KAHN SYSTEM Trussed G)ncrete Steel Co. FRANKLIN INSTITUTE LIBRARY PHILADELPHIA Class . Accession- REFERENCE GIVEN BY Digitized by the Internet Archive in 2015 https://archive.org/details/kahnsystemstandaOOtrus KAHN SYSTEM STANDARDS A Hand Book OF Practical Calculation AND Application of Reinforced Concrete ' s ' ^ 3 J ^ COMPILED AND PUBLISHED BY ENGINEERING DEPARTMENT TRUSSED CONCRETE STEEL COMPANY LONDON DETROIT TORONTO 190 7 Copyrighted 1907 by Trussed Concrete Steel Co. Price, $1.50 postpaid Edited and Published by li^ngineering Department Trussed Concrete Steel Co. Form No. 193-7-30-07 2M-Mack Ptg. House THE GETH' CEMTeB LIBRARY PREFACE The rapid growth of Reinforced Concrete Construction makes necessary a Hand Book on Design, similar to those in use for the ordinary classes of building material. The only data which has been available to the engineer or architect has been the scientific text book, in which the informa- tion presented is so involved as to be of little practical value to thg_busyJes^igner. Otherwise he has had to resort to a series of empirical formulae, or tables, which may only be justified by a few isolated tests. The object of this Hand Book is to present to the designer tables and information in such form as to be immediately available for use in actual designs, and at the same time to have these tables founded on scientific formulae approved by our very best engineer- ing practice. The data as presented is the result of a large amount of painstaking labor, and of most extensive experience in reinforced concrete, covering the design and construction of over a thousand structures, including buildings, bridges, tunnels, reservoirs, etc. The work as presented deals mainly with the Kahn Trussed Bar. The Kahn System of Reinforced Concrete, however, includes in its application two other types of reinforcement. The Kahn Rib Metal consists of a series of straight bars or ribs connected laterally by light cross members rigidly attached to the ribs. The material is made in sheets, consisting of nine ribs, and is supplied in meshes from 2 to 8 inches, varying by inches. This metal is manufactured of the highest grade medium steel. The Cup-Bar is a specially rolled section with cross ribs scientifically designed so that the bar cannot slip in the concrete. TRUSSED CONCRETE STEEL COMPANY It has positive advantages over all other deformed bars in that the fibres of the steel are not distorted in the process of rolling. The Cup-Bar develops a greater strength than any other bar having the same net area, owing to the fact that in the process of manufacture it has been rolled, or worked, in such a manner as to develop a more uniform and more compact fibre structure. This extra rolling increases the elastic limit and ultimate strength of the bar considerably but does not in the least affect its ductihty. It is manufactured in sizes from ^/g to ij^ inches, varying by of an inch, the area of the bar being equivalent to the square bar of the same designation. The Trussed Concrete Steel Co. publishes special literature descriptive of these two products, which will be gladly furnished to those interested. All of these three types of reinforcement are carried constantly in stock at our various shops, ready for immediate shipment. Trussed Concrete vSteel Co., Detroit, Mich. Trussed Concrete Steel Co., Ltd., London, Eng. Trussed Concrete Steel Co., of Canada, Ltd., Toronto, Can. 6 REINFORCED CONCRETE What It Is HOW FIRST USED When, in the late 60 's, Monier, a French gardener, began making flower pots, boxes and small water tanks out of concrete and imbedded wire in the material to increase its strength and decrease its weight and bulk, he little thought that forty years later the principle which he used and upon which he was granted a patent, would be used throughout the entire world in the erection of millions u})on millions of dollars worth of con- struction work. There has been no class of structures, no line of the building trades which has not been affected by reinforced concrete, and many of them have been revolutionized. The story of the development and growth of the use of this form of con- struction has filled volumes, while here it can only be touched upon briefly. Concrete is a rock-like substance formed by the mixture of cement, sand, stone and water. It is the result of the cementing together, through chemical action between the cement and water, of various sizes of stone so. proportioned with the other material that all voids within the resulting mass are filled. Reinforced concrete is exactly what the name implies. It is concrete in which steel has been imbedded to CONCRETE DEFINED REIN- FORCED CONCRETE DEFINED p^ive additional streno^th and elasticitv. Plain concrete when used in the form of pillars and posts, is capable of carrying heavy direct loads through its great compressive strength. But when it is subjected to a direct pull, that is, to tensile strains, it is weak. I No reinforcement. Small load — Sudden failure — like chalk. For example, if a plain concrete beam is subjected to a load it will break apart at the bottom just as a piece of chalk would under KAHN SYSTEM OF REINFORCED CONCRETE like conditions, being unable to resist the tension in the lower portion of the beam. In order to overcome this, reinforcing steel is used to give proper tensile strength and elasticity. The concrete in the top of the beam takes care of the compression. A properly rein- forced concrete beam has, therefore, the strength of stone in re- sisting compression united with the tension resisting power of steel. When a beam is loaded and supported at the two ends, it will have a tendency to deflect. To illustrate, assume that a beam is made up of a series of flat plates, or, in other words, like a pad of paper or a book, the difference being that in the pad of paper the leaves are not in any way connected to each other, whereas in a beam the adhesion of the various particles of the material ties the imaginary plates together. Now, when the supposed beam starts to deflect, one of two things will happen. Either the various plates separate, as when a book or pad of paper is bent, and in separating slide by one another: or, if the plates are held together and sliding is prevented, the particles in the upper plates compress and in the lower plates elongate. It is thus seen that in addition to the compression and tensile stresses in the top and bottom of the beam, there are internal stresses of equal importance against which the concrete must also be properly reinforced. To accomplish this it is absolutely neces- sary that there shall be diagonal steel reinforcement extending well up into the mass of the concrete. This latter reinforcement must be rigidly attached to the steel in the bottom of the beam in order that all the steel may act together with the concrete in forming a properly reinforced beam. The Kahn Trussed Bar with its rigidly attached diagonals is, therefore, the ideal reinforcement. THE KAHN TRUSSED BAR The Kahn Trussed Bar is made of a special grade of medium open-hearth steel with an elastic limit up to 42,000 KAHN pounds and an ultimate tensile strength of 70,000 BAR pounds. The cross section is diamond shaped with DESCRIBED two horizontal flanges or wings, projecting at diametrically opposite corners. These wing por- tions are sheared up at intervals and bent so as to make an angle of 45 degrees with the main portion of the bar. When the Kahn Trussed Bar leaves the factory, it looks like the following: Kahn Trussed Bar — with alternating diagonals. 8 TRUSSED CONCRETE STEEL COMPANY GENERAL HISTORY OF THE METHOD OF REINFORCING CONCRETE A brief review of the general types of reinforcement used in the past, will make clear why they have been either abandoned or revised and why the Kahn Trussed Bar is now considered the perfect reinjorcemeiit, incorporating all the advantages of the old forms with the more modern improvements and refinements. It was originally thought that merely imbedding steel bars in the bottom of a concrete beam to take the tension HORI- was sufficient. This is true in some rare instances. ZONTAL While enough steel may be placed in the bottom ONLY of a beam, which, if pulled in a testing machine, could resist the desired amount of tension, it must be remembered that it is necessary to get the stress into the steel from the concrete, and there must be some positive means of doing Horizontal reinforcement only. Method of failure when tested to destruction. Light load. Sudden failure caused by ends of reinforcement slipping and horizontal shear diagonal cracks in concrete. this. The old idea was to depend upon adhesion. This was soon found to be inadequate and unreliable, as the plain bars would slip. In order to overcome this difficulty deformed bars of various types, such as twisted bars and bars with corrugations and lugs, were used to increase the friction between the steel and the concrete. When such bars were laid in the bottom of a concrete beam they did not slip in the concrete but the concrete would shear along a plane immediately above the bar. For this reason the strength of the bar could not be developed, and the beam was practically no stronger than if reinforced with plain bars. 9 KAHN SYSTEM OF REINFORCED CONCRETE Numerous tests were made on the older form of horizontal reinforcement and it was universally observed that LOOSE when a beam was tested to destruction, it failed bv STIRRUP the breaking of the concrete along lines beginning at the reinforcement at the ends and extending diagonally upwards towards the center of the beam. The cause was not known, but it was assumed that there were stresses in the concrete, and therefore loose vertical stirrups were })laced in the Horizontal reinforcement and loose stirrups. Method of failure when tested to destruction. Medium load. Sudden failure due to slipping of horizontal rods Shear of concrete on horizontal plane above bars but no diagonal cracks. mass of the beam to resist these stresses. When beams were tested to destruction it was found that the main bar slipped and that the beam failed by shearing along a horizontal plane connecting the steel with the concrete. It was thus demonstrated that a positive connection must be made between the main steel bar and the members taking the web stresses. This led to the invention of the Kahn Trussed Bar. In this patented bar the members in the vertical plane, being made from a part of the main tension member, transmit stress from the body of the beam directly to the main steel bar. This is the ideal reinforcement. When beams, which have been reinforced with the Kahn Trussed Bar, are tested to destruction they fail by pulling the steel in two at the center, showing that there is RIGIDLY CONNECT- ED WEB MEMBERS ■j U ( i i i - Kahn reinforcement. Method of failure when tested to destruction. Max- imum load. Very gradual and ideal failure. Steel stretching in center. absolutely no unknown weakness in the beam and that the full pro- portion of the strength of all the materials is developed. It is, 10 TRUSSED CONCRETE STEEL COMPANY therefore, the only means of reinforcing concrete that makes it possible to obtain the fnll value of the materials used. This feature is clearly shown by tests made by the French government, report of which was published in "Concrete and Constructional Engineering," of London. In these tests the beams, reinforced according to the Kahn System, carried 21 per cent, in excess of the beams reinforced with a series of stirrups and hori- zontal rods, which had hitherto been considered the best means of reinforcement. (The Trussed Concrete Steel Co. will be glad to supply a copy of this test in detail to anyone desiring same,) Note from the accompanying diagrams how, when a beam reinforced with the Kahn Trussed Bar, is loaded, the stresses in the beam are resisted either by an arch or a truss. INTERNAL In the arch each individual stress is resisted by a STRESS positive abutment in the form of a diagonal. In ACTION the truss the steel diagonals form the tension web members and the compression web members are supplied by the concrete. The advantageous feature in this is that the tension in the diagonals is brought into the main tension Truss action in beam reinforced with Kahn Trussed Bars. Note the action is that of a complete Pratt truss. No tendency to slip or slide. 