.90 20 3.82 5.35 7.53 9.03 10.25 15.90 19.00 24.25 21 4.87 6.83 8.18 9.30 14.40 17.23 22.00 22 4.42 6.23 7.45 8.50 13.15 15.70 20.05 23 *4.03 5.69 6.78 7.75 12.00 14.35 18.35 24 5.23 6.28 7.13 11 .05 13.20 16.85 25 4.82 5.77 6.55 10.18 12.15 15.50 26 6.08 9.40 11.25 14.35 27 5.63 8.73 10.45 13.30 148 HANDBOOK ON REINFORCED CONCRETE. TABLE IV. Uniformly Distributed Load. Continued. Span. 5X16 5X 18 5X20 6X20 6X22 6X 24 7X 24 7X26 28 8 10 9.70 12.35 29 7.55 9.03 11.50 30 7 05 8 43 10 75 31 10.08 32 9 97 33 8 90 Span. 7X 28 8X 28 8X 30 8X 32 9X32 9X34 9X36 12 13 84.50 72 00 96.96 82 50 120 . 00 102 50 124 50 132 75 14 62 00 71 00 88 25 107 00 114 30 155 00 15 54 00 62 00 77 00 93.50 99.50 135.00 149 . 50 16 47 50 54 50 67 50 82 00 87 50 118 50 131 50 17 18 19 20 21 22 42.00 37.50 33.75 30.40 27.50 25 13 48.25 43.05 38.60 34.85 31.60 28 83 59.80 53 . 35 48.00 43.25 39.20 35 75 72.65 64.75 58.25 52.50 47.60 43 45 77.75 69.20 62.10 56.00 50.75 46 25 105.00 91.50 84.20 76.00 68.85 62 75 116.25 103.75 93.50 84.00 76.30 69 50 23 24 25 23.00 21.13 19 45 26.38 23.70 22 25 32.75 30.05 27 70 39.75 36.50 33 63 42.35 38.90 35 85 57.50 52.75 48 55 63.70 58.50 53 90 26 27 28 18.00 16.70 15 50 20.60 19.13 17 80 25.60 23.75 22 10 31.10 28.85 26 80 33.15 30.75 28 60 44.95 41.75 38 30 49.85 46.20 42 90 29 30 31 32 33 14.45 13.50 12.65 11.88 11.15 16.55 15.50 14.50 13.60 12.80' 20.55 19.20 18.00 16.85 15.90 25.00 23.35 21.85 20.50 19.30 26.60 24.90 23.30 21.87 20.60 36.15 33.75 31.65 29.75 27.95 40.00 37.38 35.00 32.88 30.90 34 10 50 12 05 15 00 18 20 19 38 26 33 29 13 35 36 9.90 11.35 14.13 13 35 17.15 16 20 18.30 17 30 24.83 23 45 27.45 26 00 37 38 12.65 12.00 15.35 14.55 16.35 15.50 22.20 21.05 24.55 23.27 39 13 80 14 73 20 00 22 10 40 41 13.13 14.00 19.00 21.00 20 00 42 19 07 43 18 18 44 17.40 DESIGNS OF CONCRETE STRUCTURES. 149 TABLE IV. Uniformly Distributed Load. Continued. Span. 10X36 10X38 10X40 11X40 11X42 11X44 12X44 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 145.25 114.70 92.90 76.85 64.60 55.00 47.40 41.30 36.25 32.15 28.65 25.75 23.25 21.08 19.20 170.00 134.00 108 . 75 90.00 75.65 64.35 55.60 48.40 42.55 37.65 33.60 30.15 27.20 24.70 22.50 20.60 18.93 158.00 127.75 105.75 89.00 75.65 65.35 57.40 50.00 44.25 39.50 35.50 32.00 29.00 26.43 24.20 22.25 20.50 173.50 140.00 115.50 97.00 82.70 71.40 62.20 54.50 48.40 43.45 38.83 35.00 31.75 28.90 26.45 24.35 22.40 200.00 162.00 134.00 112.75 96.00 82.85 72.15 63.40 56.20 50.00 45.00 40.55 36.80 33.55 30.65 28.20 26.00 24.00 229.00 206.00 153.40 129.00 110.00 94.75 82.50 72.50 64.25 57.30 51.50 46.40 42.10 38.40 35.10 32.25 29.75 27.50 25 . 50 242.00 196.00 162.25 136.50 116.25 100.25 87.20 76.70 67.90 60.50 54.35 49.00 44.50 40.60 37.05 34.10 31.40 29.00 26.90 Span. 12X46 12X48 13X48 13X50 13X52 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 221.00 183.00 153.60 130.75 113.00 98.25 86.30 76.50 68.20 61.20 55.20 50.00 45.60 41.75 38.20 35.35 32.70 30.35 28.15 251.25 207 . 50 179.90 148.50 128.40 111.90 98.25 87.00 77.50 69.70 62.80 57.00 52.00 47.55 43.65 40.25 37.25 34.50 32.10 29.95 271.50 224.50 188.75 160.50 138.50 120.50 106.00 94.00 83.80 75.15 67.75 61.50 56.15 51.30 47.65 43.45 40.15 37.25 34.60 32.30 30.15 255.00 215.00 183.00 108.00 137.50 121.00 107.00 95.50 85.75 77.35 70.10 63.90 58.50 53.75 49.55 45.80 42.50 39.50 36.85 34.38 32.25 286.50 240.75 205.00 177.00 154.00 135.50 120.00 107.00 96.00 86.50 79.75 71.50 65.50 60.20 55.50 51.25 47.55 44.25 41.25 38.50 36.05 150 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE V. This table was prepared to serve the same purpose in designing floors, as was Table I in designing beams and girders. All the columns will explain themselves after reading the description of Table I. The thickness of the floor here given, includes both the top 1-inch wearing surface and 1 inch below the steel tension members, serving for a fire- resisting medium, as well as a finish. In the tables, neither of these thicknesses is considered in obtaining the moment of resistance of the ^section. The wearing surface was not considered for reasons stated in Part I, and, of course, the protection for the steel could not be, because it lies outside the tension members. In this way, 2 inches is added to the thickness of the floor from which no benefit is expected to resist the moment caused by the loading, and accordingly as thick a concrete floor results as does a wooden one, when figuring for deflection, and a thicker one, when figuring for strength. However, when the thickness of the top wooden floor is added, the thickness of the concrete floor, for resisting strength, will compare favorably with the wooden one. Finally, in the concrete one, we have included the thickness to render the same fire resisting, and, for this reason, have more than offset any objections that might be imposed re- garding space occupied. DESIGNS OF CONCRETE STRUCTURES. 151 The moments here given in columns 5 and 6 are figured, allowing a factor of safety of 3.5, which is very ample, especially so when the top 1-inch wearing surface is considered as offering no resistance. The values of the tensile stress per square inch, given in column 11, brought to bear upon the concrete in the tensile layers, are reduced to a minimum in the case of floors where the ratio of the concrete resisting area to that of the steel, in the tensile layer, is a maximum. This must necessarily be so, since the moment of resistance of the concrete area above the neutral axis, which must withstand the moment of the loading by compression, and which varies as the square of the effective depth of the section is, in the case of floors where the depth is small, very much less for a given resisting area of concrete in the tensile layer than in the case of beams where the effective depth for a like resisting area is large. For a like reason, because the shearing force re- sulting from a loading giving a limiting bending moment is, in the case of floors, small in compari- son with the resisting area, the stress per square inch produced throughout the section is corre- spondingly small. Not only this, but the steel tension members are located quite near the neu- tral axis, and cross the lines of resultant shear at an angle, and hence offer a component to resist the resultant shear. Consequently, it was thought unnecessary to compute tables for shearing values 152 HANDBOOK ON REINFORCED CONCRETE. when failure, with ordinary spans, always results by compression of the upper fibers, allowing of course, that a sufficient tensile moment of resis- tance has been furnished. TABLE V. 1 2 3 4 5 6 7 8 9 10 11 . Dis- t-, a 0> . H-i o a j3 J2.C tance ft . S3 o . 1| L o Sfia ll z7 || ll below center ll 111 || o gg <-> ^i H g 1 1 per foot width. ll j! oment i 3er foot of gravity to neutral F si s 5 ;ress in < >er squa ft S axis. <2 1-1 CJ * fcS In W ' ' 10-14 f 18-20 | 15-19 A 20 i 11 95.0 99 40.4 8-11 i 89 36.5 8 A 12-15 10-12 f 16-20 | 13-17 A 18-20 i 12 113.0 118 48.0 8-10 1 106 43.3 8-11 f 11-14 T5 12-15 A 15-18 | 16-20 ^ 19-20 A 168 HANDBOOK ON REINFORCED CONCRETE. TABLE VII. Columns. Continued. Circular section. Octagonal section. 1 2 3 4 5 6 7 8 9 Height of col- umn. 10 Size of rods. Size. Area section. Weight per foot. Safe load. Height of col- umn. Size of rods. (Use 8.) Weight foot. Safe load. In. Sq. in. Lbs. Tons. Feet. In. Lbs. Tons. Feet. In. 13 132.7 138 56.5 8-9 1 125 51.0 8-10 |^ 10-13 7 T6 11-14 TS 14-17 J 15-19 | 18-20 T5 20 A 14 153.9 160 65.5 8-9 f 144 59.0 8-10 | 10-12 11-13 T5 13-16 f 14-18 I 17-20 TS 19-20 A 15o 176.7 184 75.2 8-11 ft 166 67.8 8 f 12-15 | 9-12 16-18 A 13-16 * 19-20 1 17-20 A 16 201.0 210 85.5 8-10 ft 189 77.0 8 f 11-14 9-11 ft 15-17 A 12-15 i 18-20 f 16-19 A 20 f 17 227.0 236 96.5 8-10 A 213 87.0 8 | 11-13 1 9-11 ft 14-16 A 12-14 i 17-20 f 15-18 ft 19-20 f 18 254.5 255 108.0 8-9 A 239 97.5 8-10 ft 10-12 i 11-13 1 13-15 A 14-17 A 16-19 f 18-20 f 20 T! 19 283.5 295 120.5 8-9 ft 266 109.0 8-9 ft 10-11 1 10-13 i 12-14 A 14-16 A 15-18 f 17-20 f 19-20 tt DESIGNS OF CONCRETE STRUCTURES. 169 TABLE VII. Columns. Continued. Circular section. Octagonal section. 1 2 3 4 5 6 7 8 9 10 Size. Area section. Weight per foot. Safe load. Height of col- umn. Size of rods. (Use 8). Weight per foot. Safe load. Height of col- umn. Size of rods. In. Sq. in. Lbs. Tons. Feet. In. Lbs. Tons. Feet. In. 20 314.1 327 133.3 8 7 295 120.0 8-9 A 9-11 1 10-12 i 12-14 13-15 A 15-17 1 16-19 f 18-20 ft 20 ft 22 380 396 161.7 8-10 1 S58 145.0 8 TS 11-12 A 9-11 % 13-15 f 12-14 A 16-19 ft 15-17 f 20 f 18-20 ii 24 452 472 192.4 8-9 i 427 173.5 8-10 i 10-11 A 11-12 A 12-14 f 13-15 I 15-17 ft 16-19 18-20 1 20 I 26 531 553 225.5 8 ^ 500 203.2 8-9 1 9-10 & 10-11 A 11-12 f 12-14 f 13-16 ft 15-18 ft 17-19 f 19-20 t 20 tt 28 616 641 262.0 8 ) 578 235.0 8 i 9 TS 9-11 A 10-12 f 12-13 f 13-15 ft 14-16 ft 16-18 f 17-20 t 19-20 ft 30 707 735 300.0 8-9 TS 662 270.0 8 1 10-11 f 9-12 A 12-14 ft 13-15 f 15-16 f 16-18 ft 17-19 ft 19-20 t 20 1 170 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE VIII. Table VIII is drawn up both to facilitate making estimates, and to show at a glance the compara- tive costs, for equal strength, of the three kinds of construction given namely, reinforced con- crete, structural steel, and slow-burning, when used in the design of floors in the shape of beams or girders. The basis of the cost of the concrete given under column 3 is from data taken by the writer upon actual work, and represents fair working condi- tions. It includes all temporary false work, and everything to make a finished piece of work, and even allows going over the exposed surface with a cement wash after pointing up and removing irregularities where necessary. The cost of the steel used in connection with the concrete, is based upon the price f.o.b of 2 cents per pound, to which is added another 2 cents per pound for handling, cutting to lengths, placing in forms, and wiring to place where necessary. The cost of the structural shapes given under column 7 is based upon a price of 2.5 cents per pound f.o.b, to which is added $10 per ton, or -J cent per pound to cover the cost of placing, bolting, or riveting to place, and painting, which is little enough. The cost of wooden beams is figured upon a basis of a price of $35 per thousand feet upon the site for planed stock, which is increased by $10 COMPARATIVE COSTS. 171 per thousand feet to cover the cost of sizing, placing, and fitting, but no other finish. The cost of the slow-burning construction, as figured here, applies principally to northern sections of the country, and should be considerably reduced to meet southern conditions. 172 HANDBOOK ON REINFORCED CONCRETE. I 9 &q slils'^ 00 xxxxxxxxxxxxxx i 00 W M CO oo 10 o o <-* I-H ^H (M CO CO CO CO CD 00 - i oo-. O ~ |XXXXXXXXXXXXXX si I safe COMPARATIVE COSTS. 173 x x x x x x x : ; ; ; : : : xxxxxxxxxxxxxxxx 174 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE IX. The purpose of this table is to give a compara- tive cost, for equal strength, of a fire resisting, reinforced concrete floor in comparison with the ordinary floor used in the slow-burning construc- tion. The cost of the concrete given under column 3 is based upon actual results under ordinary con- ditions, but differs in the price per unit of volume from that of beams and girders. The cost of steel given under column 4 is figured upon the same basis as was explained in Table VIII. The item, "Cost of Troweling," includes the cost of labor both in applying the 1-inch finish, and the screeding and troweling same to a finished surface. For wooden floors, the price here given is based upon the cost of spruce plank laid at $35 per thousand feet; of southern pine laid at $45; of 1-inch No. 2 maple top flooring laid and dressed at $60; and No. 1 maple at $80 per thousand feet. COMPARATIVE COSTS. 175 TABLE IX. Comparative Costs. Floors for Equal Strength. 1 2 3 4 5 6 7 8 9 10 11 Reinforced concrete. Wood. Safe moment Cost Cost Cost inch-lbs. Thick- ness of con- Cost of of trowel- Total cost Spruce or Cost of per sq. ft. Total cost Total cost p6r foot width. of floor. crete per sq. ft. steel per sq. ft. ing per sq. ft. per sq. ft. H.P. plank size. same per sq. ft. maple No. 2 top No. 2 top floor. No. 1 top floor. floor. In. Spruce 2,250 3.5 $0.13 $0.04 $0.03 $0.20 2" $0.07 $0.06 $0.13 $0.15 4,000 4.0 .15 .05 .03 .23 2" .07 .06 .13 .15 6,200 4.5 .17 .05 .03 .25 2 // .07 .06 .13 .15 9,000 5.0 .19 .07 .03 .29 3" .11 .06 .17 .19 12,450 5.5 .21 .10 .03 .33 3" .11 .06 .17 .19 16,000 6.0 .23 .11 .03 .37 4" .14 .06 .20 .22 20,250 6.5 .24 .11 .03 .38 4" .14 .06 .20 .22 25,000 7.0 .26 .13 .03 .42 4" .14 .06 .20 .22 * H.P. 30,250 7.5 .28 .13 .03 .44 4" .18 .06 .24 .26 36,000 8.0 .30 .13 .03 .46 5" .23 .06 .29 .31 42,250 8.5 .32 .15 .03 .50 5" .23 .06 .29 .31 49,000 9.0 .34 .15 .03 .52 5" .23 .06 .29 .31 56,250 9.5 .36 .18 .03 .57 6" .27 .06 .33 .35 64,000 10.0 .38 .18 .03 .59 6" .27 .06 .33 .35 72,250 10.5 .39 .18 .03 .60 6" .27 .06 .33 .35 176 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE X. Table X is similar in all respects to Table IX, but compares the two kinds of constructions upon a fairer basis that is, the relative costs for like stiffness or for like deflections. Since rein- forced concrete, because of a high modulus of elasticity, gives a stiffer floor than does the wood, this basis of comparison as regards cost, more nearly shows up the concrete floor in its proper merits in this particular sphere. TABLE X. Comparative Costs. Floors for Equal Deflection. 1 2 3 4 5 6 7 Reinforced concrete. Wood. Safe moment in inch- pounds per foot width. Thickness of floor. Actual resist- ing depth. Cost per sq. ft. com- plete. Thickness of spruce or H. P. plank. (Inches.) Total cost per sq. ft. with No. 2 maple top floor. Total cost per sq. ft. with No. 1 maple top floor. Inches. Inches. Spruce. 2,250 3.5 1.5 $0.20 2" $0.13 $0.17 4,000 4.0 2.0 .23 3" .17 .19 6,200 4.5 2.5 .25 4" .20 .22 H. P. 9,000 5.0 3.0 .29 4" .24 .26 12,400 5.5 3.5 .33 5" .29 .31 16,000 6.0 4.0 .37 5" .29 .31 20,250 6.5 4.5 .38 6" .33 .35 COMPARATIVE COSTS. 177 DESCRIPTION OF TABLE XI. The following table is given both to assist in estimating the cost of reinforced concrete columns, and to serve as a means of comparison in cost between the more general forms of construction namely, cast iron, steel or wrought iron, and wood. As before, the cost given here for reinforced concrete is taken from average results of actual construction of columns. The basis of computing the cost of the other kinds of columns is taken: for cast iron, 2.5 cents per pound, erected in the building; for steel, 3 cents per pound for plain shapes, and 3.5 cents for riveted sections erected; and for wood $45 per thousand feet in place. 178 HANDBOOK ON REINFORCED CONCRETE. 1 iH 6 ll S22 228 228 'i 'i I-H CO U5 i r 00 00 1-H CO H HI 1 ? 7 g TP o r>. ooco cocoi> 1 I CO b- 1 O 1-i $ II i;..v M ? i- i 0> ii .d -co -oo -co J.J, CO Tji -CO 06 00 ill ' 2 s &J : ** "I ^ .S 7 J. : H. d o g'S S : : ; : : ; : ; : x l1l x l d ; ; .' ; ; ; ^ -*> 3~sJ-S S (NiOOO COO50>050 O O i-H 00 tOI>00 t^OOOOOO I>OOOOOS 0000 OOO'tO OSCOOO 00(NCO OOrHiqp OOO ? 7 oo o 8 3 180 HANDBOOK ON REINFORCED CONCRETE. . ! 5 ! ! o . . o | S ^si : g : : : 3 Si o ' d N -co o fl . ,-1 . rH -r-l 1 S ill :g : S : : o> 1 _fl C CO lCrHt>CO lOi-l 0505 C500-; ^H rH (N rH(N R H S.|1 ^^^ ^^^rH ^^ ^ -^"-i n * ^^^ i NW NNM^ C^c5 H 1 i^lfl g i 0000 00 OCO I |S S SSS2 SISS Jb ^ s W 8 1 d _, 3 1 W S o S O rH l^ i~* a C U5 *"* Si s s s s COMPARATIVE COSTS. 181 OOJ OOO5INICOO OO'-HMcO HANDBOOK ON REINFORCED CONCRETE. - t? Sj 9 o . iH "883 a c S & 3 3 1 : : :: if: :;.: ^0^ : : ' : i : : | S 6 |I 05 CO e> l| a ' ' ' '. '.'.'. 00 iii OOiOQON-iC OOKt^iOlOCN ^ 8 ia , -i ^ ^r^^^HMHC, C^r^r^HC,^^ t- j||x| -CXXXXX XXXXXX M8 B g (0 &J5 o OOTtOOO5O I i*it! g "3 o <* 00 CO rH (N oncrete (ci eo w a g ^j rHT(O " 1 a hi g 1 Jai s rH II li i COMPARATIVE COSTS. 183 s|oo io|ao e^x |ao >o|oc wlao NI coMi wh* jj ^^ * ^ -^ co I _^j k^ ^, ^^ ^^ !_ 9 5 Q ^ ^ -* ^ . ' ' O ws j. j ^ k-- __ . \ I ^ i' L-^- -^ ^J UJ ^ ^ ^J ^ *^ 1 3 i ^- ^* o- M ^ ii ^-* ^50 -^ "U / Q. x 5 * / 1 x 1 / tri X X x O ?n ^ X X f ? O , X x j X x / > ^ < -n < ^ * / x Q- 9 ^ ^ ^ X 1 x x 00 ^ $ ^ it ^ (1 ,x -^ ^ t ^x Q_ ^r bj ^" ! ^j ^ 00 | f ^ i e ^H " 0> 5 ' c ^ o n ! 2 5 3 3 5 4 3 4J 5C 1 Span in Feet ROOF TRUSSES. 219 10 FT. BAY CURVES SHOWING THE RELATION OF COST TO SPAN (For Type of Truss see Table 15) 4C ^ 0) ^- Q. ' fX X- ^ _^. x* -^ X-* i O , |X ^" oo -r- ~ X- x^ ^* ^~ ^- - ' * on ^ iX ^- - , * fis [7 +*- - . \<- X " i ^* M- n 1 ** ^> ^- 1 k ^* ^^ ^. . 9 x r *- -- <* W -^ - .^*" >~> n Q. g / ^x t^ / 0) o ' t / o c/> / / c m ' t / X +J S X - X ^ ^ O U_ x s X ^ X X ^ X X +J x ^ ^ X ^a ^ ^ X w~ r V X ^ --- ^ 20 .n ^ ^ ^ j ^ <* > ^ * ..^ i X > , ^i -^ X ** c ^ *-* O n O 25 30 35 40 Span in Feet 45 50 220 HANDBOOK ON REINFORCED CONCRETE. 1 2 FT. BAY CURVES SHOWING THE RELATION OF COST TO SPAN (For Type of Tmss see Table 15) 25 30 35 40 Span in Feet 50 ROOF TRUSSES. 