1 A \ i I J// / '/ / / \ V \ y 1 Truss action in beam with horizontal reinforcement and stirrups. Note the unbalanced horizontal component of the inclined stress and the tendency of the stirrups to slip along the horizontal reinforcem.ent. Arch action in beam reinforced with Kahn Trussed Bars. Note the perfect abutment for the inclined stresses. Perfectly rigid and no possibility of slipping. 11 KAHN SYSTEM OF REINFORCED CONCRETE Arch action in beam with horizontal reinforcement and stirrups. Note the unbalanced horizontal stress. Stirrups slip along the horizontal reinforcement, which, therefore, cannot be developed. Beam with horizontal reinforcement only. Note arch action. Reinforcement furnishes no abutment for the inclined stresses, and will slip. member directly because tension member and diagonals are one. The thrust of the arch or the pull of the web member of the truss is resisted by the diagonal and main bar combined. It is just as essential to have rigid attachment of the diagonal members in a concrete beam as it is to have strong, close fitting rivets between the lower chord and web plate of a steel plate girder. That the calculated strength of a beam may be developed it is necessary that the materials be distributed in CERTAINTY such a manner that the ultimate strength of each OF CAL- would be attained should the beam be tested to CULATION destruction. This anticipates the prevention of slipping of the reinforcing bars and the failure by tension in the concrete. The Kahn Trussed Bar cannot slip, and the concrete is reinforced against tension by the rigidly at- tached diagonals. It is clear, then, that beams reinforced with this bar will develop the ultimate strength of the materials, and since these values are known the materials can be so propor- tioned that each will be fully developed. In other words, the calculation of a beam reinforced with the Kahn Trussed Bar is absolutely certain and exact. It is a well-known fact that concrete, when subjected to intense heat, of 1500 degrees Fahrenheit or over, for a FIRE- continuous period will loose a part of its water of PROOF- crystallization. This condition will obtain for NESS about one inch from the surface of the concrete in case of an extreme fire. Suppose the reinforcement is placed about one inch from the bottom of the beam. Incase of a 12 TRUSSED CONCRETE STEEL COMPANY very extreme fire, the lower inch of concrete will be practically ruined and its adhesion or immediate connection with a plain bar in the bottom of the beam will be completely destroyed. With the Kahn Bar, the large diagonals extend well up into the concrete beam and the effect of fire can almost be neglected, as the connection between the bar and its diagonals is still intact. (See Capt. SewelFs Report in Transactions of the Am. Soc. C. E.) This is perhaps one of the greatest features of the Kahn System of Reinforcement. A building erected on this plan is as good after a fire as before, while a building reinforced with plain bars is apt to be a complete ruin. NOTES ON DESIGN IN GENERAL The introduction of reinforced concrete into the field of building materials, has placed at the disposal of the designer and builder, a construction for which he has long been waiting. The material is plastic and monolithic and can be molded into any form to suit the highest imagination or ingenuity of the designer. It is no longer necessary to build with blocks and fixed units. Each particular structure is capable of an infinite variety of arrange- ments and combinations. The design then of a structure of maximum utility and economy requires the closest study and investigation. The primary consideration in any design is that the finished structure shall serve the purpose for which it is DESIGN built in the most adequate manner. This will FOR determine to a large extent the location of the UTILITY columns, the general framing and type of the floor construction, depth of girders, size of columns, etc. The design of a warehouse built to carry heavy loadings will vary, accordingly, from that of a residence. In the former, girders and beams placed close together might be used to advantage; in the latter, the appearance of unsightly beams in the ceiling of a room may be considered faulty design. Similarly in a factory the layout of the girders may be planned so as to accord with shafting for machinery. A bridge is similar in this respect as its purpose, location and amount of waterway will predetermine to a large extent its design. The engineer or architect will find, however, that reinforced concrete, owing to its plasticity, lends itself admirably to every possible requirement and condition. 13 KAHN SYSTEM OF REINFORCED CONCRETE Considering economy of design, the question immediately presents itself, — What system of reinforced concrete DESIGN is most economical ? It is here we set down the FOR following dictum which we stand ready to prove ECONOMY at all times: — The Kahn System of Reinforced Concrete per pound of stability of the finished structure is the most economical construction. The Kahn Trussed Bar with its rigidly attached diagonals is designed to resist every stress in the concrete ECONOMY except that of direct compression. There is no OF THE waste metal at any point and proper reinforcement KAHN BAR is provided at every place it is needed. For instance, in the central portion of the beam where the full section of the metal is needed for bending moment and no reinforcement required for shear, the bar is unsheared and the full area of the metal is available. At the ends of the beam where the shear is a maximum and bending moment a minimum the flanges of the Kahn bar are struck up to form rigidly attached shear members. Further than this, the Kahn Bar in reality consists of what may be considered a large number of separate ECONOMY members all rigidly attached and handled as a OF INSTAL- unit. The labor saving in handling a single piece LATION as compared with many separate individual parts, is well known to any builder. (The Trussed Concrete Steel Co., publishes a booklet describing an actual ex- perience proving this point. This booklet will be mailed on re- quest,) Besides this the construction can be placed more accurately, as loose pieces are almost sure to be misplaced when the concrete is poured. Strength of construction also requires that the diagonals be ligidly attached. These diagonals must trans- STRENGTH fer their shearing strains directly to the main OF THE tension member and when they are not attached KAHN BAR this is impossible except through the adhesion of the concrete, a questionable quantity at best. (See Booklet on Tests made by the French Government, reprinted by the Trussed Concrete Steel Co.) The system of construction being determined, there are many other considerations which affect the economy PRICES OF of a design. The location of the work and the MATERIAL relative prices of the different materials and various AFFECT grades of labor are determining conditions. In ECONOMY one place, lumber and carpenter labor may be cheap, while the concrete materials may be expen- 14 TRUSSED CONCRETE STEEL COMPANY sive. In such a location it would probably be economical to place girders close together. In other localities, the reverse conditions may be true and the opposite design would be the most satisfactory. In some localities, such as in the Middle West and East, hollow tile is relatively cheap and it would then be best to use reinforced hollow tile construction and not solid concrete slabs. All such conditions should have the closest study of the conscientious designer. It is to take care of all such matters as these, to study each ENGINEER particular problem from every possible angle in ING DEPT order to get the best possible construction for each ofTRUSSED i^di^id^ial structure, that the Trussed Concrete CONCRETE ^^^^^ ^^^^ organized its large Engineering De- STEEL CO partment with branches in all the principal cities. In this Department are men of technical training and of wide experience in the engineering field, who are familiar with every type of construction and have specialized in reinforced concrete. This experience in reinforced concrete in all its appli- cations places this department in a position to give expert advice on all such work. This advice together with preliminary plans and estimates is rendered gratis to all parties contemplating build- ing. The information thus given may often mean a saving of thousands of dollars in the construction. For any work in which it is decided that the Kahn System DETAIL ^^^^ used, complete detailed drawings and PLANS FOR specifications of the reinforced concrete construction REIN prepared. These drawings show clearly the FORCED Gxact location of each reinforcing bar and the CONCRETE detailed size of all the concrete work. Each bar WORK when it leaves the factory is given a distinctive mark which corresponds with its marking on the drawing. Each bar is designed for a distinct place in the struc- ture and the builder can tell at a glance where it belongs. The plans are prepared gratis for any structure in which the Kahn Trussed Bars are used. We co-operate to the fullest extent with all architects, engineers and contractors. Further information, including literature showing the applica- tion of the Kahn System to all forms of construction can be obtained by addressing Trussed Concrete Steel Co, Detroit, Mich. Trussed Concrete Steel Co., Ltd., London, Eng. Trussed Concrete Steel Co., of Canada, Ltd. Toronto. Can 15 KAHN SYSTEM OF REINFORCED CONCRETE SHEARING ON KAHN BARS Standard Shear of Kahn Bar, Middle Portion Left Unsheared. Code word — Sacalais. Center Shear of Kahn Bar. Entire Bar Sheared to Center. Code word — Sacafundo. One Way Shear of Kahn Bar. All Diagonals Sheared Inclining in one direction. Code word — Sacafacido. Special Shearing on Kahn Bars. As directed by purchaser. NOTE: — Sketch marked (*) shows shearing of bars with diagonals opposite. This type of shearing is provided on 6 in. and 8 in. diagonals. Sketch marked (f) shows shearing of bars with diagonals alternating as provided with 12 in., 18 in., 24 in. and 30 in. diagonals. 16 TRUSSED CONCRETE STEEL COMPANY SECTIONS OF KAHN TRUSSED BAR 3^''xl3^'' Kahn Trussed Bar. Weight — 1.4 pounds per foot. Area — 0.41 square inches, Standard length of Diagonals — 6 inches. Code word — Bandreich. M''x2iV Kahn^Trussed Bar. Weight — 2.7 pounds per foot. Area — 0.79 square inches. Standard length of Diagonals — 12 inches. Special lengths — 8 inches and 18 inches. Code word — Bandreifen. Z 17 KAHN SYSTEM OF REINFORCED CONCRETE U Z" VxS^' Kahn Trussed Bar. Weight — 4.8 pounds per foot. Area — 1.41 square inches. Standard length of Diagonals — 24 inches. Special lengths — 18 inches and 30 inches. Code word — Bandrjis. Kahn Trussed Bars. Weight — 6.8 pounds per foot. Area — 2.00 square inches. Standard length of Diagonals — 24 inches. Special lengths — 18 inches and 30 inches. Code word — Bangkraut. 18 TRUSSED CONCRETE STEEL COMPANY U . — 3 J ^ 2'^x33^'' Kahn Trussed Bar. Weight — 10.2 pounds per foot. Area — 3.00 square inches. Standard length of Diagonals— 30 inches. Special lengths — 24 inches. Code word — B angled. CODE WORDS FOR LENGTH OF DIAGONALS 6-inch — Sacabrocas . 8 ' ' — Sacabuxas. 12 ' ' — Sacacorcho. 18 ' ' — Sacadilla. 24 ' * — Sacadoria. 30 ' ' — Saccadirst. V.) KAIJN SYSTEM OF REINFORCED CONCRETE ALLOWABLE STRESSE, METHODS OF DESIGN, ETC. It is difficult in reinforced concrete work to adopt an arbitrary theory of design and fixed working stresses, whicfi MONO- shall apply to structures of every class. To design LITHIC correctly each particular problem should have ACTION individual attention and methods of design adopted accordingly. Concrete work being built mono- lithic should be treated accordingly and not analyzed into separate units as is done with ordinary materials where units are dealt with. The great additional strength of a monolithic construction of this kind is apparent. If any particular part of a floor is heavily loaded the floor adjacent will come to its assistance and will distribute the concentrated loading over a large area of floor space. In the case of vibratory loadings such as caused by moving EFFECT OF i^^^chinery, actual experiments have shown that VIBRA concrete is less effected than any other building TION material. The Trussed Concrete Steel Co. have built many such structures and there is not the least tremor throughout the building when machinery is in operation. Reinforced Concrete, when built continuously, over a large floor area, has great additional strength due to STRENGTH interior arch action in the concrete. This arch DUE TO action will in itself carry considerable load without ARCH causing any stress in the reinforcement. This of ACTION course is more marked in a floor where the depth is large compared with the span, than where the reverse is true. It would therefore seern proper to design a deep floor supported on all sides by similar construction with greater working stresses than a thin isolated panel built probably 20 feet in the air and unsupported by adjacent construction. Other points to be considered in this connection are the quality of the materials and the grade of the workmanship. The method of design, presented in this book, must be con- sidered in the light of the above and may be varied to agree with any s})ecial conditions as the designer sees fit. The theory as presented is conservative and accords with good practise for work of this class. The additional strength due to monolithic con- struction, arch action, and tensile strength of concrete is entirely neglected in the calcidations and thus an additional factor of safety is given to all work designed on this basis. 20 TRUSSED CONCRETE STEEL C().]fPANY THEORY OF REINFORCED CONCRETE WORK MOMENT OF RESISTANCE OF SIMPLE BEAM The followino" theoretical analysis is })ase(l on the nse of what is known as the ''Straight Line" forinnla. This is a forninla which is daily becoming more generally adopted and is embodied in tlie building requirements of almost all American cities and that of the Prussian government. It is recommended by the most authoritative text books, both foreign and native, and has the great advantage of simplicity and directness. It corresponds with the accepted theory of flexure as applied to other materials and is admittedly correct within allowable working stresses. If the theory errs at all, it errs on the side of safety. This theory is based on the following assumptions: — 1st. A section plane before bending remains plane after bending; that is, the stress on any fibre is directly proportional to its distance from the neutral axis. 2nd. The tensile strength of the concrete is entirely neglected. 3rd. There are no initial strains in the beam. 4th. All shearing strain is provided against and there is no slipping between the concrete and the steel. 5th. The modulus of elasticity of concrete iii compression is constant. COMPRESSION Referring to^figure : d ==distance from extreme compressed fibre to center of steel. X d=distance from the^^xtreme compressed fibre to the neutral axis. X =ratio of depth^ neutral axis to depth, (d) of steel, k d=distance from center of compression of concrete to center of steel. , k =ratio of this distance to depth of beam (d). ^M^yfeT =breadth of beam. 21 KAHN SYSTEM OF REINFORCED CONCRETE modulus of elasticity of steel. Ec modulus of elasticity of concrete. ^s = area of steel reinforcement. p = ratio of area of steel to area of concrete= bd. c = compressive stress in extreme fibre of concrete, f = tensile stress in steel. RM= moment of resistance of beam. RM= bending moment. The total compression in the beam must equal the total tension. Equating these forces: 'A chxd = phdi or ^cx = pf ^ D [1] ■ According to assumption 1st above C X f ~"m (1-x) Combining equations [1] and [2] >2x^ = m (1-x) p, whence X = -pm + 1 (pm)^ + 2 pm Again combining [1] and [2] 1 m P ~"2"f (f + cm) [2] [3] [4] The stress strain curve being a straight hue, the center of compression is located % x d above the neutral plane. Taking moments about the neutral axis: RM= c X 2 + p f (l-x) J bd2 [5] RM Taking moments about the center of the steel: cxbd^ X \ , c X bd^ [6] Taking moments about the center of compression in the concrete. RM-=^1-^^ d As f=k d As f [7] From equation [7] it is at once evident that the moment of resistance of a concrete beam is dependent only on the factor (A:), the area of the reinforcement, the depth of the beam, and the allowable 22 2,00 z o 1^0 ? CL 100 a E O o TRUSSED COXCRKTE STEEL ( OMPANY It 2^: 7- V- .10 .20 .ao .40 .50 .60 .70 .ao .ao ipo uo i^o ipo" PERCENTAGE OF REINFORCEMENT Fig. No. 2. 23 KAHN SYSTEM OF REINFORCED CONCRETE TOP or DEAM O 05 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 i5 r- \ s -N 's s s s H - s - p r '^ - \'-\ I t A) - St t t ,Z5 .50 75 100 125 1.50 1.75 2.0 2.25 2.50 PERCENTAGE OF REINFORCMENT Fig. No. 3. 24 TRUSSED CONCRETE STEEL COMPANY stress ill the steel, with this important proviso, — tJiat the allowable compressive stress in the concrete is not exceeded. This allowable stress will not be exceeded if the percentage of steel is kept below the value as determined by equation (4). It will be seen from equation (4) that if we assume a value for (f) equal to 10,000 pounds per sq. in. and also values for (m) that curves can be plotted showing the relation between the percentage of the metal and the com- pressive stress in the concrete. In Figure 2 these curves are shown for values of (m) equal to 10, 12 and 15 and based on a stress in the steel equal to 16,000 pounds per sq. in. From these tables it will be seen that if the percentage of steel does not exceed 1 per cent, for good rock concrete, there is no danger of the concrete failing by compression. The factor (k) in equation (7) is the distance between the center of compression of the concrete and the center of the steel. It depends entirely for its value on the position of the neutral axis. From the equation (3) it is seen that the position of the neutral axis is dependent entirely on the percentage of the reinforcement and the values of (m). Again assuming (m) equal to 10, 12 and 15, in equation (8), curves as shown in figure 3 on page 24 are drawn showing the position of the neutral axis for various percentages of metal. From these curves the values of the factor (k) are readily obtained and are shown properly plotted in the same figure. An inspection of these curves will show at a glance that for all ordinary practical percentages of reinforcement, this factor (k) does not vary appreciably. It reduces to a value equal to .86 when the percentage of metal equals 1 per cent. For all lower percentages of metal its value is greater. It is, therefore, a very safe assump- tion to reduce our equation of (7) to the following simple formula : — For isolated beams, the percentage of reinforcement must not exceed 1 per cent for good rock concrete. This does not apply to beams with double reinforcement and T beams, which will be treated later. RM= .86dAsf [8] or for f=16,000 pounds per sq. in. RM=13,760 d As [9] 25 KAUN SYSTEM OF RKINFORC'ET) CONCRETE TRUSSED CONCRETE STEEL COMPANY DOUBLE REINFORCEMENT. In the case of isolated beams when the percentage of tensile reinforcement exceeds 1 per cent., it is cnstomary to provide com- pressive reinforcement to take care of this excess. The formnlse for design of beams with double reinforcement as ordinarily pre- sented in text books are so complicated and involved as to be of little practical value. The following method of determining the amount of compressive reinforcement is sim})le, direct and accurate. Assume an extreme fibre stress in the concrete of 750 pounds per sq. in. and a value of ni equals 15. The stress in the fibre near the compressive reinforcement will be slightly less, say 720 pounds per s(|. in. As (m) equals 15, the compressive stress in the steel is 10,800 pounds per sq. in. or slightly more than two- thirds of the allowable stress of steel in tension. In other words, the steel in tension is 50 per cent, more available than that in compression. That is if there is one square inch of reinforcement in excess of the allowable percentage in an isolated beam, there must be provided 1^2 sq. in. of compressive reinforcement. The neutral axis in the beam remains in the same location as in the simple beam, as the allowable unit stresses are the same and the location of the neutral axis is determined by equation (2.) The steel in compression being placed above the center of com- pression in the simple beam, the value of the factor k would tend to be increased so that equation 9 can be used with perfect safety in this case. To summarize: — In the case of isolated beams, in which the percentage of tensile reinforcement exceeds 1 per cent, provide compressive reinforcement equal in area to I of the excess area of tensile reinforcement. Then design by equation 9. T BEAMS When beams or girders are built so as to form part of a floor construction, the floor slab will act with and may be considered part of the same. In the construction of such a floor the concrete in the beam and slab must be placed continuously so that the two will be perfectly united. In the design of such a T beam, there are four points which must be investigated and the design must satisfy each of these conditions. These four considerations govern the width of the floor slab that shall be considered as acting with the beam. It is assumed in this discussion, that sufficient steel has been provided in tension and that the beams are spaced sufficiently far apart so that the spacing of beams will not determine the width of slab available. With these assumptions the four points in the design each of which must be investigated and satisfied are: (See figure 4.) 27 KAHN SYSTEM OF REINFORCED CONCRETE 1st. Shear along the plane m n. 2nd. Shear along the planes ni o and n p. 3rd. Span of beam as affecting width of T. 4th. Weakness in conn)ression. I I -a I X _1_ Neutral axis SHEAR ALONG PLANE m 71 Fig. No. 4. It is possible to make a complete analytic discussion of this matter, but the practical results of such analysis are alone interesting to the designer. Governed by this consideration, different authori- ties have given the width of slab available as acting with the beam, as from *3 to |10 times the width of beam. Good practice w ould limit this width to 5 times, i. e., b' must not be greater than 5 b. SHEAR ^^^^ shear along either of these planes is one-half ALONG ^^^^^ along mn and according to the above discussion, PLANES ^ width of slab, equal to twice the width of beam mo and n either side of such beam, acts with the beam. mo an np Therefore, the floor slab to the extent of four times its depth on either side of the beam, may be considered as acting with the beam, i. e., b' must not be greater than h-\-S t d. The span of beam affects the width of slab available in that it takes a certain distance to distribute the stress to the outer edges of the T section. A width of slab not greater than 1-5 of the span of the beam may be considered as acting with the beam; i. e., b' must not be greater than 4 b. The width of flange necessary for compression is dependent on the area of the tensile reinforcement and the ratio of the thickness of the slab (t d) to the depth of beam (d.) The table given on page 29 shows the width of flange necessary in_the terms of the width of beam, for various percentages of rein- forcement and ratios of slab depths. This table is based on the following theoretical analysis: *Capt. John S. Sewell, Proceed. A. S: C. E. Dec, 1905. |New York and Buffalo Building Laws. SPAN OF BEAM WEAKNESS IN COMPRES- SION 28 TRUSSED CONCRETE STEEL COMPANY RATIO OF WIDTH OF TABLE OF *'T" REQUIRED TO WIDTH OF BEAM FOR VARYING PER CENTS OF STEEL AND DEPTHS OF SLAB. Maximum Compression in Extreme Fibre = 750 Pounds per square inch. Stress at Points Equidistant from Neutral Axis, same at all Points of Tee. (t) Ratio OL depth of Slab to depth of Steel .05 .10 15 .20 .25 .30 .35 .40 .413 Percentage of Area of Steel, A, to Rectangular Area of Concrete, bd. IK IK 2 2X 2>2 2H 3 3X 3K 3K 4 2.3 3.4 4.6 1.7 2.3 2.9 3.5 4.1 1.5 1.9 2.4 2.8 3.2 3.7 4.1 1.4 1.8 2.1 2.5 2.8 3.2 3.5 3.8 4.2 1.4 1.7 2.0 2.3 2.6 2.9 3.2 3.5 3.8 4.1 1.3 1.6 1.9 2.2 2.4 2.7 3.0 3.3 3.6 3.8 4.1 1.3 1.6 1.8 2.1 2.4 2.6 2.9 3.2 3.4 3.7 3.9 4.2 1.3 1.5 1.8 2.0 2.3 2.6 2.8 3.1 3.4 3.6 3.9 4.1 1.3 1.5 1.8 2.0 2.3 2.6 2 8 3.1 3.4 3.6 3.9 4.1 NOTE: — For all ratios greater than .413, —j^ has same value as given for .413. NOTE:— Table gives vahies of See figure 4. 