14 FT. BAY CURVES SHOWING THE RELATION OF COST TO SPAN, For Truss see Table 15 ) 40 <^s c CD Q. x^ S ^ ' O ^* ** X ^ I ,-* >** ^^ -- 1 O p sQ ** ^** ^" ^. -" 20 \, p,s * **** \** -- 1 - .- ^~~ H- _j 1 ,**" ^ ^ _^ .^^ cr i j <=!<" > * w >?o o T IU Jn c I Q. V) Q C On i> 1 - ^- ** ** *** ** *-*- -^* . ' ^ ^ > ^" f ^ ^ I ^ ** , ( i ^x ^ c -< ^ ,- ^^ ^ 10 |- to O o 2 3 6 J s pa n J in b f "e el t ^ ) 4 b b 222 HANDBOOK ON REINFORCED CONCRETE. 1 6 FT, BAY CURVES SHOWING THE RELATION OF COST TO SPAN. ( For Truss see Table 15 ) 30 35 40 Span in Feet ROOF TRUSSES. 223 DESCRIPTION OF TABLE XVI. This table treats the type of truss shown as does Table XV its type. By reference to the description of the latter, this table will be readily understood. No further mention need be made except in cases where excessively long spans cause CENTER Of TRUSS CENTER OF TRUSS PLAN TYPE 16 ELEVATION diagonal braces longer than thirty times the least dimension of the brace section, in which cases, when the reinforcement will not carry the tension caused by the eccentric loading, either the rein- forcement should be increased, or the unsupported length diminished by struts or braces of small section. NOTE. For reinforcement in upper chord, use that re- quired in Table XV for one-half the span given here. NOTE. The reinforcement sizes of lower chord are the same for both the 45 slope and the 30 slope. 224 HANDBOOK: ON REINFORCED CONCRETE. TABLE XVI. 40-Foot Span. 1 Sizes of Upper Chord. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 10 4X16 5X16 5X16 6X16 5X18 6X18 5X18 6X18 5X20 6X20 5X18 6X18 5X18 6.5X18 5X20 6.5X20 6X20 7.5X20 6X22 7.5X22 5X20 6.5X20 6X20 7.5X20 6X22 7.5X22 6X22 8X22 6X24 8X24 4X14 5X14 4X16 5.5X16 5X16 6.5X16 5X16 7X16 5X18 7X18 5X16 6.5X16 5X16 7X16 5X18 7X18 5X20 7X20 5X20 7.5X20 5X18 7X18 5X20 7X20 5X20 7.5X20 6X20 9X20 6X22 9X22 12 14 16 Sizes of Lower Chord. 8 9 10 11 12 13 8 10 4X16 5X16 4X16 5X16 4X16 5X16 4X16 5X16 4X16 5.5X16 4X16 5X16 4X16 5.5X16 4X16 5.5X16 5X16 7X16 5X18 7X18 4X16 5.5X16 5X16 7X16 5X18 7X18 5X20 7X20 6X20 8X20 5.5X16 6X16 6.5X16 5.5X16 6.5X16 8X18 12 6X16 7X16 7X16 7.5X16 8X16 8.5X20 10X20 14 16 6X16 6.5X16 Area of Truss Rod (sq. in.). Diagonal Braces. 1 14 15 16 17 18 19 20 21 22 Bay (feet). Load sq.ft. (Ibs.). 45 Slope. Load sq. ft. (Ibs.). 30 SloDe. Load sq. ft. (Ibs.). 50 75 100 50 75 100 50 75 100 4X7 8 1.38 1.98 2.58 4X3 4X5 4X6 4X4 4X6 10 1.68 2.43 3.22 4X4 4X6 5X6 4X5 4X7 5X7 12 1.78 2.88 3.88 4X5 4X7 5X7 4X5 4X8 5X9 14 2.28 3.37 4.48 4X5 5X6 5X8 4X6 5X8 5X10 16 2.58 3.88 5.13 4X6 5X7 6X8 4X7 5X9 6X10 ROOF TRUSSES. 225 TABLE XVI. Continued. 50- Foot Span. 1 Sizes of Upper Chord. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 10 6X18 6X20 7X20 7.5X22 7.5X22 7X20 7.5X22 7.5X24 8.5X26 9X26 7.5X22 7.5X24 9X26 9X26 9X28 6.5X16 6.5X18 7X18 7X20 8X20 7X.18 8X20 8.5X20 8.5X22 8.5X24 8X20 8.5X22 8.5X^4 9X24 10.5X24 12 14 16 Sizes of Lower Chord. 8 9 10 11 12 13 8 10 5X20 6X20 5X20 6X20 5X20 6X20 5X20 6.5X20 5X20 6.5X20 5X20 6X20 5X20 6.5X20 5X20 6.5X20 5X20 7X20 6X20 8X20 5X20 6.5X20 5X20 7.5X20 6X20 8X20 6X22 8X22 6X24 8.5X24 6.5X20 7X20 7.5X20 6.5X20 7X20 7.5X20 7.5X20 8.0X20 9.5X20 12 14 7.5X20 8X20 10X22 16 7.5X20 9.5X20 10X24 Area of Truss Rod (sq. in.). Diagonal Braces. 1 14 15 16 17 18 19 20 21 22 Bay (feet). Load sq. ft. (Ibs.) 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 50 75 100 5X7 8 1.8 2.6 3.4 5X3 5X5 5X6 5X4 5X6 10 2.2 3.2 4 10 5X4 5X6 5X7 5X5 5X7 5X9 12 2.6 3.8 5.0 5X5 5X7 6X7 5X6 5X8 6X9 14 3.0 4.4 5.8 5X5 5X8 6X9 5X6 5X9 6X10 16 3.4 4.9 6.6 5X6 6X7 6X10 5X7 6X9 6X12 226 HANDBOOK ON REINFORCED CONCRETE. TABLE XVI. Continued. 60-Foot Span. 1 Sizes of Upper Chord. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 7X20 7X22 7.5X24 7.5X24 7.5X26 7X24 8.5X24 8.5X26 8.5X28 10X28 8X26 8.5X28 10X28 10X30 11.5X32 6.5X20 7.5X20 8X20 8X22 8X24 8X20 8X22 8.5X22 9.5X24 10X26 8X24 9.5X24 10X26 10X28 11.5X28 10 12 14 16 Sizes of Lower Chord. 8 9 10 11 12 13 8 10 6X24 7X24 6X24 7X24 6X24 7X24 6X24 7.5X24 6X24 7.5X24 6X24 7X24 6X24 7.5X24 6X24 7.5X24 6X24 8X24 6X24 8X24 6X24 7.5X24 6X24 8X24 6X24 8X24 7X24 9.5X24 7X24 10X24 7.5X24 7.5X24 8X24 8.5X24 8.5X24 9X24 12 14 16 .... 8X24 8.5X24 9.5X24 8X24 8.5X24 9X24 9.5X24 11X24 11.5X24 Area of Truss Rod (sq. in.). Diagonal Braces. 1 14 15 16 17 18 19 20 21 22 Bay (feet). Load sq.ft. (Ibs.). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 50 75 100 8 2.4 3.3 4.2 6X3 6X4 6X6 6X4 6X5 6X7 10 2.9 4.0 5.1 6X4 6X5 6X7 6X5 6X7 6X9 12 3.3 4.7 6.0 6X4 6X6 6X8 6X5 6X8 6X10 14 3.8 5.3 7.0 6X5 6X7 7X8 6X6 6X9 7X10 16 4.2 6.0 7.9 6X6 6X8 7X9 6X7 6X10 7X12 ROOF TRUSSES. 227 TABLE XVI. Continued. 70- Foot Span. 1 Sizes of Upper Chord. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 10 7X24 8X26 8.5X28 8.5X28 9.5X28 8X28 9.5X28 10X30 10X32 11X32 9.5X28 9.5X32 11X32 11X34 11.5X36 7.5X20 7.5X22 8X24 9X24 9.5X26 8X24 9X26 9.5X26 10.5X28 11X30 9X26 9.5X28 11X28 11X32 11.5X32 12 14 16 Sizes of Lower Chord. 8 9 10 11 12 13 Reinforcement Size, 7 X 28 for whole span. 8 10 12 8X28 8X28 8X28 8.5X28 8.5X28 8X28 8.5X28 8.5X28 9X28 9X28 8.5X28 9X28 9X28 9.5X28 10X28 8.5X28 8.5X28 9X28 9X28 9.5X28 9X28 9.5X28 10X28 10X28 10.5X28 9.5X28 10X28 10.5X28 11X28 11.5X28 14 16 Area of Truss Rod Uq. in.). Diagonal Braces. 1 14 15 | 16 17 18 19 20 21 22 Bay (feet). Load sq. ft. (Ibs.). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 50 75 100 8 3.05 4.10 5.15 7X3 7X4 7X5 7X3 7X5 7X7 10 3.58 4.89 6.20 7X3 7X5 7X6 7X4 7X6 7X8 12 4.10 5.68 7.25 7X4 7X6 7X8 7X5 7X7 7X10 14 4.58 6.59 8.30 7X5 7X7 7X9 7X6 7X8 7X11 16 5.15 7.25 9.35 7X5 7X8 7X10 7X7 7X10 7X13 228 HANDBOOK ON REINFORCED CONCRETE. TABLE XVI. Continued. 80- Foot Span. 1 Sizes of Upper Chord. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 10 12 8X28 9X28 9.5X30 9.5X32 10.5X32 9.5X30 9.5X32 10.5X32 11X34 11X36 9.5X32 11X34 11X36 12X38 12.5X40 7.5X24 9X24 10X28 lOXcO 11 X3k 9X26 10X28 11.5X32 11.5X34 13X36 10.5X28 11.5X32 12X36 13.5X36 13.5X40 14 16 Sizes of Lower Chord. 8 9 10 11 12 13 Reinforcement Size, 8 X32 for whole span. 8 9X32 9X32 9X32 9.5X32 9.5X32 9X32 9.5X32 9.5X32 10X32 10X32 9.5X32 10X32 10.5X32 10.5X32 11 X32 9.5X32 9.5X32 10X32 10X32 10.5X32 10X32 10.5X32 10.5X32 11 X32 11.5X32 10.5X32 11X32 11.5X32 12X32 13X32 10 12 14 16 Area of Truss Rod (sq. in.)- Diagonal Braces. 1 14 15 16 17 18 19 20 21 22 Bay (feet). Load sq. ft. 45 Slope. 0"*) Load sq. ft (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 50 75 100 8 10 12 14. ... 16 3.8 4.4 5.0 5.6 6.2 5.0 5.9 6.8 7.7' 8.6 6.2 8X3 7.4 8X3 8.6 8X4 9.8 8X4 11.0 8X5 8X4 8X5 8X6 8X6 8X7 8X5 8X6 8X7 8X8 8X10 8X3 8X4 8X5 8X5 8X6 8X5 8X6 8X6 8X8 8X7 8X9 8X8 8X11 8X9 8X12 ROOF TRUSSES. 229 TABLE XVI. Continued. 90-Foot Span. 1 Sizes of Upper Ohor d. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 10 12 9X30 9X32 10.5X32 10.5X34 12X36 10.5X32 10.5X36 11.5X36 12X38 12X40 10.5X36 12X38 12X40 13X42 13.5X44 8.5X26 X28 10X28 10X30 11.5X32 10X28 10X32 11.5X32 12X34 12X36 10.5X24 11.5X33 12X36 13.5X36 13.5X40 14 16 Sizes of Lower Chord. 8 9 10 11 12 13 Reinforcement Size, 9 X36 for whole span. 8 10 10X36 10X36 10X36 10.5X36 10.5X36 10X36 10.5X36 10.5X36 11X36 11X36 10.5X36 11X36 11X36 11.5X36 12X36 10.5X36 10.5X36 11X36 11X36 11.5X36 11 X36 11.5X36 12X36 12X36 12.5X36 11.5X36 11.5X36 12.5X36 13X36 13.5X36 12 14 16 Area of Truss Rod (sq. in.). Diagonal Braces. 1 14 15 16 17 18 19 20 21 22 Bay (feet). Load sq. ft. (Ibs.). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 30 75 100 50 75 100 50 75 100 8 4.7 6.1 7.4 9X3 9X4 9X5 9X3 9X5 9X6 10 5.4 7.1 8.8 9X3 9X5 9X6 9X4 9X6 9X7 12 6.1 8.2 10.2 9X4 9X5 9X7 9X5 9X7 9X9 14 6.8 9.2 11.6 9X4 9X6 9X8 9X5 9X8 9X10 16 7.4 10.1 12.8 9X5 9X7 9X9 9X6 9X9 9X12 230 HANDBOOK ON REINFORCED CONCRETE. TABLE XVI. Continued. 100-Foot Span. 1 Sizes of Upper Chord. 2 3 4 5 6 7 Bay (feet). 45 slope. Load sq. ft. (Ibs.). 30 slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 8 10X34 11X36 11.5X36 11.5X38 11.5X40 11.5X36 11.5X40 12.5X40 13X42 13X44 11.5X40 12.5X42 13X44 14.5X44 15.5X48 9.5X28 10.5X30 11 X32 11X34 12.5X36 10X32 11.5X34 11.5X36 13X38 13X40 11.5X34 13X36 13X40 14.5X42 15X44 10 12 14 10 Sizes of Lower Chord. 8 g 10 11 12 13 Reinforcement Size, 10 X38 for whole span. 8 11X38 11X38 11X38 11.5X38 11.5X38 11X38 11.5X38 11.5X38 12X38 12.5X38 11.5X38 12X38 12X38 12.5X38 13X38 11.5X38 11.5X38 12X38 12.5X38 13X38 12X38 12.5X38 13X38 13.5X38 14X38 12.5X38 13X38 13.5X38 14X38 15X38 1 ) 12 14 10 Area of Truss Rod (sq. in.). Diagonal Braces. 