29 KAHN SYSTEM OF REINFORCED CONCRETE Extreme fibre stress in concrete in compression c=750 pounds per sq. in. Tensile stress in steel=16,000 pounds per sq. in. m=l5, . c X l^rom equation, page 22 ^-^ — y Solving, x=AlS. The stress at lower edge of slab=^^ c Total compressive stress= C b X d + (b -b) ' ctd. Total tensile stress= 16,000 p h cU b ' Equating and solving for ^, 32,000 p-cx — = 1 + 2^^^t b c t X Substituting values of c and x above. J/_^_^ 32,000 p-310 b (.826-t) 1816 t. When the lower edge of the slab falls below the neutral axis, the analysis of the beam is the same as for a simple beam of width b' and depth d. An inspection of the table will show that under ordinary con- ditions of design, the slab will supply sufficient compressive rein- forcement. In case it does not, steel must be provided in com- pression as indicated under design for "Double Reinforcement," page 27. As the center of compression in the T beam will be relatively higher or equally as high as in the simple beam, the equation for moment of resistance for a simple beam may be used safely in the design of T beams, i. e., R M = .86 f As^l = 13760 Ag^- To summarize, the design for T beams must satisfy each of the following conditions: 1st. b' must not be greater than 5 h, 2nd. b' " " " " ^td + h, 3rd. b' " " " " " i of the span of beam, 4th. b' " " " " " the distance between the beams. 30 TRUSSED CONCRETE STEEL COMPANY 5th. Sufficient compressive area must be provided as shown in table. 6th. The tensile reinforcement may be proportioned bvthe formula R M = 13,760 A^d. The designer will readily see that shear plays an important part in beam design and that shear reinforcement must be provided. This shear reinforcement should be rigidly attached to the main tension member so that its stress may be transferred directly to this member. The Kahn Trussed Bar, with its rigidly attached diagonals, accomplishes this result in a simple, adequate and economical manner. DESIGN OF BEAM LIMITED BY COMPRESSION IN CONCRETE The theory of design for beams presented up to this point has been based on a safe working stress of 16,000 pounds per sq. in. in the steel in tension and an extreme fibre stress of 750 pounds per sq. in. in the concrete in compression. It has been shown that where the percentage of tensile reinforcement is less than 1 per cent, the compressive stress will be less than 750 pounds and therefore need not be considered. In the previous discussion where more than 1 per cent, of reinforcement is required the extreme fibre stress is limited to 750 pounds, either by the use of compressive reinforcement or by making the beams T section. On rare occasions, in the case of isolated beams and floor slabs, the percentage exceeds 1 per cent, and it is not found practical to use either of the two alternatives just mentioned. Under such circumstances the moment of resistance of the beam is limited by the extreme fibre stress (750 pounds) in the concrete, irrespective of the stress in the tensile reinforcement. The moment of resist- ance is then determined by equation 6 page 22, i. e. The table given on page 82 gives the computed value of the moments of resistance and position of neutral axis for various percentages of reinforcement, based on this formula. The designer should remember that it is usually decidedly un- economical of material to design so as not to fully develop the strength of the steel reinforcement. Such a design should be avoided wherever possible. RM As d p 31 KAHN SYSTEM OF REINFORCED CONCRETE Moments of Resistance of Beams, when the design is limited by the compression of the concrete and the full tensile strength of steel is not developed. Percentage of Reinforcement Position of Neutral Axis Values of X. R M Depending on /vrea oi oteei R M Depending on Area of Concrete 11% 0.4327 12620 dAs 139 bd^ 1.2% 0.4464 11880 dAs 142 bd^ 1.3% 0.4592 11220 dAs 146 bd^ 1-4% 0.4712 10640 dAs 149 bd^ 1.5% 0.4825 10120 dAs 152 bd^ 1.6% 0.4932 9660 dAs 155 bd^ 1-7% 0.5033 9240 dAs 157 bd^ 1.8% 0.5129 8860 dAs 159 bd^ 1.9% 0.5220 8510 dAs 162 bd^ 2.0% 0.5307 8190 dAs 164 bd^ 2.1%o 0.5389 7890 dAs 166 bd^ 2.2% 0.5468 7620 dAs 168 bd^ 2.3% 0.5545 7370 dAs 170 bd^ 2.4% 0.5617 7130 dAs 171 bd^ 2.5% 0.5687 6910 dAs 173 bd^ 2.6% 0.5755 6710 dAs 174 bd^ 2.7% 0.5819 6510 dAs 176 bd^ 2.8% 0.5882 6330 dAs 177 bd^ 2.9% 0.5942 6160 dAs 179 bd^ 3.0% 0.6000 6000 dAs 180 bd^ Where percentage is 1 % or less RM = 13760 d As 32 TRUSSED CONCRETE STEEL COMPANY KAHN SVSTEM OF REINFORCED CONCRETE SHEAR IN REINFORCED CONCRETE BEAMS The vertical shear at any section of a beam is the reaction at one end minus that part of the load lying between the end and the section. It is shown in mechanics that at any point in a beam the vertical unit shear is equal to the horizontal unit shear. The distribution of the shearing stresses on the vertical section of a beam of homogeneous material is shown in figure No. 5. It will ^^eVTRAL AX/5 Fig. No. 5. be noted that the shear varies as the ordinates to a parabola with the maximum shear at the neutral axis and equal in magnitude to I the mean unit shear. The distribution of shearing stresses on a vertical section of a reinforced concrete beam is shown by figure No. 6. The shear CompreSSiOfN Shearing Stress Fig. No. 6.— Distribution of Horizontal and Vertical Shear. distribution in the beam of homogeneous material is similar to that of the reinforced concrete beam except for that portion of the curve below the neutral axis. As no tension is considered as acting in the concrete there will be no change in the intensity of the horizontal and vertical shearing stresses below the neutral axis, whereas in the beam of homogeneous material the intensities vary as shown by the figure. V^t^ ^ In the flexure of a simple beam the upper fibres are compressed and the lower fibres are stretched in amounts proportionate to the distance of these fibres from the neutral axis. From the above it is evident that at every point of a beam there exists a horizontal and vertical shear and also a longitudinal tension or compression. 34 TRUSSED CONCRETE STEEL COMPANY By combining the bending moment stresses with the shearing stresses at the various points in a beam lines of so-called principal stress are drawn as shown in figure No. 7. At the center of the Fig. No. 7. — Lines of Stress in a Beam Under Flexure. span the tensile and compressive stresses are horizontal; but as the ends are approached the lines of tensile stress incline upwards and those of compressive stress incline downwards so that at all points away from the center of the span these stresses have both horizontal and vertical components. The horizontal components reach a maximum at the center of the span and the vertical at the ends. It will be noticed from the above figure that the lines of tension stresses incline up and away from the center at an average angle of 45 degrees, while the lines of compressive stresses cross these tension lines at right angles and incline down toward the ends of the span. If the fundamental idea of reinforcing the concrete for tension is carried out, it is evident that steel members traversing the lines of principal tension stresses must be included in the design. If these members are to carry stresses they must be connected to some part of the structure that is capable of receiving it. The main tension member in the bottom of the beam provides such a connec- tion, and it is only natural that this main tension member be utilized for this purpose. The web members in the Kahn System of Reinforcement are rigidly connected to the main bar so that there can be no slipping at the connection. These web members extend up into the compressed area of the concrete and the upper portion is gripped and held in place not only by the adhesion to the con- crete, but also by the thrust in the concrete acting at right angles to the axis of the web member. A complete truss is thus formed with tension flange of steel, compression flange of concrete and steel tension diagonals rigidly held at either end. Merriman in his text book on mechanics gives an expression for maximum diagonal tension as t= 3^s-[-y/3^s^-|-v^ Where "t" is the diagonal tensile unit-stress, ''s" is the hori- zontal tensile unit-stress existing in the concrete, and "v'' is 35 KAHN SYSTEM OF REINFORCED CONCRETE the horizontal or vertical shearing unit-stress. The direction of this maximum diagonal tension makes an angle with the horizon- tal equal to one-half the angle whose cotangent is 3/2-1 • If there is no tension in the concrete, this reduces to t=v, and the maximum diagonal tension makes an angle of 45 degrees with the horizontal, and is equal in intensity to the vertical shearing stress. When the diagonal tensile stresses developed become as great as the tensile strength of the concrete, the beam will fail by diagonal tension, provided there is no metallic web reinforcement. The accompanying cut gives the typical form Avhich this failure takes. As the value of the maximum diagonal tensile stress developed in a beam is, by equation (t=3^s-^ j/l/^s'^+v^) , dependent upon the horizontal tensile stress developed at the same point, it is difficult to compute its actual amount. The best method seems to be to compute the horizontal and vertical shearing unit-stress, and make all comparisons on the basis of this value. BESSEMER STEEL, HIGH CARBON, DEFORMED BAR See Report of Boston Transit Commission, June 30, '04. Fracture showing method of failure, due to shear, which occurs almost invariably when horizontal reinforcement is used. Steel stretched only to its elastic limit BEAM REINFORCED WITH THE KAHN TRUSSED BAR See Eng. News, vol. L, p. 349. See Eng. Record, vol. 48, p. 465. Note that when tested to destruction the steel pulls in two. Ultimate strength of steel developed, 36 TRUSSEJ) CONCRETE STEEL COMPANY KAHN SYSTEM OF REINFORCED CONCRETE PIECES UNDER DIRECT COMPRESSION Unhooped Columns In combining steel and concrete to resist compression, theo- retically the load is borne by the two materials in a ratio determined by their relative modulii of elasticity. With this ratio 1 to 15 and a safe stress in the concrete of 500 pounds the steel will carry 7500 pounds per square inch. The natural disposition of this rein- forcing steel is near the periphery of the column. In this position the reinforcing steel will take up whatever secondary stresses may occur caused by the possible eccentric application of the applied loads or by unequaled settlement of the footings. The longitudinal reinforcing rods should be stayed at intervals not exceeding fifteen times the diameter of the rod, or the least dimension of the column. With twisted and plain bar columns this staying is done by horizontal bands extending around the column or by spirally-wound hooping. The cut on page 65 shows the adaptability of the Kahn bar to column construction. The prongs are of such length that they reach diagonally across the column and tie in the main bar at intervals of 6'' to Columns loaded unsymmetrically and especially corner col- umns should be figured with lower unit stresses. On account of the monolithic nature of construction it is somewhat difficult to say just what eccentricity a certain loading gives. In outside columns there is, undoubtedly, an eccentric load, and this should be pro- vided for in the design by allowing a lower fiber stress. Hooped Columns Hooped columns as developed by M. Considere consist of a number of longitudinal bars arranged on the circumference of a circle with a steel band wrapped around these bars in spiral turns varying from ij^'' to 4'' apart, depending upon the design. This form of reinforcement increases the compressive strength of the concrete greatly and enables it to withstand much greater deformation and unit stresses. Considere shows that plain concrete under compressive stresses tends to fail by splitting longitudinally and bulging laterally. By enclosing it in a spiral wrapping of sufficiently small pitch the lateral bulging is resisted and the con- 88 TRUSSED CONCRETE STEEL COMPANY Crete will not only stand higher stresses without failure, but will also undergo much greater shortening. For a theoretical dis- cussion of this subject the reader is referred to "Experimental Researches on Reinforced Concrete," by Armand Considere, published by the McGraw Publishing Co. under date of 1906. The table on page 64 is based upon the theory as developed bv Considere. This theory is outlined by the following formula: P=:Ae Fe=m (A,+2.4A;) X F,. Where P=safe load on column. Fc==load per sq. in. on net section of core, Ae=net area of concrete inside of hooping. modules of elasticity of steel. m = — — ' modules of elasticity of concrete. Ag— Total area of cross section of vertical rods. As=area of cross section of imaginary vertical rods having same quantity of steel as the hooping. The following values were used in figuring the tables. F,=750 lbs. m=15, Ag=approximately \}/2 per cent, of cross section of core. As=approximately 2}/2 per cent, of cross section of core. Typical Roof Construction Showing Application of Reinforced Concrete and Hollow Tile Design on Steel Trusses. 39 KAHN SYSTEM OF REINFORCED CONCRETE BENDING MOMENTS Reinforced concrete differs from the ordinary types of building construction in that it is built continuous and monolithic. For this reason, girders and slabs must be designed to a large extent as continuous structures and provision must be made to take care of the negative bending moments occuring at the supports. This is done in practise by inverting Kahn bars in the top of the concrete over the support. It will often be found that in order to make the construction perfectly continuous in accordance with the accepted theory of continuous beams, the negative bending moment over the support will exceed the positive bending moment at the center of the span. It has not been found practical, however, to design in this way. The reasons for this are: — 1st. The top bars cannot be laid with as great accuracy as the bottom bars. 2nd. The concrete cannot be placed as well. 3rd. Each span in a structure would not be independently stable, as it would depend for its stability upon the cantilever action of the adjacent span. Sufficient top reinforcement, however, must be provided to thoroughly tie the construction together and to prevent the occurence of hair cracks due to slight deflection. The use of this top rein- forcement reduces the bending moment at the center of the span. The following scale of bending moments has been adopted by good practise in this country and abroad, is considered conserva- ative, and gives satisfactory results: — B M= bending moment at center of span of the beam. W= total uniform load on beam. B M==jq^ W 1 . 1 == span of beam. For beams and slabs built in or continuous at both supports, For beams and slabs built in or continuous at one support only BM=^W1 For beams and slabs freely supported, BM=4^W1 o 40 TRUSSED CONCRETE STEEL COMPANY DETAILS OF FLOOR CONSTRUCTION FRAMING BETWEEN STEEL GIRDERS Reinforced Solid Slab Resting on Top of I^JBeams. r Solid Concrete Floor Slabs for Short or Long Spans. Reinforced Hollow Tile Long Span Construction. " 'a'"* " ^ ' ' ' is.-^ / / / / / . / / / Z^ Slab Resting on Lower Flange of I Beam. Note flat Ceiling and Cinder Fill Over Concrete Construction. 41 KAHN SYSTEM OF REINFORCED CONCRETE Typical Floor Slab Construction Framing Between Concrete Beams. TOP REiNfORCINQ Finished floor Note Continuous Action Over Supports Produced by Inverting Kahn Bar in Top of Beam. 42 Last foi-Mula on Kahn p 40; u- _ v.;"ere L - span, r-^— ^ In a plate, supported along its sidei D = span; and H = — b. t^t^ ■ - 8 y, ' hcct r&xxiE to Kahn p 43, in a plate supported or fixed at its 4 ed^es, tl raaxiKur.1 ^moments, tiven on p 40, raust be reduced by the factor (our s:/m>)ols, P 493) L*^ supported on its 4 sides, M = — b KAHN SYSTEM OF REINFORCED CONCRETE EXPLANATION OF TABLES FOR SOLID CONCRETE FLOOR SLABS. The tables for floor slabs given on pages 45 to 50 inclusive, are based on the theory of design as given in the preceding pages. They are computed as being built continuous over the supports and for a bending moment equal to lo W P. The loadings given are ^afe live loads per sq. ft. The full dead weight of the slab has been deducted in every case in preparing the tables. They can be used with safety in any slabs in which Kahn bars are used. In order to produce proper continuous action, top reinforcing bars must be provided over the supports equal in area to one-fourth of the area of the bars in the floor. These bars should have a length equal to A of the span of the floor. In case the slabs are not built continuous but are freely sup- ported, these tables can be used, but from the safe live loads given must be deducted. Safe live load+dead w^eight of slab per sq. ft. 5 in order to find the safe live loading on the slab. Floor slabs should have a thickness equal to at least one- thirtieth of the clear span. EXPLANATION OF TABLES FOR REINFORCED HOL- LOW TILE CONSTRUCTION These tables, pages 53-56, are prepared on exactly the same basis as regards bending moments, loadings and use, as the tables for solid concrete floor slabs. This construction consists of a series of hard burned hollow tiles, laid with a space between. In this space is placed a Kahn bar and a rich mixture of concrete. In this way are obtained reinforced concrete joists separated by hollow tiles. These joists carry all the load while the tile serves merely as a filler to produce lightness. In the case of the floors reinforced with KxlK'' bars the con- struction is covered with a coat of concrete, and the floor with K''x2 fV bars with a 2'' coat. This is in order to provide suflS- cient compressive area. These thicknesses may be increased if conditions warrant it. The tables given cover the general cases occurring in practice. The designer will readily see a varied number of other combinations of hollow tile and concrete joists which he can use as occasion demands and which can be readily computed from the general theory already given. Floors should not have a thickness less than one-thirtieth of the clear span. 44 TRUSSED CONCRETE STEEL COMPANY SPACING OF BARS IN INCHES FOR VARIOUS SAFE LIVE LOADS PER SQUARE FOOT 4 Slab y^" xlVi" Kahn Trussed Bars, Area = 0.41 sq. in. Load in Pounds SPAN IN FEET 6 7 8 9 10 50 18.7 75 18.3 14.9 100 19.4 15.3 12.4 125 16.6 13.1 10.6 150 18.9 UA 11.4 175 16.8 12.8 10.1 B. M. = 200 20.5 15.1 1 11.5 "lo 250 300 350 17.1 14.6 12.8 12.5 10.7 9.4 R. M.=0.8QxS.25 x 0.41 x 16000 Maximum Spacing = 16" 400 11.4 8.3 Minimum Spacing = 12.6" 4'/^" Slab y^" Kahn Bars, Area — 0.41 sq. in. Load in SPAN IN FEET Pounds 6 7 8 9 10 11 50 16.8 75 16.4 13.6 100 17.0 13.7 11.3 125 18.5 14.6 11.8 9.8 150 16.2 12.8 10.4 8.6 175 18.9 14.4 11.4 9.2 200 17.0 13.0 10.3 8.3 250 19.4 14.2 10.9 8.6 300 16.6 12.2 9.3 350 14.5 10.7 8.2 400 12.9 9.5 B. M. IV V' 500 10.6 ^ Jo R. M. =0.86X3.75X0.41X16000 Maximum Spacing = 16 " Minimum Spacing = 10.9" 45 KAHN SYSTEM OF REINFORCED CONCRETE SPACING OF BARS IN INCHES FOR VARIOUS SAFE LIVE LOADS PER SQUARE FOOT 5 Slab V2" X V/i" Kahn Trussed Bars, Area 0.41 Sq. in. Load SPAN IN FEET in Pounds 6 7 8 9 10 11 12 50 18.0 15.1 75 17.7 14.6 12.3 100 18.5 15.0 12.4 10.4 125 16.0 13.0 10.7 9.0 150 17.8 14.1 11.4 9.4 175 20.8 15.9 12.6 10.2 8.4 200 18.8 14.4 11.4 9.2 250 21.5 15.8 12.1 9.6 ' B. M.= 300 18.5 13.6 10.4 8.2 To 350 16.2 11.9 9.1 R. M=om x4.25x0.41x 16000 400 14.5 10.6 8.2 oUU 11.9 8.7 Maximum Spacing 16" 600 10.1 7.4 Minimum Spacing 9.7" 6' Slab V:2" X W Kahn Bars, Area 0.41 Sq, in. Load SPAN IN FEET in Pounds 8 9 10 11 12 13 14 15 50 16.8 14.4 12.4 10.8 75 16.7 14.0 11.9 10.3 8.9 100 17.2 14.2 11.9 10.2 8.8 7.6 125 18.6 15.1 12.5 10.4 8.9 7.7 150 16.5 13.4 11.0 9.3 7.9 175 18.7 14.8 12.0 9.9 8.3 7.2 200 17.0 13.4 10.9 9.0 7.6 2 250 14.4 11.4 9.2 7.6 300 12.5 9.8 8.0 R. M. ==0.86x5.25x0.41x 16000 350 10.9 8.7 7.0 400 9.8 7.7 Maximum Spacing 16" 500 8.1 6.4 Minimum Spacing 7.8" 46 TRUSSED CONCRETE STEEL COMPANY SPACING OF BARS IN INCHES FOR VARIOUS SAFE LIVE LOADS PER SQUARE FOOT 7 Slab 34" X 2iV Kahn Trussed Bars. Area = 0.79 Sq. in. Load in SPAN IN FEET Pounds 8 9 10 11 12 13 14 15 16 17 50 75 100 18.1 15.8 16.0 13.9 16.8 14.2 12.2 125 18.4 15.9 13.9 12.2 150 175 200 19.0 17.5 15.9 16.5 14.8 13.6 14.2 12.9 11.7 12.4 250 300 19.5 17.0 16.1 14.0 13.6 11.8 11.6 350 400 18.6 16.6 15.0 13.5 12.4 11.1 500 17.4 13.8 11.2 600 14.9 11.8 800 11.5 R. M. = 0.86 X 6 X 0.79 x 16000 Maximum Spacing =16" Minimum Spacing = 13.2" 47 KAHN SYSTEM OF REINFORCED CONCRETE SPACING OF BARS IN INCHES FOR VARIOUS SAFE LIVE LOADS PER SQUARE FOOT 8 Slab 3^" x2i%' Kahn Trussed Bars. Area = 0.79 sq. in Load in Pounds SPAN IN FEET 6 7 8 9 10 11 12 13 14 250 oUU 1 Q 9 18.2 1 Q lo.y 15.3 13.0 11/1 11.4 11.2 O Q y .o 350 17.1 14.1 11.9 10.1 400 19.0 15.3 12.7 10.6 500 19.9 15.8 12.8 10.6 600 17.1 13.5 10.9 800 17.3 13.3 10.5 1000 1200 16.3 14.2 12.0 10.9 9.2 1400 14.1 10.4 Load in Pounds SPAN IN FEET 12 13 14 15 16 17 18 19 20 50 18.0 16.1 14.4 13.0 75 17.4 15.4 13.7 12.3 11.1 100 17.2 15.2 13.4 12.0 10.7 125 17.6 15.3 13.4 11.9 10.6 150 18.3 15.8 13.8 12.1 10.7 175 200 17.9 16.6 15.2 14.3 13.1 12.5 11.4 11.0 10.0 250 15.3 13.0 11.2 Maximum Spacing 16 " B. M. = - 10 Minimum Spacing 11.3" R. M. = 0.86 X 7 X 0.79 X 16000 48 TRUSSED CONCRETE STEEL COMPANY SPACING OF BARS IN INCHES FOR VARIOUS SAFE LIVE LOADS PER SQUARE FOOT 10 Slab 34" X 2i\' Kahn Trussed Bars. Area = 0.79 sq. in. Load in SPAN IN FEET Pounds 6 7 8 9 10 11 12 13 14 15 125 17.7 150 16.1 175 16.9 14.8 200 18.1 15.6 13.6 250 18.4 15.6 13.5 11.8 300 16.2 13.8 11.9 10.4 350 17.2 14.4 12.3 10.6 9.2 400 18.8 15.5 13.1 11.1 9.6 8.4 500 19.5 15.8 13.0 10.9 9.3 8.1 600 16.8 13.6 11.2 9.4 8.0 800 16.6 13.1 10.6 8.8 7.4 1000 17.8 13.7 10.8 8.7 1200 20.6 15.1 11.6 9.2 1400 17.9 13.1 10.1 7.9 Load in SPAN IN FEET Pounds 16 17 18 19 20 21 22 23 24 25 50 17.7 15.9 14.4 13.1 11.9 10.9 10.0 9.2 75 17.3 15.4 13.9 12.5 11.4 10.3 9.5 8.7 8.0 100 17.4 15.4 13.7 12.3 11.1 10.] 