1 14 15 16 17 18 19 20 21 22 Bay (feet). Load sq. ft. Clbs.). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 7.1 100 50 75 100 50 75 100 8 5.6 8.6 10X3 10X4 10X5 10X3 10X4 10X6 10 6.4 8.2 10.1 10X3 10X4 10X6 10X4 10X5 10X7 12 7.1 9.4 11.6 10X4 10X5 10X7 10X4 10X6 10X8 14 7.9 10.2 13.1 10X4 10X6 10X8 10X5 10X7 10X10 16 8.6 11.6 14.6 10X5 10X7 10X9 10X6 10X8 10X11 ROOF TRUSSES. 231 DESCRIPTION OF TABLE XVIa. Like Table XVa, this table has computed values of the weights of various truss skeletons, of the type shown under Table XVI, per square foot of projected area for different bays and spans. Like uses may be made of this data, as stated under the description of Table XVa. TABLE XVIa. Weight of Truss Skeleton per Square Foot of Area Covered. 40-Foot Span. 1 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 g 26 23 21 19 18 32 28 26 26 25 38 36 33 31 30 23 21 20 18 17 30 26 24 22 21 34 32 28 30 30 10 12 14 16 Average . . 21 27 34 18 25 31 50-Foot Span. 8 37 32 29 28 25 44 40 36 36 34 50 45 45 41 40 34 35 26 24 23 39 37 32 30 29 47 42 40 37 37 10 12 14 16 Average 30 38 44 28 33 41 60-Foot Span. g 49 42 38 33 30 55 51 44 41 40 65 59 53 51 48 45 39 34 31 29 52 53 38 37 36 59 52 48 46 44 10 12 14 . . 16 Average 38 46 55 36 43 50 . 232 HANDBOOK ON REINFORCED CONCRETE. TABLE XVIa. Continued. 70-Foot Span. 1 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 75 63 60 57 52 8 10 62 56 51 45 43 73 68 60 55 52 85 74 69 64 60 56 48 43 39 39 64 60 52 49 47 12 14 16 . . Avftraffe . . 51 62 70 45 54 61 80- Foot Span. g 81 93 99 69 80 92 10 69 79 92 60 71 84 12 62 71 81 58 69 79 14 56 66 76 52 62 74 16 53 60 73 50 62 71 64 74 84 58 69 80 90-Foot Span. g 100 113 122 87 98 109 10 12 83 75 98 87 113 97 73 65 85 78 95 87 14 75 81 92 58 71 81 16 67 73 87 57 65 76 Average 80 90 102 68 79 90 100-Foot Span. 8 122 106 91 83 74 136 118 100 96 88 146 131 116 108 106 103 87 78 71 69 113 101 89 85 78 127 108 101 97 91 10 12 14 16 Average 95 108 121 82 93 105 ROOF TRUSSES. 233 8 FT. BAV CURVES -SHOWING 1 HE^RELATION OP COST TO SPAN, .For Type of Truss see -Table. 16 - 70 X" / 60 c x o y o x' ^ x 1 y / \* X x o >r ^x X LL, ,j 1 " y ^**. JW x* / / -M ^* t IS / S 3 / , ' ^ 14 -N^ 'TTj / o- 2lE X* x^ V 30 w X J^X -^ o X x* 1, ^x 2 Q. XXX x X ^^ x ^ i ^/ /J -2 ? 1 x^ X "^ x / > 20 ^ 5 * ** ^ / ^ z^ LL^ ' S[t ? ^ ^ > 1 Jf "* ' ^ ^/ ^ _.^. 40 ^ 5 / y ^ r-IQ II Jj ^; ? k 7 x^ _ 10 (J CT 35 ? y ' ^X X * s ^- 3 * , * 7 CL on ^^Tt^ - w 3 ^ \%X i / ^ ^^ o^- x c ^ / / o ?n > 40 o /u / ^ ' c . ~? ~? O y ^ ** /_ ^ ^ ^ / S > (/) ^> X S 30 "c .Q <^ Is , ^' ^ y 7 rt ^ ^ ^ X ^ Q- -M W ft X ' 2 ^ / w H ii ^_ "o ^ ^* p 10 o s / 1 x i_ ts r o ^ S X w td/ 30 ^ '\ X X X ' */ 1- ' ^' . #- on 3^ X ^ 20 UJ ^S ^s o s s Q s ir * 50 60 70 Span in Feet 80 90 100 ROOF TRUSSES. 235 12 FT. BAY CURVES SHOWING THE RELATION OF COST TO SPAN. (For Type of Truss see Table 16) ,' 50^; x c ^, o > ^ ^x in a - 70 > x * *0 x co x x X X ^ x >^ n r^ X S 30 i- C 60 < ^ ' X 1 J. r S x ^ / u_ <1> Y V- r I. ' 1 x* x ^ Q. ,- > 5 X ( ^ X / ^J o ^ HH ^ >/ *+- CO bU J x' " ^ ^ , ' ^ x 2 5 ^ / w ^f ^, ^ x* D^ X* / / ^ u S .x *^ X- / 0) o 1Q , to ^ ** ^ s x* in ^ u_ i-u tf ^x ^x ^ IU CO -^ X ,x c +j S x* X x ^ X* ft x- ^ c 3 X* pj to 10 -r O 4 5 6 D 70 8 9 z 10 Span in Feet 236 HANDBOOK ON REINFORCED CONCRETE. tso o o Q-30 20 10 14 FT. BAY CURVES SHOWING THE RELATION OF COST TO SPAN. (For Type of Truss see Table 16) ? ^ 0,0.. 50 40 30 Q. c> CO 20? 10" 40 50 60 70 Span in Feet 80 90 100 ROOF TRUSSES. 237 ;eo 50 10 16 FOOT BAY CURVES SHOWING THE RELATION OF COST TO SPAN For Type of truss. see'Table 16 i -f 40 40 50 60 70 Span in Feet, 90 100 238 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE XVII. The type of truss here shown is treated similarly to those shown under Tables XV and XVI, giving complete designs of all the members. The only peculiarity of this table over Table XVI is that, to reduce the roof span on account of widen- ing the bays, intermediate rafters carried on pur- lins, have been interposed as the sketch will clearly show. It has been figured to keep the same size for the purlins as for the intermediates. CENTER OF TRUSS J < i z " - , RAFTERS z -> 1 1 , TRUSS a PLAN TYPE 17 ELEVATION To do so the span of the purlin can be but one- half that of the intermediates for a given case, since there is a concentrated load on the former equal to the uniformly distributed load on the latter. To reduce the span of the purlins the amount just stated, purlin braces have been figured to be placed diagonally between the under- side of the purlins and their adjacent vertical tie members at the panel points. These braces serve as sway bracing to the lower chords of the main trusses as well. ROOF TRUSSES. 239 TABLE XVII. Sizes of Intermediates. Sizes of Purlins. 30-Foot Span. Bay (feet). Upper Chord. Reinforcement Sizes. 45 Slope. Load per sq. ft. (Ibs.). 30 Slope. Load per sq. ft. (Ibs.). 50 75 100 50 75 100 18 . . 4X14 4X16 4X16 5X16 5X18 5X18 3X14 3X14 4X16 4X16 5X16 5X16 20 40-Foot Span. 18 5X18 5X18 5X20 6X20 6X22 6X22 4X16 4X16 5X16 5X18 5X20 5X20 20 50-Foot Span. 18 20 6X20 6X22 6X24 7X24 7X26 7X28 5X16 5X18 5X20 6X20 6X22 6X22 60-Foot Span. 18 20 6X24 7X24 7X28 7X28 8X30 8X30 6X20 6X20 6X20 6X24 7X24 7X26 70-Foot Span. 18 7X28 8X28 8X30 8X32 9X34 9X34 6X24 6X24 7X26 7X26 8X28 8X28 20 . . 30-Foot Span. Bay (feet). Reinforce- ment Sizes, any slope. Lower Chord. Concrete Sizes. 45 Slope. Load per sq. ft. (Ibs.). 30 Slope. Load per sq. ft. (Ibs). 18 2") 2.5X12 2.5X12 50 75 100 50 75 100 4X12 5X12 5X12 6X12 6X12 7X12 6X12 7X12 7X12 8X12 9X12 9X12 40-Foot Span. 18 20 4X16 4X16 6X16 6X16 7X16 7X16 8X16 8X*16 7X16 8X16 9X16 9X16 10X16 11 X16 240 HANDBOOK ON REINFORCED CONCRETE. TABLE XVII. Continued. 50- Foot Span. Bay (feet). Reinforce- ment Sizes, any slope. Lower Chord. Concrete Sizes. 45 Slope. Load per sq. ft. (Ibs.). 30 Slope. Load per sq. ft. (Ibs.). 50 75 100 50 75 100 12X20 13X20 18 20 6X20 6X20 8X20 8X20 9X20 9X20 10X20 10X20 9X20 10X20 10X20 11 X20 60-Foot Span. 18 20 6X24 6X24 8X24 8X24 9X24 9X24 10X24 10X24 9X24 10X24 11X24 11 X24 12X24 13X24 70-Foot Span. 18 20 7X28 7X28 9X28 9X28 10X28 10X28 11X28 11X28 10X28 11X28 12X28 12X28 13X28 11X28 30-Foot Span. Bay (feet). Upper Chord. Concrete Sizes. 45 Slope. Load per sq. ft. (Ibs.). 30 Slope. Load per sq. ft. ()bs.). 50 75 100 50 75 100 10X16 10 5X16 18 20 6X14 6X16 7X16 8X16 8X18 9X18 6X14 6X14 8X16 8X16 40-Foot Span. 18 20 7X18 8X18 8X20 9X20 10X22 10X22 7.5X16 8X16 10X16 10X18 10.5X20 11X20 50- Foot Span. 18 20 9X20 9X22 9X24 10X24 11 X26 12X28 9.5X16 9.5X18 10X20 11.5X20 12.5X22 13X22 60-Foot Span. 18 9 X24 10 X28 13X30 10 5 X20 12X20 14X24 20 10X24 11 X28 13X30 11X20 12X24 14X26 70-Foot Span. 18 20 10X28 12X28 12X30 12X32 13X34 13X34 10X24 10.5X24 12.5X26 14X26 15X28 15.5X28 ROOF TRUSSES. 241 TABLE XVII. Continued. 30-Foot Span. Diagonal Braces. Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.) 50 75 10.0 50 75 100 18 20 4X6 5X5 5X7 6X6 6X8 7X7 6X6 7X6 7X7 8X7 9X9 9X8 40-Foot Span. 18 6X6 6X6 7X7 7X8 8X8 8X9 7X7 8X7 9X8 9X9 10X10 11X11 20 50-Foot Span. 18 8X7 8X7 9X8 9X9 10X10 10X11 9X10 10X10 10X12 11X12 12X13 13X13 20 60-Foot Span. 18 20 8X8 8X9 9X10 9X12 10X13 10X14 9X14 10X14 11X15 11X17 12X17 13X17 70-Foot Span. 18 20 9X10 9X12 10X12 10X12 11X14 11X15 10X15 11X16 12X17 12X19 13X20 14X20 30-Foot Span. Purlin Braces. 18 20 3X3 3X3 3X4 3X4 4X4 4X4 3X4 3X4 4X5 4X5 5X5 5X5 40-Foot Span. 18 .... 4X4 4X4 5X5 5X5 X6 X6 5X5 5X5 6X6 6X6 6X8 6X8 20 ., 50-Foot Span. 18 5X5 5X5 6X6 6X6 7X7 7X7 6X6 6X6 7X8 7X8 7X10 7X10 20 . . 60-Foot Span. 18 6X6 6X6 7X7 7X7 8X8 8X8 7X7 7X7 7X11 7X11 8X13 8X13 20 70-Foot Span. 18 20 7X7 7X7 8X9 8X9 9X11 9X11 8X9 8X9 8X13 8X13 9X55 9X15 242 HANDBOOK ON REINFORCED CONCRETE. TABLE XVII. Continued. 30-Foot Span. Truss Rods at Apex. 18 . . .18 .92 1.06 1.37 1.43 1.74 .93 1.06 1.36 1.50 1.77 1.94 20 40-Foot Span. 18 20 1.34 1.37 1.78 1.95 2.36 2.56 1.42 1.53 2.01 2.20 2.60 2.85 50-Foot Span. 18 20 2.04 2.18 2.73 3.00 3.56 4.04 2.44 2.70 3.22 3.66 4.06 4.56 6:-Foot Span. 18 20 . . 2.58 2.87 3.59 3.90 4.82 5.20 3.40 3.82 4.40 4.86 5.45 6.00 70-Foot Span. 18 3.46 4.02 4.66 6.07 5.95 6.33 4.24 4.94 5.74 6.34 7.19 7.79 20 30-Foot Span. Panel Point Rods. 18 .31 .33 .47 .48 .62 .63 .48 .49 .70 .74 .93 .95 20 40-Foot Span. 18 20 .60 .60 .87 .87 1.14 1.14 .87 .87 1.28 1.28 1.67 1.67 50-Foot Span. 18 20 1.02 1.02 1.45 1.45 1.88 1.88 1.44 1.44 2.08 2.08 2.73 2.73 60-Foot Span. 18 20 1.40 1.40 1.89 1.89 2.58 2.58 2.03 2.03 2.95 2.95 3.83 3.83 70-Foot Span. 18 20 .. 2.03 2.03 2.87 2.87 3.70 3.70 2.76 2.76 3.99 3.99 5.16 5.16 ROOF TRUSSES. 243 18-20 FT. BAYS CURVES SHOWING THE RELATION OF COST TO SPAN (For Type of Truss see Table 17) 4U / x x ^ x ^ x ^ ' c,C 1- , x- X 9 tj ^ ' x^ X X" "X 1 x- ^ ' x^ X- " ^ x- ^0 _, x- 1 j ^* XH *" Q. ^ x' b 3 x _^- ^* ' c O. /m 40 x (/) x ^ 4 o x s ^ X x J ^ .30 X 9." X x ^ CT ^ H x" ^ ' x (0 a^j x ,v X^ " x- x t- > / X" ' X 05 20 / XI ,1 X , 7 1 > -M x ^x PI ^ x' 05 s ^ x- n 1D -J X* x' 1 n x- ^ ^_, o O n Sf 30 40 50 60 Span in Feet 70 244 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE XVIIa. Under this table may be found values of the weights per square foot of projected area covered of the type of truss skeletons shown in the de- scriptions of Table XVII for different bays and spans. TABLE XVIIa. Weight of Truss Skeleton per Square Foot of Area Covered. 30-Foot Span. 1 2 3 4 5 1 7 Bay (feet). Load 45 Slope sq. ft. (11 )S.). 3( Loac ) Slope, sq. ft. (1 OS.). 50 75 100 50 75 100 18 20 16 16 20 21 26 26 15 15 21 19 33 31 40-Foot Span. 18 20 25 24 30 39 30 37 24 24 27 32 33 39 50-Foot Span. 18 20 36 33 42 42 52 56 31 31 36 38 45 45 60-Foot Span. 18 42 42 53 50 72 67 39 39 46 46 57 54 20 70-Foot Span. 18 54 59 67 70 81 74 47 46 60 58 72 68 20 KOOF TRUSSES. 245 DESCRIPTION OF TABLE XVII6. This table, with appended notes, gives complete designs of trusses of the types shown for the spans and bays indicated. The only change from Table XVII is that wider bays are treated. To keep the span of the roof slabs for this type of truss within bounds, two intermediates or rafters are used, carried by purlins, spanning from truss to truss and supported by purlin braces, molded CENTER OF TRUSS 0- < ^ ,, z ,, RAFTER z z " % ., 1 \ * ,, - M TRUSS a * diagonally between the rafter bearings and the adjacent vertical panel point members. The pur- lins have been kept the same size as the rafters, to give sufficient bearing for the braces. Whenever braces are longer than the limit stated under Table XVI, they should be cared for as there stated. This applies to all tables. 246 HANDBOOK ON REINFORCED CONCRETE. TABLE XVII6. 30-Foot Span. Bay (feet). Upper Chord. Concrete Sizes. 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 24 30 7X14 7X16 8X16 9.5X16 9X18 11 X18 7X14 7.5X14 9.5X16 10X16 11.5X16 13.5X16 40-Foot Span. 24 30 8X18 9.5X18 9X20 10.5X20 11.5X22 12X22 9X16 10X16 12 X 16 12.5X18 12.5X2Q 14X20 50-Foot Span. 24 30 10X20 10.5X22 10X24 11.5X24 12.5X26 15X28 11 X16 12X18 12X20 14.5X20 13.5X22 15.5X22 60-Foot Span. 24 10X24 11X28 15X30 12X20 14X20 16.5X24 30 11.5X24 13X28 15.5X30 13.5X20 15X24 17.5X26 70-Foot Span. 24 11X28 13.5X30 14.5X34 11.5X24 14.5X26 17.5X28 30 14X28 14X32 15X34 13X24 17.5X26 19X28 Lower Chord. Concrete Sizes. 30-Foot Span. 24 30 4.5X12 6.5X12 6X12 8X12 7.5X12 9.5X12 7.5X12 9.5X12 8.5X12 11X12 11X12 12X12 40-Foot Span. 24 7 X16 8X16 9 5 X16 8 X16 11 X16 12X16 30 .. 7X16 8.5X16 10X16 10X16 11.5X16 14.5X16 ROOF TRUSSES. 247 TABLE XVII6. Continued. 50- Foot Span. Bay (feet). Lower Chord. Concrete Sizes. 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 24 30 9X20 9X20 10X20 10.5X20 11.5X20 12X20 10X20 12X20 11.5X20 13.5X20 14X20 16.5X20 60-Foot Span. 24 9X24 10X24 11.5X24 10X24 13X24 14X24 30 9X24 10.5X24 12X24 12X24 13.5X24 16.5X24 70-Foot Span. 24 30 10X28 10X28 11X28 11.5X28 12.5X28 13X28 11X28 13X28 14X28 14.5X28 15X28 17.5X28 30-Foot Span. Diagonal Braces. 24 30 4.5X7 6.5X6 6X8 8X7 7.5X8 9X8 6X8 8X8 8X9 9X10 10X10 10X11 40-Foot Span. 24 7X7 7X8 8X8 8.5X9 9.5X9 10X11 8X9 9X10 10X10 11X11 11X12 13X13 30 50-Foot Span. 24 9X8 9X9 10X10 10X12 11X12 12X12 10X12 12X12 11.5X13 13.5X16 14X14 16X16 30 60-Foot Span. 24 9X10 9X12 10X13 10X15 11.5X14 12X16 10X16 12X17 13X17 13.5X20 14X19 16.5X20 30 70- Foot Span. 24 30 10X11 10X15 11X14 11.5X16 12.5X16 13X19 11X18 13X21 14X20 14.5X24 15X24 17.5X24 248 HANDBOOK ON REINFORCED CONCRETE. TABLE XVIIfc. Continued. 30-Foot Span. Purlin Braces. Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 0X0 24 3X4 4X4 5X5 4X4 5X6 30 4X4 4X5 5X5 4X5 5X6 6X7 40-Foot Span. 24 30 . . 4X5 5X5 5X6 6X6 6X7 6X8 5X6 6X6 6X8 7X8 8X8 8X9 50-Foot Span. 24 30 5X6 6X6 7X7 7X8 8X8 8X9 7X7 7X8 8X9 9X9 10X10 10X11 60-Foot Span. 24 30 6X7 7X7 8X8 8X9 9X10 10X10 8X8 8X9 10X10 11X11 11X12 12X12 70-Foot Span. 24 30 . . 8X8 9X9 10X10 10X11 10X12 9X10 11X12 10X10 11X12 12X13 13X14 14X14 NOTE. For reinforcement sizes of upper and lower chords; for sizes of purlins and intermediates or rafters, see Table XVII, noting that the 24 and 30-foot bays here correspond with the 18 and 20-foot bays there, respectively. For truss rod and panel point rod, sizes for 24 and 30-foot bays for this table, refer to Table XVII, and increase the values given for 18 and 20-foot bays for like spans, respec- tively, by one-third in the first case, and one-half in the second. ROOF TRUSSES. 249 24-30 FT, BAYS CURVES SHOWING TH'E RELATION OF COST TO SPAN (For Type of Truss see Table 17-2) ( 4U- x c X o X* X 0) |X x / ^ x^ Q. c crt / C ft. in ^ X n o 4U x > C/) ^ X tT> X x X to J / ^x ? V X , i X X cr ^ ^ / ,v X ^ v) 20 N ^ / ', k ^ I x X V , / / X" CL S 1 ^ 3 s S > ' c en ^ IU 5 . 00 o o 3 4 5 6 7 Span in Feet 250 HANDBOOK ON REINFORCED CONCRETE. TABLE XVII&!. Weight of Truss Skeleton per Square Foot of Area Covered 30-Foot Span 1 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 38 33 24 19 18 23 24 31 30 18 17 25 22 30 40-Foot Span. 24 29 27 36 34 45 40 28 27 31 35 37 42 30 50-Foot Span. 24 41 51 48 46 60 62 35 34 42 42 53 49 30 60-Foot Span. 24 48 46 61 56 82 74 45 43 53 51 65 60 30 70-Foot Span. 24 62 65 76 63 93 81 53 51 68 59 82 74 30 ROOF TRUSSES. 251 DESCRIPTION OF TABLE XVIIc. Table XVIIc, with notes, treats the design of truss here shown for the same bays as Tables XVII and XVII6, using similar construction details as CENTER OF TRUSS SPAN } there stated. The only change has been the add- ing of two more panel points, thereby obtaining satisfactory designs for longer spans. TABLE XVIIc. 45-Foot Span. Upper Chord. Concrete Sizes. 1 2 3 4 1 6 7 Bay (feet). Load i 45 Slope >er sq. ft. (Ibs.). Load ] 30 Slop( aer sq. ft. & "(Ibs.). 50 75 100 50 75 100 18 20 7X14 7X16 8.5X16 9 5 X16 9.5X18 11 X18 7.5X14 7 5 X14 10X16 10X16 12.5X16 13X16 24 8 5X14 9 X16 11 X18 9 X14 12X16 14 5X16 30 . 8 5X16 11 5X16 12 5 X18 9 5 X16 12 5X16 17 5X16 NOTE. For sizes of purlins, intermediates, purlin braces, diagonal braces, truss and panel point rods, and reinforce- ment sizes for upper and lower chords, see Table XVII, span 30 feet, and corresponding bays. 252 HANDBOOK ON REINFORCED CONCRETE. TABLE XVIIc. Continued. 60-Foot Span. 1 Upper Chord. Concrete Sizes. 2 3 * 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 18 20 8X18 9.5X18 9.5X18 11.5X18 9.5X20 10.5X20 11X20 12.5X20 12X22 12X22 14.5X22 15X22 9.5X16 10X16 11.5X16 13X16 12.5X16 12.5X18 16.5X16 16.5X18 13.5X20 14X20 16.5X20 18.5X20 24 30 NOTE. Corresponds with Table XVII, 40-foot span, for all sizes not given here. 75-Foot Span. 18 20 10.5X20 10.5X22 12X20 13X22 10.5X24 11.5X24 12X24 13X24 13X26 14.5X28 15.5X26 19X28 11.5X16 11.5X18 14X16 15.5X18 12.5X20 14.5X20 15.5X20 18X20 15.5X22 16.5X22 17.5X22 20.5X22 24 30 NOTE. Corresponds with 50-foot span, Table XVII, for all sizes not given here. 90-Foot Span. 18 20 10.5X24 11.5X24 12X24 14X24 11.5X28 13X28 13X28 16X28 15.5X30 15.5X30 19.5X30 20X30 13X20 13.5X20 15X20 18X20 15X20 15X24 18X20 19.5X24 17.5X24 17.5X26 21.5X24 22.5X26 24 30 105-Foot Span. 18 20 .... 11.5X28 14X28 13X28 17X28 14X30 14X32 17X30 17X32 15X34 15X34 18X34 18X34 12X24 13X24 15X24 16.5X24 16X26 17.5X26 19X26 22.5X26 18.5X28 20X28 23X28 26X28 24 30 .. NOTE. For weight per square foot of projected area covered see Tables XVII and XVII&, and add about 10 per cent. ROOF TRUSSES. TABLE XVIIc. Continued. 45-Foot Span. 253 Bay (feet). Lower Chord. Concrete Sizes. 8 9 10 11 12 13 45 Slope. Load per sq. ft. (Ibs.). 30 Slope. Load per sq. ft. (Ibs.). 50 75 100 50 75 100 11.5X12 11.5X12 15X12 17X12 18 5X12 6X12 7X12 8.5X12 6X12 7X12 8X12 11.5X12 7X12 9X12 10X12 13X12 7X12 9X12 10X12 13X12 9X12 11X12 11.5X12 15X12 20 . . 24 30 60-Foot Span. 18 7 X16 8 5 X16 10 X16 8 5 X16 11 5X16 13 X16 20 24 7X16 8 5 X16 8.5X16 10 X16 10X16 12 5 X16 10X16 10 X16 11.5X16 14 5 X16 14.5X16 16 X16 30 8.5X16 10.5X16 13X16 13X16 15.5X16 19.5X16 75- Foot Span. 18 9X20 9X20 10.5X20 10.5X20 10.5X20 10.5X20 12X20 12.5X20 12X20 12X20 14.5X20 15X20 10.5X20 12X20 12X20 15X20 12X20 13.5X20 14.5X20 17.5X20 15X20 16.5X20 18X20 21.5X20 20 24 30 .. 