9.2 8.4 125 15.6 13.8 12.3 11.1 10.0 9.1 8.2 150 14.2 12.5 11.2 10.1 9.1 8.2 175 13.0 11.4 10.2 9.2 8.3 200 11.9 10.6 9.4 8.5 250 10.3 9.1 8.2 300 9.1 8.1 350 8.1 Maximum Spacing = 16 B. M. - 1 Minimum Spacing := 9" R, M. -- = 0.86 X 9 X 0.79 X 16000 49 KAHN SYSTEM OF REINFORCED CONCRETE SPACING OF BARS IN INCHES FOR VARIOUS SAFE LIVE LOADS PER SQUARE FOOT. 12 Slab 34" X 2i%' Kahn Trussed Bars. Area = 0.79 sq. in. Load SPAN IN FEET in Pounds 8 9 10 11 12 13 14 15 16 17 18 75 16.8 100 16.9 15.1 125 17.3 15.4 13.7 150 15.9 14.0 12.5 175 16.6 14.6 12.9 11.5 200 17.7 15.4 13.6 12.0 10.7 250 17.9 15.5 13.5 11.8 10.5 9.3 300 15.9 13.7 11.9 10.5 9.3 8.3 350 16.8 14.3 12.3 10.7 9 5 8.4 7.4 400 18.2 15.2 13.0 11.2 9.7 8.6 7.6 6.8 500 18.6 15.3 12.9 11.0 9.5 8.2 7.2 6.4 600 19.8 16.0 13.2 11.1 9.5 8.2 7.1 6.3 800 15.6 12.6 10.4 8.8 7.5 6.5 5.6 1000 16.3 12.9 10.4 8.6 7.2 6.2 1200 14.0 11.0 8.9 7.3 6.2 1400 12.1 9.5 7.7 6.4 Load SPAN IN FEET in Pounds 19 20 21 22 23 24 25 26 27 28 29 50 17.1 15.4 14.0 12.7 11.6 10.7 9.8 9.1 8.4 7.9 7.3 75 15.1 13.6 12.4 11.3 10.3 9.5 8.7 8.1 7.5 7.0 6.5 100 13.6 12.3 11.1 10.1 9.3 8.5 7.8 7.2 6.7 125 12.3 11.1 10.1 9.2 8.4 7.7 7.1 6.6 150 11.2 10.2 9.2 8.4 7.7 7.1 6.5 175 10.4 9.4 8.5 7.7 7.1 6.5 200 9.6 8.6 7.9 7.2 6.5 250 8.4 7.6 6.9 6.3 300 7.5 6.7 ^2 Maximum Spacing = 16'' B.M.=— Minimum Spacing = 7.2" 10 R. M. := 0.86 X 11x0.79x16000 50 TRUSSED CONCRETE STEEL COMPANY Detail of Window Framing Into Concrete Lintel Beam. 1 1 ... ^^^H Cross Section Reinforced Hollow Tile Floor. Detail of Framing Reinforced Concrete Columns, Beams and Floors. 51 KAHN SYSTEM OF REINFORCED CONCRETE SAFE LIVE LOADS PER SQUARE FOOT FOR HOLLOW TILE FLOORS OF VARIOUS THICKNESSES Reinforced with 54' x IV^" Kahn Trussed Bars Depth CI +-> o Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile-f Concrete Tile Tile+ Concrete Tile+ Concrete Tile Tile+ Concrete Tile+ Concrete CD 00 rH 00 C-l o T-H o ^ O (M T— t T-H Weight of floor in Pounds Per sq. foot 38 50 47 59 56 68 54 66 78 63 75 87 Spacing > 378 464 565 651 752 838 852 938 1024 1039 1125 1211 7 268 328 403 462 538 598 612 672 732 747 807 867 8 196 239 297 340 398 442 456 499 542 557 600 643 9 147 178 225 256 303 335 349 380 412 427 458 490 FEET 10 112 135 173 196 235 258 272 295 319 334 357 380 11 86 103 135 152 184 202 216 233 250 265 282 299 12 66 7Q 1 1 ft 1 lo 146 159 173 185 1 Q7 919 13 59 83 92 116 125 139 148 157 172 181 190 14 44 65 71 92 98 112 118 124 139 145 151 < 15 32 51 54 73 77 91 95 98 113 117 121 en 16 39 41 58 59 73 75 77 92 94 96 17 29 29 45 45 59 59 59 74 75 75 18 34 33 47 45 44 59 58 57 19 25 36 34 32 47 45 42 20 28 36 33 30 21 27 52 rRUSSED;^C()NCRE TE^ S TEELICOMPAN Y SAFE LIVE LOADS PER SQUARE FOOT FOR HOLLOW TILE FLOORS OF VARIOUS THICKNESSES Reinforced with J" x 2j\' and 1 x 3 Kahn Trussed Bars 3 " X 2,\ ^> 1 "x3" Depth Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile 4- Concrete Tile4- Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile + Concrete b CM CM ^ CM CO 00 CM b CM CM CM CM CO Weight of floor in Pounds Per Sq. foot 59 68 78 87 98 104 61 71 82 92 108 Spacing <— -16"C to C- — > 15" 13" < -17"C to C- 18" 8 686 887 1090 1293 1374 1595 639 827 1018 1208 2167 9 528 687 845 1003 1065 1238 492 638 786 935 1687 10 416 543 669 796 844 983 387 504 621 739 1347 11 334 437 540 643 681 795 309 404 499 595 1094 12 271 357 441 526 556 651 250 329 406 485 902 13 222 294 364 436 459 539 204 269 334 399 752 14 182 244 303 363 383 451 167 222 276 332 634 15 152 204 254 306 321 379 138 185 230 277 538 16 127 171 214 257 270 320 114 154 193 233 460 fee: 17 106 144 181 218 228 272 94 128 161 196 395 18 88 121 153 185 193 231 77 107 135 165 341 19 / O ioo bo QQ OO 1 1 o 1 io ioo 20 60 137 167 51 73 94 116 256 < 21 49 116 142 59 77 97 222 22 39 97 121 48 63 80 192 23 80 101 38 51 65 167 24 66 85 29 40 52 145 25 53 70 30 41 125 26 41 57 31 107 27 31 45 92 28 78 29 65 B.M. wl 2 10 "Tile On Edge 8 "Tile On Edge 53 RAHN SYISTEM OF REINFORCED CONCRETE SAFE LIVE LOADS PER SQUARE FOOT FOR HOLLOW TILE FLOORS OF VARIOUS THICKNESSES Reinforced with V2" x IV^" and -M' x 2iV Kahn Trussed Bars Spaced Alternately 0 Depth Tile+ Concre Tilef Concre Tile^- Concre Tile + Concre D U '-I r a Tile + Concre Tile + Concre Tile+ Concre Tile+ Concre ooi-i 00 rH Weight of floor in Pounds Per Sq. foot 50 98 59 56 68 66 78 75 87 Spacing < 16" C. to C, •> 7 447 583 yj 1 0 7R7 i 0 1 880 QS7 iUoU 1 ioy 1282 8 000 435 658 740 ouy 961 9 267 334 00 1 505 ^^71 OZO Aon oyU 741 t ^ X 10 206 262 302 396 450 584 11 163 208 239 316 360 391 437 467 12 129 167 191 231 255 292 316 355 13 103 x 00 1 ^4 1 207 258 291 FEE' 14 R9. (j^> 1 9^^ 1 1.00 169 1 Q7 212 241 15 64 90 101 128 138 163 174 200 211 16 73 82 105 113 136 144 167 175 17 60 66 87 93 113 118 139 145 <: 18 52 71 75 93 97 116 120 CO 19 41 58 61 77 79 97 99 20 31 47 48 63 64 80 81 21 38 0 / 51 51 65 65 22 29 28 41 39 53 52 23 32 29 42 40 24 32 29 25 B. M.= ' 10 54 TRUSSED2C0NCRE TE S TEELJCOMPAN Y Showing Floor Plan and Typical Slab Construction Anderson Carriage Co. Detroit, Mich. Geo. D. Mason, Architect. 55 KAHN SYSTEM OF REINFORCED CONCRETE SAFE LIVE LOAD PER SQUARE FOOT FOR HOLLOW TILE FLOORS OF VARIOUS THICKNESSES Reinforced with ¥2" x IV2" and W x 2^^" Kahn Trussed Bars Spaced Alternately Tile+ Concrete (D +-» Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Tile+ Concrete Depth TileH- Concr CO ' CO 00 1— ( 0 Weight of Floor in Pounds Per Sq. Foot 51 49 60 59 71 70 82 80 92 Spacing 17" r to r. ^> 7 446 544 635 734 821 921 1008 1109 1196 Q 329 405 472 548 612 689 753 830 894 9 250 310 361 421 469 529 577 639 687 10 193 242 280 330 366 416 452 503 539 11 151 191 222 262 290 331 359 402 430 w 12 13 119 94 153 123 177 142 211 171 233 188 267 217 289 234 325 265 346 281 14 74 99 114 139 152 178 191 217 230 15 58 80 92 114 123 146 155 179 188 < 16 65 74 93 100 120 127 148 155 17 18 51 59 46 76 61 80 64 98 80 103 83 122 100 126 103 19 35 49 50 64 66 81 83 20 38 38 51 52 66 66 21 29 28 40 39 52 51 22 30 28 40 38 23 30 27 B. M.=jo- 56 TRUSSED CON CRETE STEEL COMPANY 57 KAHN SYSTEM OF REINFORCED CONCRETE EXPLANATION OF TABLES OF SAFE LOADS FOR KAHN BAR BEAMS. The tables for beams on pages 59 to 63 give the loads which a beam will safely carry, distributed uniformly over its length. These loads include the weight of the beams, which must be deducted in order to arrive at the net load which the beam will carry. The carrying capacity in this table is based on beams 1^1. freely supported at the ends that is, B. M. — . In building 8 construction it is usual to take advantage of continuous action and to provide reinforcement at the top of the beam over the support. For beams continuous at both ends the bending moment at the io\ center of the span may be taken ^s-j^ in which case the safe loads as given in the tables should be increased 25 per cent. Where the area of the steel reinforcement exceeds 1 per cent, of the area of the concrete above the steel the beam must be made of T section. This can readily be done by using table on page (29) for ratio of width of T to width of beam. For beams carrying plastered ceilings it is found by experience that their depth should be at least 1-15 of the clear span. Where this limit is exceeded there is danger of the ceiling cracking. These tables show the sizes of beams to which the various section of Kahn Bars are adopted. For loadings that exceed those given in the table, one or more bars are added to the beam. The widths of beams shown are sufiicient to accommodate a center bar, but where more than one bar is added the width of beam must be increased. Um'Uvi: 'FINI5NED FLOOR ^PLA3TER KAhN BAR3-' Kahn Reinforced Hollow Tile Floor Construction . 58 TRUSSED CONCRETE STEEL COMPANY SAFE TOTAL LOAD IN HUNDREDS OF POUNDS UNIFORMLY DISTRIBUTED FOR CONCRETE BEAMS Reinforced with Two 3^" x 2^\" Kahn Trussed Bars Area = 1,58 sq, in. Qp A N DEPTH IN INCHES (D) IN FEET 8 10 12 14 16 18 6 169 217 266 314 362 411 7 1 rtcJ 186 228 269 310 352 Q o 1 27 163 199 236 272 308 Q J -L 1 O 145 177 209 242 274 10 101 130 159 188 217 246 11 119 145 171 198 224 12 109 133 157 181 205 1 o 123 145 167 190 14 114 135 155 176 15 106 126 145 164 16 118 136 154 17 111 128 145 18 121 137 19 114 130 20 109 123 21 117 22 112 NOTE:— Make Beam of T Section. 7)=Total depth of Beam in inches. NOTE: — For loads above heavy Hne beam must be reinforced ^ for shear. 8" V2 59 KAHN SYSTEM OF REINFORCED CONCRETE SAFE TOTAL LOADS IN HUNDREDS OF POUNDS UNIFORMLY DISTRIBUTED FOR CONCRETE BEAMS Reinforced with Two Area : 1 X 3 Kahn Trussed Bars. = 2.82 sq. in. SPAN DEPTH IN INCHES (D) IN FEET 12 14 16 18 22 24 26 30 12 216 259 302 345 388 431 474 517 560 603 13 199 239 278 318 358 398 438 477 517 557 14 185 222 259 296 332 370 406 443 480 517 15 172 207 241 276 310 345 379 414 448 483 16 194 226 259 291 323 356 388 420 453 17 182 213 244 274 304 335 365 396 426 18 172 201 230 258 287 316 345 374 402 19 190 218 245 272 300 327 354 381 20 181 207 233 258 284 310 336 362 21 197 222 246 271 295 320 345 22 188 212 235 259 282 305 329 23 202 225 94-7 270 292 315 24 194 216 9*^7 258 280 302 25 186 907 99^ 248 269 290 26 1 QQ 91 Q 239 258 278 27 191 211 230 249 268 28 203 221 240 258 29 196 214 232 250 30 189 207 224 241 31 200 217 233 32 194 210 226 33 204 219 34 198 213 35 192 207 36 201 37 196 g NOTE:— Make Beam of T Section, f B.M.= ^ Z)=Total depth of Beam in inches. NOTE: — For loads above heavy line beam must be reinforced for shear. -10- 60 TRUSSED CONCRETE STEEL COMPANY SAFE TOTAL LOADS IN HUNDREDS OF POUNDS UNIFORMLY DISTRIBUTED FOR CONCRETE BEAMS Reinforced with Two x 2W Kahn Trussed Bars. Area=4 sq. in. SPAN DEPTH IN INCHES {D) IN 1 FEET 16 18 20 22 24 26 28 30 32 34 - ■ ■ 16 321 367 413 459 504 550 596 642 688 734 17 302 345' 389 432 475 518 561 604 647 690 18 285 326 oD / 408 448 489 530 571 612 652 19 270 309 o"±o ooD 425 463 502 541 579 618 20 257 294 QA7 oD / 404 440 477 514 550 587 21 280 A oi'± 384 A1 Q 454 489 524 559 22 267 300 334 367 400 434 467 500 534 23 287 319 351 383 415 447 479 510 24 275 306 336 367 398 428 459 489 25 264 294 323 352 382 411 440 470 26 282 310 339 367 395 423 452 27 272 299 326 353 380 408 435 28 288 314 341 361 393 419 29 278 304 329 354 380 405 30 269 294 318 342 367 391 NOTE:— Make Beam of T Section. D = Total depth of Beam in inches. B.M.= I - NOTE: — For loads above heavy Hne beam must be rein- forced for shear. 61 KAHN SYSTEM OF REINFORCED CONCRETE SAFE TOTAL LOADS IN HUNDREDS OF POUNDS UNIFORMLY DISTRIBUTED FOR CONCRETE BEAMS Reinforced with Two 2 x 3V2" Kahn Trussed Bars Area=6 sq. in. Span DEPTH IN INCHES (D) in Feet 18 20 22 24 26 28 30 12 13 14 15 16 17 18 19 20 734 677 629 587 550 518 489 440 oZD / DZ 708 660 619 583 550 521 495 Q1 7 QA7 o4 / 786 734 688 648 612 579 550 1 noQ iuuy QQ1 865 807 757 712 673 637 605 1 iUl lUio 944 881 826 777 734 695 660 I iy 0 I I ni 1022 954 894 842 795 753 716 1284 1185 1101 1027 963 907 856 811 771 21 419 472 524 577 629 681 734 22 23 400 450 431 500 479 550 526 600 574 650 622 701 670 24 413 459 505 550 596 642 25 396 440 484 528 572 616 26 423 466 508 550 593 27 408 448 489 530 571 28 29 30 31 32 33 34 35 36 37 432 404 472 440 426 413 511 ^y 0 477 462 447 434 421 409 550 531 514 497 482 467 453 440 428 417 NOTE:— Make Beam of T Section. jr)=Total depth of Beam in inches. Note : — For loads above heavy line beam must be reinforced for shear. f f > • u f 62 TRUSSED CONCRETE STEEL COMPANY SAFE LOADS FOR REINFORCED CONCRETE COLUMNS Size of Stress per sq. in. (0) on concrete in lbs. Columns Kahn Bars 300 350 400 500 600 10x10 4u KxiK 36900 43000 49200 61500 73800 12x12 4u Kxl>^ 50100 58400 66800 83500 100200 12x12 4u > // y2 ^ Ya 0 // 2 353500 22 18" 6 " square IX 319100 oo // 22 18" 8 Y" square y2 X . 