90-Foot Span. 18 20 9X24 9X24 10.5X24 10.5X24 12X24 12X24 10.5X24 12X24 13.5X24 13 5 X24 15X24 16 5X24 24 30 10.5X24 10.5X24 12X24 12.5X24 14.5X24 15X24 12X24 15X24 16.5X24 17.5X24 18X24 21.5X24 105-Foot Span. 18 10 X28 11.5X28 13X28 11 5X28 14 5X28 16 X2S 20 10X28 11.5X28 13X28 13X28 14.5X28 17.5X28 24 11.5X28 13X28 15.5X28 13X28 17.5X28 19X28 30 11.5X28 13.5X28 16X28 16X28 18.5X28 22.5X28 254 HANDBOOK ON REINFORCED CONCRETE. DESCRIPTION OF TABLE XVIId This table, with notes, contains data for design- ing trusses of the class shown. The only change over Table XVIIc is that longer spans have been treated by using eight panels. TABLE XVIW. 60-Foot Span. Sizes of Upper Chord. Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 9X14 f X14 11X14 12X14 75 100 18 20 8X14 8X16 10X14 10X16 10X16 11X16 13X16 14X16 11X16 13X18 13X18 14X18 12X16 12X16 15X16 16X16 15X16 16X16 18X16 22X16 24 30 80-Foot Span. 18 9X18 11X20 14X22 11 X16 15X16 16X20 20 11X18 12X20 14X22 12X16 15X18 17X20 24 12X18 13X20 17 X22 14 X16 19X16 20X20 30 14X18 13X20 18X22 16X16 20X18 23X20 ROOF TRUSSES. 255 TABLE XVIId. Continued. 100-Foot Span. Bay (feet). Sizes of Upper Chord. 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 18 20 24 12X20 12X22 14X20 15X22 12X24 13X24 14X24 16X24 15X26 17X28 18X26 23X28 14X16 14X18 18X16 19X18 15X20 17X20 19X20 23X20 19X22 20X22 21X22 25X22 30 120-Foot Span. 18 12 X24 13 X28 18X30 15 X20 18 X20 14 X24 20 24 13X24 14X24 15X28 15X28 18X30 23X30 16X20 18X20 18X24 22X20 21X26 24X24 30 .. 16X24 19X28 23X30 21X20 24X24 28X26 140-Foot Span. 18 13X28 16X30 17X34 14X24 18X26 22X28 20 14X28 16X32 17X34 15X24 21X26 23X28 24 15X28 19X30 20X34 17X24 22X26 25X28 30 20X28 20X32 21X34 20X24 28X26 30X28 60-Foot Span. Sizes of Lower Chord. Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 18 5.5X12 7.5X12 6.5X12 10.5X12 7.5X12 9.5X12 9.5X12 13.5X12 9.5X12 11.5X12 12.5X12 16.5X12 9.5X12 11.5X12 12.5X12 16.5X12 11.5X12 13.5X12 14.5X12 19.5X12 15.5X12 15.5X12 19.5X12 21.5X12 20 24 30 80- Foot Span. 18 8X16 10X16 12 X16 10 X16 14X16 16 X16 20 8 X16 10 X16 12 X16 12 X16 14 X16 18 X16 24 10X16 12X16 15X16 12X16 18X16 20X16 30 10X16 12X16 16X16 16X16 19X16 25X16 256 HANDBOOK ON REINFORCED CONCRETED TABLE XVIId Continued. 100-Foot Span. Bay ffeet). Sizes of Lower Chord. 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 14X20 16X20 17X20 21X20 100 18 10X20 10 X20 12X20 12X20 12X20 12X20 14X20 15X20 14X20 14X20 17X20 18X20 12X20 14X20 14X20 18X20 18X20 20X20 22X20 27X20 20 24 30 .. 120-Foot Span. 18 20 10X24 10X24 12X24 12X24 14X24 14X24 12X24 14X24 16X24 16X24 18X24 20X24 24 12X24 14X24 17X24 14X24 20X24 22X24 30 12X24 15X24 18X24 18X24 21X24 27X24 140-Foot Span. 18 11 X28 13X28 15 X28 13X28 17X28 19X28 20 24 11 X28 13X28 13X28 15 X28 15X28 18X28 15X28 15X28 17X28 21X28 21X28 23X28 30 13X28 16X28 19X28 19X28 22X28 28X28 NOTE. For all sizes not given here, refer to Tables XVII and XVII6 to corresponding bays, bearing in mind the following change in spans: A 60-foot span here corresponds with 30-foot span under Tables XVII and XVII6. A 80-foot span here corresponds with 40-foot span under Tables XVII and XVII6. A 100-foot span here corresponds with 50-foot span under Tables XVII and XVII6. A 120-foot span here corresponds with 60-foot span under Tables XVII and XVII6. A 140-foot span here corresponds with 70-foot span under Tables XVII and XVII6. For weight per square foot of projected area covered, see Tables XVII and XVIIfe, and add about 20 per cent. Ref- erence spans under Tables XVII and XVII6 are one-half those given here for obtaining corresponding weights. ROOF TRUSSES. 257 GENERAL DESCRIPTION OF TYPES OF TRUSSES "XVII TO XVIId." The upper chord in Tables XVII to XVIM have been figured for a uniform section through- out their length, and of a section to withstand the stress at the most stressed part, namely at the center between either of the two bearings and the first panel point from either bearing. In cases where the conditions will allow, it is very econom- ical to vary the section, either by tapering the width uniformly from the bearings to the apex, called "condition A," or by forming steps at each panel point, termed " condition B." The sizes were figured with this in view, as it may be noted that the depths are such as to withstand the bending moment due to the distributed loads for econom- ical widths and, to care for concentrated loads, these widths were increased, keeping the same depths as previously determined. If condition B is adopted, the sizes of sections in the different panels for the tables specified will be as follows: TABLES XVII AND XVII6. Panel. Concrete Sizes. First from apex. . Table 17-c. First from apex. . . Second from apex. Table 17-rf. First from apex... Second from apex. Third from apex. . Reinforcement size + f the difference between the reinforcement sec- tion and the concrete section given for upper chords. Call this dif- ference x. Reinforcement size'+ x. Reinforcement size + | x. Reinforcement size + f x.. Reinforcement size + f x. Reinforcement size + 5 x. 258 HANDBOOK ON REINFORCED CONCRETE. If condition A is adopted, sizes corresponding with the above should be used at the center of the different panels. DESCRIPTION OF TABLE XVIII. This table covers the complete design of a dif- ferent class of truss, shown by the sketch. In the design the purlins are kept near enough to- gether to carry the roof slabs. Two spacings of purlins have been used, namely 8-foot and 10-foot. The span headings of each set of bays clearly state which of the two panelings to use, or has been used. CENTER OF TRUSS t 1 OH WALL -BAY PURLIN PURLIN - ~ PURLIN 1 c ENTER DF TRU r SS HALF PLAN PLAN HALF ^^ 18 <& ZO FT. BAYS 24 A 30 FT. BAYS TYPE 18 The table, as drawn up, has limited the purlin span or the bay to 24 feet. It will be readily seen that this may be increased, using the same sizes of purlins* required for the bays given, by molding in braces diagonally between the purlins and the adjacent vertical tie members, so as to ROOF TRUSSES. 259 limit the purlin span proper to the values used in the table. Under "Diagonal Braces" it is noted that the sizes given are for the worst cases. Such cases, as may be seen, occur at the first panel point from the bearings where the braces make angles of 60 degrees when a 30- degree slope of truss is used, and 45 degrees when a 45- degree slope truss is used, with vertical through the panel points in question. Accordingly, the sizes of the other diagonals may be reduced in accordance with the relation that the sines of the angles between ver- ticals through such panel points and their cor- responding braces bear to the sine of 60 degrees for a 30-degree slope truss, and to the sine of 45 degrees for a 45-degree slope truss. Again, it may be discovered that the sizes figured are for 10-foot panels. If 8-foot panels are used instead, the values given may again be reduced 20 per cent. If the first reduction is adhered to, particular attention should be paid to excessively long, unsupported lengths, and the effect of eccentricity thereon as previously treated. This type of truss may be tapered uniformly, or offset in width over panel points as stated in the general description for Tables XVII to XVlId. 260 HANDBOOK ON REINFORCED CONCRETE. GENERAL DESCRIPTION OF " XVIII" TYPE TRUSS. In designing trusses of this type, the following formula is submitted in determining the total stress in pounds in any part or panel of the upper chord. Let k = a factor to be determined from the following plot. 6 = bay in feet, s = span in feet. w = total load per square foot including weight of roof proper. n = total number of panels into which the span is divided, either 8 or 10 feet. W = total stress in pounds in any panel. For 45-degree slope : 1st. Panel from apex,TF equals 1.5 ( k ' b - s - w ) x 1.42. 2d. Panel from apex,F equals 2.5 ( k ' b ' 8 - w ) x 1.42. 3d. Panel from apex,TF equals 3.5 3^Sl X 1.42. 4th. Panel from apex,F equals 4.5 ( k - b ' s ' w ) x 1.42. etc. For 30 degree slope use factor 2.0 instead of 1.42 as given for 45 degree slope. The above stress divided by 500 will give the area of concrete section required for concentrated loading in addition to the section which has to care for the distributed loading and which equals the section so called " Reinforcement Size in Table XVIII." ROOF TRUSSES. 261 1.90 TABLE 18 PLOTTO DETERMINE VALUES FOR FACTOR "K" IN FORMULA. 1.80 1.70 1.60 1.50 1.40 1.30 1.20 1.10 246 8 10 1.2 Total Number of Panels. 