14 0 // z 350900 22 " 18" 8 5^ " square 72 ^ X 14 IX 389800 24" 20" 6 % " square 1^ " X y 0 // 2 425100 24" 20" 6 % " square M X X A 1 / // IX 388800 24" 20" 8 % " square A / // \ / // 72 ^ 74 0 // 2 424100 24" 20" 8 " square 1 / // \ / // 72 ^ /a IX''- 448900 26 " 22 " 8 ^4 " square ^ / // ^ \ / // y2 X X 0 // 2 487800 26 " 22 " 8 y " square ^ / // ^ T > // H X X It/// IX 460700 26" 22" 10 " square ^ / // T / // 0 // z 499600 26" 22" 10 " square ^ / // ^ / // 3^ X X It//' -L72 530800 28" 24" 8 n / ft „„„ J/g square 3^ X X 0 // 2 573200 28" 24" 8 square 34 X X 1 T / // IX 525500 28" 24" 10 y^ " square 0 // 2 567900 28" 24" 10 " square ly" 619900 oU ZD Q o 1 " square i X /4 A " 665800 30" 26" 8 ] " square l"xM'' 3 " 616300 30" 26" 10 " square l"xM'' 4 " 662200 30" 26" 10 % " square l"x 1^" 3 " 694200 32" 28" 8 1 " square l"x M'' 4 " 743600 32" 28" 8 1 ^' square l"x M'' 3 " 690600 32" 28" 10 % " square l"x X'' 4 " 740000 32" 28" 10 J/g " square l"xM'' 3 " 795400 34" 30" 8 1 " square l"xX'' 4 " 848400 34" 30" 8 \y^" square l"xM'' 3 " 794100 34" 30" 10 1 " square l"x 3^" 4 " 847100 34" 30" 10 1 " square l"xX'' 3 " 64 TRUSSED CONCRETE STEEL COMPANY FOOTING TABLES The tables given on pages 66 to 70 are for square footings. Soil values from 1 to 5 tons have been assumed, and the footings figured for column loads from 75,000 pounds to 600,000 pounds varving by 25,000 pounds. Typical Column Footing Plan. The tables show the total num- ber of Kahn Bars required in each footing, half the number shown being placed in each direction. The footing tables are figured for a depth of footing slab equal to one-fifth the width. The cap at the foot of the column is to have a projection "c" from the face of the column of 6'' for columns less than 24'' in least diameter and 8'' where the column is 24'' and over. The depth of the cap should be twice this projection. 1 t^uu wx Typical Column Detail Typical Column Footing Elevation 65 KAHN SYSTEM OF REINFORCED CONCRETE TABLE OF FOOTINGS Soil Value per Sq. Foot 2000 Pounds 2500 Pounds Load on Footing Size of Footing Kahn Trussed Bars Size of Footing Kahn Trussed Bars 75000 6'3'' sq. 5'6'' sq. 10-K''x2iV 100000 7,3,, . 12- 6^6^' 12- 125000 14- 7,3/, a 14- 150000 16- 7,9,, a 16- 175000 12-1^x3'' g,g// a 18- 200000 WO'' " 14 g,Q// a 12-rx3'' 225000 18- " grg// a 14- 250000 ir3'' " 20- " 1Q,Q// a 18- " 275000 20- " ^Q,g// a 20- " 300000 12^3'^ " 22- iro'^ " 20- " 325000 12^9'^ " 22- ir6'' " 22- 350000 J 3,3,, a 22- " ir9'' 22- 375000 24- 12'3'' " 22- 400000 14'0'' " 24- 24- 425000 26- " 13'0'' " 24- 450000 15'0^' " 28- 13'6'' " 26- 475000 15^6^' " 28- " J 3,9// a 28- " 500000 15'9'' " 30- " J 4, 3,/ a 28- " 525000 16'3^' u 30- " 30- " 550000 16'9'' " 32- 14^9// " 30- 575000 jy/Q// a 32- 15'3'' 32- " 600000 ^7,3,, a 34- " 15'6'' " 32- 66 TRUSSED CONCRETE STEEL COMPANY TABLE OF FOOTINGS Soil Value per Sq. Foot 3000 4000 Load on Footing Size of Kahn Trussed Bars . Size of H c\r\\ y n rr Kahn Trussed 75000 5'0'' sq. 10-K^'x2i^6^' 4'6'' sq. 8-K"x2iV' 100000 12- " 5'0^^ " 10- 125000 14- 12- 150000 16- g,3„ u 14- 175000 18- g/g,, u 16- 200000 3,3,, u 18- " yr3„ u 18- 225000 grg/, » 14-1^x3'^ 18- 250000 grgv u 14- 3,Q,/ u 14-1^x3'^ 275000 g,g,/ . 16- 14- 300000 18- 3,g„ u 16- 325000 20- " g,Q„ u 16_ " 350000 jQrg,, u 22- g,g/, u 16- 375000 ir3'^ " 22- g,g„ u 18_ " 400000 IIT/ " 22- 20- " 425000 12^0'' " 24- " ^Q,3„ u 22- 450000 12'3'' " 26- " ^grg/r a 24- " 475000 26- iro'' " 24- 500000 28- " irs'' " 26- " 525000 ^3,3,, a 28- " ir6'' " 26- " 550000 13'6'' " 30- " ir9'' " 28- " 575000 13'9'' - 32- " 12^0'' " 28- 600000 14/3,, u 32- " 12'3'' " 30- " 67 KAHN SYSTEM OF REINFORCED CONCRETE TABLE OF FOOTINGS Soil Value per Sq. Foot 5000 Pounds 6000 Pounds Load on Footing Size of Th^ooI"! ti or Kahn Trussed Bars Size of Kahn Trussed Bars 75000 '± u bq. I9_iyvl I//' 100000 Tb 0 oq. 125000 o u 1 9- " 1 0- " 150000 o u 0 u 175000 u u 1 4— " 0 u 1 4._ " 200000 a. raft u u u 1 ft— " 1 4— " 225000 U i7 10 u 0 1 fi- " 1 U 250000 7/0// U 90- " u u 1 0 275000 / 0 90- " D y 90— " 300000 7/Q// « 1 1^ — 1 AO 7/0// « 1 AO 325000 0 U / 0 14. " i'i— 350000 0//?// " 0 0 1 4.— " 375000 0 XJ 1 f^— " 0 U 1 4— " 400000 16- g/3,/ « 14- " 425000 g/3// u 16- g/g// « 16- 450000 18- " g/g,/ u 18- " 475000 g/g,, u 18- " g/Q// « 18- " 500000 22- " g,3// u 18- " 525000 10' 3'' " 24- g/g// u 20- " 550000 10'6'' " 24- " g/g// « 22- " 575000 10'9'' " 26- " g/g,/ « 22- " 600000 iro'' " 28- " lO'O" " 24- " 68 TRUSSED CONCRETE STEEL COMPANY TABLE OF FOOTINGS Soil Value per Sq. Foot 7000 Pounds 8000 Pounds Load on Footing Size of Footing Kahn Trussed Bars Size of Footing Kahn Trussed Bars 100000 4'0'' sq. 14->^"xl>^'' 125000 4,3,/ u 10-K''x2A'' 4'0'' sq. 150000 12- 4/5// - 175000 5^0'' " 12- 4'9'' " 12- 200000 5'6'' " 14- 5'0'' " 12- 225000 5^9'' " 16- 5'6'' " 16- 250000 16- 5'9'' " 16- 275000 18- 16- 300000 18- 6' 3" " 18- 325000 g/g// u 20- 18- 350000 20- grg,/ u 20- 375000 12-r'x3'' 20- 400000 12- y/Q// U 20- 425000 y/g// u 14- 7^3'' " 12-l"x3'' 450000 16- 7'6'' " 14- 475000 8'3" " 16- 7'9'' " 14- 500000 16- " 16- " 525000 g,g„ u 18- " 8'3'' " 16- 550000 g,Q,r . 18- g,3/, u 16- " 575000 g,Q,/ u 18- " g,g„ u 18- " 600000 9' 3" " 20- " g,g„ w 18- " 69 KAHN SYSTEM OF REINFORCED CONCRETE TABLE OF FOOTINGS Soil Value per Sq. Foot 9000 Pounds 10,000 Pounds Load on Footing Size of Footing Kahn Trussed Bars Size of Footing Kahn Trussed Bars 1 0\J\J\J\J sq. 10-K"x2ry' 4'0'' sq. 14-K''xlK'' 1 4 0\J\J\J 12- " 4,3,, u 12-K''x2A'' 900000 4/9,, u 12- " 4^5// " 10- " 99p;ooo 5'0'' " 14- " 4,9,/ u 12- " 9^0000 14- 5'0'' 14- " 97^000 5'6'' " 14- 5'3^ " 14- QOOOOO 5^9^' " 16- 5'6'' " 14- " Q9f;000 16- 5'9'' " 16- Qc^OOOO 16- 16- " •^7^000 18- " 5,3,/ u 16- 400000 grg// " 18- " g,3„ u 16- " 49Pi000 20- " 6'6" " 18- " /t^iOOOO 20- " 18- " 47^^000 14-1^x3'' 20- " 500000 14- " 20- 525000 y/g// u 16- 7,3,/ u 14-^x3'' 550000 16- " 7'6'' " 14- " 575000 16- 14- " 600000 3,3,, u 18- " 7'9'' " 16- " 70 rm SSEl) CONCRETE STEEL COMPANY Coal Bin. Diamond Crystal Salt Co., St. Clair, Mich. Weil & Shaw, Engineers. James O 'Sullivan, Contractor. 71 KAHN SYSTEM OF REINFORCED CONCRETE EXPLANATION OF TABLES FOR BIN DESIGN. These tables are taken from: *^Some Formulae and Tables for Bin Designing." R. W. DULL, M. E. Engineering News, Vol. LII, No. 3, July 21, 1904. See above article for complete discussion of the theory on which these tables are based. 0 = angle of repose of material. 0 ' = angle of friction between material and bin-wall = angle between direction of thrust and normal to bin-wall. P = total thrust against bin- wall. N = horizontal component of P. ^ = angle of slope of surface of material. TABLES OF PRESSURES ON VERTICAL BIN-WALLS. See page 73 Column 1 gives the normal component of the total pressure on the (vertical) side, when the surface of the material is level. N =( Cose y ^^^^^ ^ _ / sin (e + oQsino Column 2 gives the pressure against the vertical plane A B, when angle of friction is not considered, i. e., 0' = 0 Column 3 gives the normal component of total pressure on the vertical side when the surface of the material is surcharged to the angle of repose, and the bin is unlimited in horizontal extent. N = Cos^ 0 -j- Column 4 gives the same as Column 3, but for the case where friction is neglected, i. e.y 0' =0 E — 0. P = cos 0 -TT Column 5 gives the normal component of the total pressure on the vertical side when the material slopes downward along the angle of repose, i. e., 0' = 0 N = ( where n J sin (0 + 0-) sin {0 + E) . Vn+1/ 2 \ COS0' cos^; Column 6 gives the same as Column 5, but for the case where friction is neglected, i.e., 0' =0. 72 TRUSSED CONCRETE STEEL COMPANY TOTAL PRESSURE FOR DEPTH *7^" FOR BITUMINOUS COAL IN VERTICAL BINS Wt. per Cu. Ft.=50 lbs. Angle of repose=o=35 . NOTE:- -THESE PRESSURES ARE FOR A SECTION OF MATERIAL ONE FOOT WIDE CD 1 3 1 4 5 6 )th in h h \- V 1 f h 1 y [ 1 t id a; Q 0' = -18° 0' = =o =0 =0 E =0 E==0 1 6 7 17 20 4 5 2 23 97 67 82 17 20 3 52 D 1 1 ^^ 1 8zl 38 46 4 93 1 08 lUo ^Oo oZo 68 82 5 146 1 AQ 4-1 Q 0 i O 107 128 6 209 DUO 7QS 156 184 7 286 ooo 1 1 OO ^ 209 257 8 373 1 079 1 9 i oi Z 273 328 9 472 1 'X^l 1 oO / iOD i 346 415 10 583 D / O 1675 2050 427 513 11 705 817 2027 2481 516 615 12 840 972 2412 2952 615 738 13 985 1141 2831 3465 722 866 14 1143 1323 3283 4018 838 1005 15 1312 1519 3769 4613 960 1152 16 1492 1728 4288 5248 1093 1311 17 1685 1951 4841 5945 1232 1480 18 18 89 2187 5427 6642 1382 1660 19 2105 2437 6047 7400 1541 1852 20 2332 2700 6700 8200 1708 2052 21 2571 2977 7387 9041 1883 2262 22 2821 3267 8102 9922 2067 2483 23 3084 3571 8861 10845 2259 2560 24 3358 3888 9648 11808 2460 2810 25 3644 4219 10469 12813 2669 3206 26 3941 4563 11323 13858 2887 3468 27 4250 4923 12211 14945 3113 3740 28 4570 5292 13142 16072 3348 4022 29 4903 5677 14087 17241 3591 4314 30 5247 6075 15075 18450 3843 4617 73 KAHN SYSTEM OF REINFORCED CONCRETE TOTAL PRESSURE FOR DEPTH '/^" FOR ANTHRACITE COAL IN VERTICAL BINS Wt. per Cu. Ft. =52 Lbs. Angle of Repose=0=27" NOTE— THESE PRESSURES ARE FOR A SECTION OF MATERIAL ONE FOOT WIDE Depth in Feet 1 2 3 4 5 6 A i__ A T r~ h y T B 16° 0' = =o° = 0 -0 = 0 E^ = 0 1 8 10 20 23 6 8 2 33 39 82 93 25 31 3 75 88 184 209 57 69 4 134 1 ^fi ± 0\J 328 371 102 122 5 210 244 513 579 159 191 6 302 351 738 834 230 267 7 411 1005 1135 313 374 8 536 1312 1482 402 489 9 680 790 1661 1876 517 619 10 839 975 2050 2317 638 764 11 1014 1180 2481 2802 773 925 12 1209 1405 2952 3340 920 1100 1 Q 1 0 1418 1648 3465 oy io 1080 1290 14 1643 1910 4018 4540 1250 1497 15 1887 2193 4613 5220 1436 1720 16 2145 2500 5248 5930 1636 1953 17 2421 2808 5945 6696 1845 2207 18 2718 3160 6642 7507 2064 2471 19 3030 3521 7400 8363 2310 2758 20 3350 3902 8200 9268 2554 3053 21 3700 4303 9041 10218 2820 3372 22 4061 4718 9922 11214 3086 3701 23 4438 5156 10845 12257 3372 4040 24 4833 5611 11808 13346 3680 4398 25 5244 6097 12813 14481 3985 4770 26 5672 6600 13858 15663 4521 5160 27 6116 7112 14945 16891 4650 5560 28 6578 7638 16072 18165 5000 5979 29 7056 8202 17241 19486 5370 6421 30 7551 8775 18450 20853 5742 6880 74 TRUSSED CONCRETE STEEL COMPANY Cross Section Retaining Wall for Broadway Warehouse, Cleveland, Ohio. W. Kingsley, Architect. Masters & Mullen, Contractors. NOTE: — This building is eight stories high but only four floors show above the street level at the front. The retaining wall is 20 feet high from the footing level to the second floor level, the face being on the building line. The third floor is excavated under the sidewalk to the curb line with a second 20 foot retaining wall running to the pavement. The lower wall is 16 inches thick at the bottom, 10 inches at the top with the upper wall 14 and 8 inches. 75 KAHN SYSTEM OF REINFORCED CONCRETE EARTH PRESSURES Angle of Repose = 0 = 33 Degrees Depth Total Inclined Press. Total Hor. Press. Hor. Press, per Sq. Foot Depth Total Inclined Press. Total * Hor. Press. Hor. Press, per Sq. Foot 5 335 280 112 23 7080 5935 516 480 135 24 7710 6460 538 7 655 OOVJ 157 25 8365 7015 561 8 855 720 180 26 9045 7585 583 9 1085 910 202 27 9755 8180 606 10 1340 1120 224 28 10490 8800 628 11 1620 1355 246 29 11255 9435 650 12 1930 1615 269 30 12040 10100 673 13 2260 1895 291 31 12860 10780 696 14 2625 2200 314 32 13700 11490 718 15 3010 2525 337 33 14705 12220 741 16 3425 2870 359 34 15455 12960 763 17 3865 3245 381 35 16390 13745 785 18 4335 3635 404 36 17340 14540 808 19 4830 4050 426 37 18315 15360 830 20 5350 4490 449 38 19275 16200 853 21 5900 4950 471 39 20350 17065 875 22 6475 5430 493 40 21410 17950 896 Earth Level. coseeh'^ Total Inclined Pressure = 2(1 -f sine v^2)^ ~ .1338 eh' Total Hor. Pressure = 11.22 /i^ acting at depth = Note : e = 100 lb. per cu. ft. ; h = Depth 76 TRUSSED CONCRETE STEEL COMPANY GRAIN PRESSURES IN DEEP BINS The pressures existing in full sized grain bins were investigated by Mr. J. A. Jamieson in 1903 and a very complete report of this inves- tigation was published in the "Engineering News," March 10, 1904. Grain in this country is usually stored in deep bins, and it has long been known that in these deep bins there is a head or depth of grain, which, were the grain a liquid, would produce enormous bursting pressures. The actual pressures recorded by Mr. Jamieson permits us at once to draw a curve showing the ratio of observed grain pressure to a corresponding liquid pressure supposing the bin to be filled to the same depth with a liquid of the same weight per cubit foot as the grain. Such a curve is drawn on page 78. The ratio is shown as values of K for different values of h b It should be noted from Mr. Jamieson's tests that the pressures were somewhat increased when grain was running out of the bin and also that by tapping the sides of the model bins an increased pressure of 20 per cent, was obtained. The presence of moisture will also have considerable influence. For these reasons it is recommended that a factor of safety of six be used in designing grain bins. Example — Let it be required to find the vertical and horizontal pressures at the bottom of a bin lO'O'' square and 40'0'' high, h b=^- From the curve K=.149. Side pressure=KWh=.149 x 50 x 40=298 pounds per square foot. Bottom pressure= 1.667 KWh=: 1.667 x side pressure=497 pounds per square foot. Vertical load carried by side walls=200,000— (497 x 100)= 150,300 pounds. 