262 HANDBOOK ON REINFORCED CONCRETE. To determine the size of lower chord correspond- ing to any upper chord to care for concentrated loading, reduce the concrete section of the upper chord for concentrated loading by 29.5 per cent for 45 degree slopes, and by 13.5 per cent for 30 degree slopes. In addition to this section, increase the size by the section required to support this distributed load over a length equal to the panel, as stated earlier in the description. TABLE XVIII. 30-Foot Span (8-Foot Panels). 1 Upper Chord. Concrete Sizes. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 6.5X16 6.5X18 7.5X20 8X22 8X24 9X24 7X20 8.5X20 8.5X22 9.5X24 9.5X26 10.5X28 8.5X20 8.5X24 10X24 10X28 11X28 11X32 7X16 7X18 8X20 8.5X22 8.5X24 9.5X24 7.5X20 9X20 9X22 10X24 10X26 11X28 9.5X20 9.5X24 10.5X24 10.5X28 12X28 12X32 16 18 20 22 24 . . 40- Foot Span (10-Foot Panels). 14 7X18 7X20 8X22 8X24 9X24 9X28 8.5X20 8.5X22 9.5X24 9.5X28 10.5X28 10.5X30 9X22 10X24 10X26 11X28 11X32 12X32 7.5X18 7.5X20 8.5X20 8.5X24 9.5X24 9.5X28 9.5X20 9.5X22 10.5X22 11X26 11.5X28 11.5X30 10X24 11X22 11X26 12.5X28 12.5X32 13.5X32 16 18 20 22 24 ROOF TRUSSES. 263 TABLE XVIII. Continued. 50-Foot Span (8-Foot Panels.) 1 Upper Chord. Concrete Sizes. 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 16 18 20 22 7.5X16 7.5X18 8.5X20 9X22 9X24 10X24 8X20 9.5X20 9.5X22 10.5X24 11X26 12X28 10X20 10X24 11.5X24 11.5X28 12.5X28 12.5X32 8.5X16 8.5X18 9.5X20 10X22 10X24 11X24 9.5X20 11X20 11X22 12X24 12X26 13X28 11.5X20 11.5X24 13X24 13X28 14X28 14.5X32 24 60-Foot Span (10-Foot Panels). 14 8X18 10X20 10.5X32 9X18 11.5X20 12.5X22 16 18 8X20 9X22 11X20 11 X22 11.5X24 12X26 9X20 10X22 11.5X22 13X24 14X24 14X26 20 22 24 9X24 10.5X24 11.5X24 11X24 12.5X26 12.5X28 13X28 13X32 14.5X32 10.5X24 11.5X24 11.5X28 13X26 14X28 14X30 15X28 15X32 16.5X32 80-Foot Span (10-Foot Panels). 14 8X18 11.5X20 12.5X22 10.5X18 13.5X20 15X22 16 9X20 11.5X22 14X24 10.5X20 14X22 16X24 18 10X22 12.5X24 14X26 12X22 15X24 17X26 20 10 5X24 13X26 14X28 12X24 15X26 18X28 22 11.5X24 14X28 15X32 13.5X24 16X28 18X32 24 11.5X28 14X30 16.5X32 13X28 16.5X30 19.5X32 100 Foot Span (10 Foot Panels). 14 .... 10X18 13X20 14.5X22 12X18 16X20 17.5X22 16 10X20 13X22 15.5X24 12.5X20 16X22 15X24 18 . . 11.5X22 14.5X24 16X26 14X22 17X24 20X26 20 22 11.5X24 13X24 14.5X26 16X28 17X28 17X32 14X24 15.5X24 17.5X26 19X28 21X28 21X32 24 13X28 16X30 19X32 15.5X28 19X32 23X32 264 HANDBOOK ON REINFORCED CONCRETE. TABLE XVIII. Continued. 30-Foot Span (8-Foot Panels). Bay (feet). Lower Chord. Concrete Sizes. 8 9 10 11 12 13 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 4.5X8 5X8 4.5X10 5X10 5X10 5X12 5X10 5X12 5.5X12 6X12 6.5X12 6.5X12 5.5X12 6X12 6X12 6.5X12 7X12 7.5X12 5.5X10 6X10 5.5X12 6X12 6.5X12 7X12 6X12 6.5X12 6X14 6.5X14 7X14 7X16 6.5X14 7.5X14 8X14 8X16 8.5X16 9X16 16 18 20 22 24 40-Foot Span (10- Foot Panels). 14 4 5X10 5 5X12 6 X12 5 5X12 6 X14 8X16 16 18 5X10 5 5X10 6X12 6 5X12 6.5X12 7 X12 6X12 6 5X12 6.5X14 7 X14 8X16 8 5 X16 20 22 24 . . 5X12 5.5X12 6X12 6.5X12 7X12 7X12 7.5X12 7X14 7.5X14 7X12 6X14 6.5X14 7X16 8X16 8.5X16 9X16 9.5X16 10 X16 50- Foot Span (8-Foot Panels). 14 5X12 6X12 7X12 6.5X12 8X14 8.5X16 16 5.5X12 6.5X12 7X14 6X14 8X16 9.5X16 18 6X12 7X12 7.5X14 6.5X14 8.5X16 10X16 20 6 5X12 7 5X12 7 5X16 7X14 9X16 10X18 22 6.5X12 7X14 8X16 7X16 9.5X16 10.5X18 24 .. 7X12 7.5X14 8.5X16 8X16 10X16 10.5X20 ROOF TRUSSES. 265 TABLE XVIII. Continued. 60-Foot Span (10-Foot Panels). Bay (feet). Upper Chord. Concrete Sizes. 8 9 10 11 12 13 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 16 6.5X12 6.5X12 7X12 7X12 7X12 7.5X12 7X12 7.5X12 7X14 7.5X14 7.5X16 8X16 7.5X14 7.5X16 8X16 8.5X16 8.5X18 9.5X18 6.5X14 7X14 7X16 8X16 8.5X16 9X16 8.5X16 9X16 9.5X16 10X16 10X18 10.5X18 10X16 10X18 10.5X18 10.5X20 10.5X22 11 X24 18 20 22 24 80- Foot Span (10-Foot Panels). 14 6X14 7.5X14 8X16 8X16 8X20 8X2G 16 6.5X14 8X16 8X18 8.5X16 8X22 8.5x:s 18 7X14 8.5X16 8X20 8X18 8X24 9XCO 20 7.5X14 8X18 8X22 8X20 8X26 10X30 22 7X16 8.5X18 8X24 8.5X20 8X28 11X30 24 7.5X16 9X18 8X26 8X22 8X30 12X30 100-Foot Span (10-Foot Panels). 14 16 7X14 7 5X16 8.5X16 8X18 8X20 8X22 8X18 8X20 8X24 8X26 9X30 10X30 18 20 8X16 8.5X16 8X20 8X22 8X26 8X28 8X22 8X24 8X30 10X30 12X30 13X30 22 24 8X18 8X18 8X24 8X26 8.5X28 9X28 8X26 8.5X26 11X30 12X30 14X30 15X30 266 HANDBOOK ON REINFORCED CONCRETE. TABLE XVIII. Continued. Reinforcement Sizes for Upper Chord. 8-Foot Panels. 10-Foot Panels. Bay (feet). Load sq. ft. (Ibs.) Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 5X16 5X20 6X20 5X18 6X20 6X22 16 5X18 6X20 6X24 5X20 6X22 7X24 18 6X20 6X22 7X24 6X22 7X24 7X26 20 6X22 7X24 7X28 6X24 7X26 8X28 22 6X24 7X26 8X28 7X24 8X28 8X32 24 7X24 8X28 8X32 7X28 8X30 9X32 Diagonal Braces (Figured for Worst Case). Sizes in Sq. In. 14 16 45 Slope (10-Foot Panels). 30 Slope (10-Foot Panels). 1 15 17 19 21 23 20 23 26 29 32 35 26 30 34 38 42 46 19 21.5 24 26.5 29.0 31.5 28 32 36 40 44 48 38 43 48 53 58 63 18 20 22 24 Truss Rod Sizes at Panel Points. (Sq. In.) 14 16 18 20 8-Foot Panels. 10-Foot Panels. .56 .64 .72 .80 .88 .96 .84 .96 1.08 1.20 1.32 1.44 1.12 1.28 1.44 1.60 1.76 1.92 .70 .80 .90 1.00 1.10 1.20 1.05 1.20 1.35 1.50 1.65 1.80 1.40 1.60 1.80 2.00 2.20 2.40 22 .... 24 For truss rod sizes at apex, double the values given above. ROOF TRUSSES. 267 EXPLANATORY NOTE. For the sizes of purlins and reinforcement for this type of truss, see Table II, Part III, for the corresponding spans and loading. AVERAGE OF BAYS 14-24 FT. CURVES SHOWING THE RELATION OF COST TO SPAN (For Type of Truss see Table 18) x-s 30 20 10 o Ll_ 10 ^ 6- o 1 ^. nO ^ S " u- * "^ Q 1 t^ x^ x f** ** o i <;n " ^ "r ** * ' o 50 I i e r :J ;2^* 20 o m **'*<*'* X i $ J 09 DRE) ^ = t- ^4.n ^ w -50^^ Q.-cj,_j32- - e-= " 10 ^ 42 : 6 v ? **- ^ c- Q ? c 30 - - - -5 > ^ S ^^ x -^ J U x , o p | , . ' 1 8" 0) w on _ Q. iX L nS. o y/ ^ & * tf - x S 2 ? ! c ^ ^ P; - ' * 2l (45! S f >b . trt - -= * fl ''\ 5( UBS o 10- T' ^J m -- 30 40 50 60 70 80 90 100 Span in Feet. 270 HANDBOOK ON REINFORCED CONCRETE. beams to carry these distributed loads for the required spans may be found. Again, by referring this latter size to Table I, Part III, the required reinforcement may be found. TABLE XVIIIa. Weight of Truss Skeleton per sq. ft. of- Area Covered. 30-Foot Span (8-Foot Panels). 1 2 | 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 16 18 14 14 15.5 16.5 16.5 17. 19.5 20.5 20.5 21.8 21.3 22.5 24 25 25.5 26.3 26.4 28.5 14.3 14.2 15.2 15.6 15.5 15.7 18.5 19.6 19.2 20.1 20.0 21.4 24.4 24.5 25. 25.7 26.3 27.2 20 22 24 Average 15.6 20.9 25.9 15.1 19.8 26.6 40-Foot Span (10-Foot Panels). 14 17.6 24.5 28.3 17.7 23.8 28.8 16 17.2 23.4 29.1 16.9 23.0 30.0 18 18.4 24.5 28.2 16.6 22.3 28.6 20 18.3 25.8 27.7 18.5 24.3 30.5 22 18.6 25.1 30.2 17.3 24.9 29.9 24 19.5 24.4 30.2 18.6 24.6 30.5 Average 18.3 24.6 28.9 17.4 23.8 29.7 50- Foot Span (8- Foot Panels). 14 18.3 25.1 29.9 18.2 26.0 31.6 16 18.1 25.2 31.0 18.3 26.3 32.6 18 19 4 25 31 3 19 25 6 32 20 19.9 26.4 32.6 19.3 26.2 33.1 22 19.4 26.7 32.4 19.4 24.9 32.2 24 19.7 27.2 33.4 19.8 26.6 34.3 Average 19.1 26.1 31.7 19.0 25.9 32.6 ROOF TRUSSES. 271 TABLE XVIIIa. Continued. 60- Foot Span (10-Foot Panels). 1 2 3 4 5 6 7 Bay (feet). 45 Slope. Load sq. ft. (Ibs.). 30 Slope. Load sq. ft. (Ibs.). 50 75 100 50 75 100 14 22.7 21.6 22.8 22.1 22.9 23.6 30.2 28.8 30.0 29.3 32.0 31.0 35.9 36.7 36.4 37.5 38.8 39.4 22.4 21.2 22.9 23.4 23.0 23.8 32.2 30.9 31.6 30.7 31.9 31.1 38.7 39.5 37.9 38.8 39.8 40.0 16 18 20 22 24 Average 22.6 30.2 37.5 22.8 31.4 39.1 80-Foot Span (10-Foot Panels). 14 16 24.0 24 9 35.0 35 9 43.5 45 3 27.3 26 8 38.0 37 3 47.4 48 18 20 22 26.1 26.7 26 1 36.7 36.1 37 44.0 42.5 46 27.8 27.4 28 4 38.0 37.0 38 48.7 49.5 50 7 24 27.4 36.5 46.5 27.6 37.9 50.5 Average 25.9 36.2 44.6 27.6 37.7 49.1 100-Foot Span (10-Foot Panels). 14 16 29 3 29 4 42.5 40 4 51.8 49 5 31.5 31 5 45.0 43 9 57.8 58 18 20 31.8 30.7 42.5 41 .6 52.4 52 8 32.8 32 3 44.4 46 2 60.0 60 22 24 30.8 31.6 43.5 43 54.0 54 2 32.4 33 4 49.0 49 2 61.0 61 Average 30.6 42.6 54.1 32.3 46.3 59.6 JUST PUBLISHED. 8vo, Cloth, Illustrated, 365 pages. Price $3.00 net. Earth and Rock Excavation A PRACTICAL TREATISE. BY CHARLES PRELINI, C.E., AUTHOR OF "TUNNELINC," With Tables, and many Diagrams and Engravings. CONTENTS Preface, Introduction. Chapter I. Graphical Representation of Earthwork ; Plans and Profiles. II Methods of Calculating Quantities and Cost of Earthwork. III. Cuts and Fills; Borrow-pits and Spoil-banks. IV. Classification of Materials; Rock Excavations witho.it Blasting. V. Excavation of Rock by Blasting; the Drilling of the Holes. VI. Rock Excavation by Blasting; Explosives and their Transportation and Storage. VII. Rock Excavation by Blasting; Fuses, Firing and Blasting. VIII. Earth Excavation; Hand-tools, Machine Excavation. IX. Earth Excavation ; Continuous Digging-machines. X. Earth Excavation ; Inter- mittent Digging-machines. XI. Methods of Hauling Excavated Materials on Level Roads. XII. Hauling Excavated Materials on Horizontal Roads. XIII. Method of Hauling Excavated Materials on Inclined Roads. XIV. Vertical Haul- ing or Hoisting of Excavated Materials. XV. Transporting Excavated Materials by Aerialways. XVI. Transporting Excavated Materials by Cableways, XVII. Transporting Excavated Materials by Telpherage. XVIII. Chains, Ropes, Buckets, Engines, and Motive Power. XIX. Animal, and Mechanical Labor. XX-XXI. The Direction of Excavation Work. XXII. Shrinkage of Earth ; Cost of Earthwork. XXIII. Examples of Large Canal Excavation Works. Index. D. VAN NOSTRAND COMPANY, Publishers and Booksellers, 23 Murray and 27 Warren Sts. NEW YORK. TH I RD EDITION, REVISED. 8vo. Cloth, 31 I Pages, 150 Illustrations. - - Price, S3.OO. TUNNELING: An Exhaustive Treatise, containing many Working Drawings and Figures. BY CHAS. PRELINI, C. E. WITH ADDITIO- S BY CHARLES 5. HILL, C. E. Associate Editor "Engineering News." INTRODUCTION CHAP. III. IV. V. VI. VII. VIII. IX-XI. XII. XIII-XIV. XV. XVI. XVII. XV1II-XXI. XXII. XXIII. XXIV. XXV. Index. CONTENTS. The Historical Development of Tunnel Building. Preliminary Considerations, Choice Between a Tunnel and an Open Cut. Method and Purpose of Geological Surveys. Methods of Determining the Center Line and Forms and Dimen- sions of Cross-Section. Excavating Machines and Rock Drills ; Explosives and Blasting. General Methods of Excavation; Shafts : Classification of Tunnels. Methods of Timbering or Strutting Tunnels. Methods of Hauling in Tunnels. Types of Centers and Molds Employed in Constructing Tunnel Lin- ings of Masonry. Methods of Lining Tunnels. Tunnels Through Hard Rock; General Discussion; Excavation by Drifts. Mont Cenis Tunnel: The Simplon Tunnel: St. Gothard Tunnel: Busk Tunnel. Representative Mechanical Installations for Tunnel Work. Excavating Tunnels Through Soft Ground; General Discussion; The Belgian Method: The German Method: Baltimore Belt Line Tunnel. The Full Section Method of Tunneling; English Method; Austrian Method. Special Treacherous Ground Method; Italian Methodj Quicksand Tunneling; Pilot Method. Open-Cut Tunneling Methods; Tunnels under City Streets. Bos- ton Subway, and New York Rapid Transit. Submarine Tunneling: General Discussion: The Severn Tunnel: The East River Gas Tunnel ; The Van Buren Street Tunnel, Chicago The Milwaukee Water- Works Tunnel : The Shield System. Accidents and Repairs in Tunneling during and after Construction. Relieving Timber-Lined Tunnels with Masonry. Ventilating and Lighting of Tunnels during Construction. Cost of Tunnel Excavation, and the Time required for the work. D. VAN IMOSTRAIMD COMPANY, Publishers and Booksellers, 23 Murray 23 Murray Street and 27 Warren Street, New York JUST PUBLISHED. 8vo. Cloth, 174 Pages, Illustrated, Price $2.00, Net, THE STATICALLY-INDETEEHINATE STRESSES IN FRAMES COMMONLY USED FOR BRIDGES BY ISAM! HIROI, C. E., Dr. Eg., Professor of Civil Engineering in the College of Engineering Tokyo Imperial University. EXTRACT FROM PREFACE. The present work is the outgrowth of a series of lectures given to the students of CiviJ Engineering in the Tokyo Imperial Univer- sity. It contains the solution of those problems most commonly met in the practice of a bridge engineer, the aim of the author being to save time and labor of those intent on a more rational design of the class of the structures treated, than is generally followed, by furnish- ing them with necessary formulas for which rough approximation or even guess-work frequently forms a substitute. INTRODUCTORY CHAP.-Qeneral Principles. CHAP. I. Trussed Beams. CHAP. II. Viaduct Bents. CHAP. III. Continuous Girders. CHAP. IV. Arches with Two Hinges. CHAP. V. Arches without Hinges. CHAP. VI. Suspension Bridges. Trusses with Redundant Members. CHAP. VII. Secondary Stresses due to rigid= ity of Joints. D. VAN NOSTRAND COMPANY, Publishers and Booksellers, 23 Mwrray and 27 Warren Streets, - - NEW YORK. JUST PUBLISHED. 4to, 7% x 11, Cloth, 530 pages, 511 illustrations. Price $7.00 net. Reinforced Concrete BY CHARLES F. MARSH Assoc. M. Inst. C. B., Assoc. M. Inst. M. E. With many Tables, Diagrams and Engravings CONTENTS: General View of the Subject. Systems Employed. Ma- terials. Practical Construction. Experimental Re- search and Data Deduced Therefrom. Calcu- lations. Some Structures which have been Erected in Reinforced Concrete. Appendix. INTRODUCTION In the following pages the author has endeavoured to place before engineers, architects, and others, a complete treatment of, the subject of reinforced concrete, in so far as is possible at the present day. All the subject matter has been so arranged as to facilitate reference as much as possible, and the several systems used up to the present have been placed in alphabetical order, so that any particular one may be readily found when desired. It is believed that the part relating to the calculations, covers all forms of construction in as concise and clear a manner as possible. The formulae for slabs and beams, although giving some- what smaller dimensions than those recommended by M. Christophe in Le Beton Arme (a standard French work on the subject), are still well on the side of safety, and it is hoped that the tables and diagrams may be of use in saving the labour necessary in making the requisite calculations. The subject of arches has been dealt with in as condensed a. form as possible, compatible with a clear demonstration of the methods adopted for locating the pressure curve. The graphical method -for finding the stresses to be resisted in domed coverings, is believed to be entirely new and greatly simplifies the treatment of these structures. It has been considered advisable to illustrate the book Very fully, in order that all the subject matter,where possible, may be rendered clearer, and that a true idea may be formed of the remarkable adaptability of reinforced concrete for constructural purposes. D. VAN NOSTRAND COMPANY Publishers and Booksellers *3 HURRAY AND 37 WARREN STREETS, NEW YORK. FOURTH EDITION, REVISED AND ENLARGED. 16mo. Cloth, 212 Pages, Illustrated. Price 50 cents, THEORY OF STEEL = CONCRETE ARCHES AND OF VAULTED STRUCTURES BY WILLIAM CAIN, Member Am. Soc. C. B., Prof, of Mathematics, University of North Carolina. CONTENTS. CHAP, i. Arches of Variable Section under Vertical Loads. In- troductory Formulas for unit stress for a steel-concrete arch Con- ditions for equilibrium for arch with no hinges Deflection at the crown --Division of the neutral axis Complete graphical treatment for a steel-concrete arch with partial load Arch loaded with its own weight Demonstration Unit stresses, etc. Temperature stresses- Properties of Concrete Change of span Arch hinged at end only- Abutments Spandrel resistance for Voussoir arches Methods of failure of arches Height of surcharge for equilibrium. CHAP. II. Culverts and Tunnel Arches. Formulas for passing a line of resistance through three given points Application to cul- vertsTunnel arches The ellipse, the proper form for a tunnel arch. CHAP. III. Groined and Cloistered Arches. Groined arch- Evaluation of thrusts Formulas for volume Arch of groin and abutment Cloistered arch. CHAP. IV. Domes of Masonry. Forces acting Example of a dome with backing Formulas for volume Dome of two shells with lantern Tensions in iron bands Thrusts Dome without lantern Suggestion Reinforced concrete on metal dome Open spherical dome with lantern Spherical dome Analytical theory Conical dome Graphical treatment Conical dome Analytical theory. APPENDIX. Resume of operations for arch. D. VAN NOSTRAND COMPANY, Publishers and Booksellers, 23 Murray and 27 WajgE*fca. NEW YORK. RETURN TO the circulation desk of any University of California Library or to the NORTHERN REGIONAL LIBRARY FACILITY Bldg. 400, Richmond Field Station University of California Richmond, CA 94804-4698 ALL BOOKS MAY BE RECALLED AFTER 7 DAYS 2-month loans may be renewed by calling (510)642-6753 1-year loans may be recharged by bringing books to NRLF Renewals and recharges may be made 4 days prior to due date. DUE AS STAMPED BELOW DEC 15 1999 12,000(11/95) ! 101