77 KAHN SYSTEM OF REINFORCED CONCRETE WHEAT PRESSURES IN GRAIN BINS, ao i I I I I I I I I I I I I I I O i I I I I I I I I I I I I I 1 I i I I ~r-| 1 23456789 lO Values of ~ b Derived from experiments and formulae) by J. A. Jamieson in Eng. News, 3-10-'04. Angle of repose^28°. Coeff. of friction=41667. Lat. Pres. =0.6 Vert. Pres. H=height or depth of grain. h=side of sq. bin or least width of rect. bin. K^Ratio of actual grain pressure to liquid pressure. ]V=weight of wheat=50 lbs. per cu. ft. Side pressure per sq. ft. =KWh. Bottom pressure at any depth =1.667 KWh. Max. bottom pressure occurs when ^ + 3.5 Max. bottom pressure per sq. ft=Wb. TRUSSED CONCRETE STEEL COMPANY ALLOWABLE FLOOR LOADS IN ACCORDANCE WITH THE BUILDING LAWS OF VARIOUS CITIES LIVE LOADS FOR FLOORS IN DIFFERENT CLASSES OF BUILDINGS EXCLU- SIVE OF THE WEIGHT OF THE MATERIALS OF CONSTRUCTION. New York 1902 Chicago 1902 Phila- delphia 1902 Boston 1902 San Francisco 1906 Pounds per Square Foot Dwellings, Apartment Houses, TT i. 1 rj^ J. TT Hotels, lenement Houses or Lodging Houses 60 40 7U K A A A Omce Buildings, 1st J^loor 150 lUU lUU 1 AA 1 KA loU fir* T* "II" Al -11 TM Omce Buildings, Above Istlloor 75 100 100 100 75 Schools or Places of Instruction 75 80 75 Stables or Carriage Houses 75 40* loot 75 Buildings for Public Assembly 90 100 120 150 125 Buildings for ordinary stores, light manufacturing and light storage 120 100 120 120 Stores for Heavy Materials, Warehouses and Factories 150 150 250 250 Roofs — Pitch less than 20 degrees 50 25 30 2511 50 Roofs — Pitch more than 20 degrees 30 25 30 251[ 30 Sidewalks 300 300 Public Buildings Except Schools 150 * Stables less than 500 square feet in Area, t Stables over 500 square feet in Area. ^ Make proper allowance for wind at 30 lbs. per square foot hor. 79 KAHN SYSTEM OF REINFORCED CONCRETE DIGEST OF BUILD- ING LAWS GOVERN- ING REINFORCED CUIN L^KCj 1 1^. New York Cleveland San Francisco Buffalo Toronto Prussian • Requirements Katio or Modulus oi r^las- ticity of Steel to Concrete 12 15 15 12 12 Tensile Stress in Steel 16000 16000 ^EL 16000 16000 17000 Compressive Stress in Steel 12000 10000 12000 Shearing Stress in Steel 10000 10000 10000 10000 Extreme Fibre Stress on Concrete in Compression 500 * 500 500 500 500 Concrete in Direct Compression 350 * 400 t 450 350 350 Tensile Stress in Concrete 0 0 0 0 0 0 fenearmg btress in Concrete 50 50 75 50 50 64 Bending Moment in Beam Continuous ^wl -g- wl ~wl Bending Moment in Slabs Continuous Bending Moment in Square Floor Panels ^wl ^wl -^wl Method of Calculation S. L. S. L.^ S. L. S. L. S.L. S.L. 1 -bection Amount Allowed as part of Beam 10 h 6 h 5 t 10 h 5b Columns-Maximum Ratio of Height to Width 12 16 15 16 12 18 Requirements of Tests SL SL 2L SL SL 2L+D NOTE:— S. L. = Straight Line Formula. h = Breadth of Beam, t = Thickness of Slab. w = Total Uniformly Distributed Load. / = Length of Beam. U = Ultimate. L = Live Load. D — Dead Load. E L = Elastic Limit. t Hooped Columns— 700 lb. * 600 lb. If tests show factor of safety of 5 in ninety days. 80 TRUSSED CONCRETE STEEL COMPANY REINFORCED CONCRETE BRIDGES Reinforced concrete bridges are built of various types depend- ing on the length of span, the amount of loading, and the require- ments of the particular locations. Flat slabs or plates spanning directly between the abutments without any supporting beams are used over small openings. On longer spans the girder bridge with comparatively thin concrete floor slab is used. The cantilever bridge is a variation of the girder design in which the loads are carried by cantilever action over the support instead of as a simple beam. The arch bridge is employed in long spans and is built in the form of a continuous section arch ring or merely a rib. Bridges of all these types have been built extensively for highway, electric car and railway traffic. HIGHWAY BOX CULVERTS AND GIRDER BRIDGES Flat slabs or culverts resting directly on the abutments are employed in spans of from 4 to 16 feet. The construction is simple and can be readily installed. Either of the two smaller sizes of Kahn trussed bars are used for reinforcement, and these bars are given a bearing of from 6 to 12 inches on the abutments. To take care of temperature and shrinkage stresses, small round rods are placed over and at right angles to the Kahn bars. On page 84 is given the tabulated design for various spans, computed for heavy highway loadings. Girder bridges are most often used in spans of from 12 to 50 feet, although spans as great as 70 feet have been built in this way. The design usually consists of a reinforced slab supported by girders projecting underneath. Many bridges have been built, however, in which the girders are extended above the floor to form a hand rail on either side of the roadway. The floor slab would then span directly the width of the roadway between these girder rails. The cantilever bridge is built for longer spans than the girder bridge. The secret of its great carrying capacity lies in its great depth at the abutment. At the center of the span, the girder is shallow giving ample headroom where required. The cantilever design should not be confused with an arch as there is no thrust and the reactions are all vertical. The hand rail or balustrade for the concrete bridge can be built of reinforced concrete, ornamental iron, or plain gas pipe as desired. The experienced builder knows that there is no class of structure subjected to such severe conditions of loadings and 81 KAHN SYSTEM OF REINFORCED CONCRETE TRUSSED CONCRETE STEEL COMPANY rough iisuage as a bridge. Therefore, only the best concrete should be used and this concrete must be reinforced for the severe stresses coming upon it. The shearing stresses are very great due to heavy moving loads and shear reinforcement must be provided. This shear reinforcement should be rigidly attached to the main tension member. The adhesion of the concrete cannot be de- pended upon. The bond between the concrete and steel is com- pletely destroyed by the repeated loading and unloading of the stress in the steel.* That the Kahn trussed bars are especially suited for such work is evident. On page 85 is given a table for the design of girder bridges covering spans from 12 to 40^ The width of roadway is taken as 16', the standard for the country highway bridge. Where the width of roadway varies from this, the design can be revised to meet the new conditions. Showing Application of Kahn Trussed Bar to Culvert Construction. *See "The Fatigue of Concrete" by I. D. Van Ornum, M. A. S. C. E, Proceedings A. S. C. E. Dec. 1906. 83 KAHN SYSTEM OF REINFORCED CONCRETE Slab Highway Bridges or Culverts 70 Cross Section Live Load — 15 Ton Roller or 100 pounds per sq. ft. wSPAN IN FEET Thickness of Slab .JCAHN BARS CUP-BARS SIZE SPACING SIZE spacing 4 6 >^''xlK'' \r 6 K'^xlK'' 8'' 2V 8 i' 12^' 2V 10 8" 10'' W 12 9 ir w 14 lO' 9'' Cup -Bars are placed over and at right angles to Kahn Bars. 84 TRUSSED CONCRETE STEEL COMPANY GIRDER HIGHWAY BRIDGES. Live Load — 15 Ton Roller or 100 pounds per sq. ft. 12 14 10 18 20 22 24 26 28 30 32 34 36 38 40 BEAM A SIZE 10''xl6'' 10''xl6'^ 10''xl8'' 12^^x18'' 12''x20'' 12''x22 12''x22'' 12''x26' 12''x28'' 12^'x30'' 14''x30'' 14''x32^' 14''x34'' 14''x36'' KAHN BARS STANDARD SHEARED SIZE r'x3'' iK"'x2K'' lK''x2K'' iK''x2K'' lX''x2K'' lK''x2K'' 2''x3K'' 2''x3K'' .2''x3K'' 2''x3>^'' CENTER SHEARED No. SIZE r'x3'' K''x2// r'x3'' r'x3'' ^''x2rV' r'x3'' r'x3'' K"x2,V r'x3'' BEAM B SIZE 12''xl6'' 12''xl6'' 12''xl8'^ 14''xl8'' 14''x20'' 14''x22'' 14''x22'' 14''x24'' 14''x26'' 16''x28'' 16''x30'' 16''x30'' 16^^x32'' 18^^x34'' 18''x36'' KAHN BARS STANDARD SHEARED No. SIZE r'x3'' r'x3'' r'x3^' \y^"y.2y^" 2"x?>y2" 2"xzy2" 2"xzy2" 2"y.Zy" 2"y.Zy" 2''x3K'' 2''x3>^'^ 2''x3K'' 2''x3>2"'' CENTER SHEARED No. 1 1 *1 1 1 1 1 1 1 1 1 2 3 2 2 SIZE K'^x2A'' r'x3'' \y"x2y" \y"x2y" \y"y.2y" r'x3'' 2''x3K'' 2''x3>^'' 2''x3K'' K''x2A'' y"x2-h" y"x2h" *Bars full length. FLOOR SLAB.— 6'' thick, reinforced with % "^.Xy * Kahn Bars, spaced 12'' c. to c. and Y^" Cup- Bars spaced 16" c. to c. 85 KAHN SYSTEM OF REINFORCED CONCRETE RAILROAD BOX CULVERTS Box culverts for railroad work are similar to highway culverts except that they must be built much heavier to carry the greatly increased loading coming upon them. The side walls are usually reinforced to withstand the earth pressure due to dead and live loads. If sufficient abutment is provided for this wall at the base, it may be designed as a simple slab supported at the top and bottom. In this way the walls can be greatly reduced in thickness over what would be required for a plain concrete wall. . The footings for culverts are determined by local conditions. It will often be found necessary to carry an inverted slab continuous between the side walls in order to provide ample bearing for the heavy loads coming on these foundations. Under such circum- stances this floor slab would be of the same strength as the cover slab, with the bars inverted in the top of the slab. The wing walls of culverts can be built of reinforced concrete, their design being the same as for an ordinary retaining wall. In the calculation of moments in culverts, a live load is assumed of 50,000 pounds on axles, 5 feet centers, 10,000 pounds per foot of track. This load may be taken as distributed uniformly over ties 8 feet long. The manner in which this live load will be dis- tributed when it reaches the culvert cover will depend on the nature of the overlying material. In this discussion it will be assumed that the line of zero stress in the enbankment due to live load is much more nearly vertical than the ordinary angle of repose of the material and it will be taken to follow a slope of 3^ to 1 . For a fill of less than 2 feet, the impact allowance should be 100 per cent.; between 2 feet and 4 feet, 75 per cent.; above four feet an allowance of 50 per cent, will be made. Let Pl =unit pressure on cover per sq. ft. due to live load. Pd = unit pressure on cover per sq. ft. due to dead load. Total load per lineal foot =10,000 pounds, adding 50 per cent, for impact. =15,000 pounds. Pd =100 h, p= ^Q^QQ _|_ __ ^Q^^i superimposed load per sq. ft. P = Pl +Pd 15,000 = Pl or Pl = 30,000 h + 16 on cover. 86 TRUSSED CONCRETE STEEL COMPANY COVERS FOR RAILWAY BOX CULVERTS Cooper's E 50 Loading H 0 - Fill / M in C Size of Kahn Bars Size of Kahn Bars pacing Inche ckne in I )paci Inc SPA IN FE M-l ckne in I 1— 1 1—1 .s Q Thi' i Slab 4 10 15 8 8 10.0 9.0 12 10 15 19 20 r'x3'' 8.5 7.5 20 9 9.5 20 22 7.5 25 9 8.0 25 23 lK''x2K'' 10.0 30 10 8.0 30 24 9.0 35 10 7.5 35 26 9.0 40 11 7.5 40 27 8.0 1 1 1 6 10 11 10.0 14 10 21 10.0 lo 1 1 8 . O 15 23 y . 5 20 12 8.5 20 25 9.0 25 13 8.0 25 27 12.0 30 13 7.0 30 28 12.0 35 14 7.0 35 29 11.0 40 15 6.5 40 32 11 .0 8 10 13 7.5 16 10 25 2''xSy" 13.5 15 14 6.5 15 26 12.5 20 15 11.0 20 28 11.5 25 16 10.5 25 30 11 .0 30 17 10.0 30 32 10.5 35 18 13.0 35 33 9.5 40 19 12.0 40 36 9.5 1 1 n lU 10 16 10. 0 18 10 28 2'^x3K'' 12.0 15 17 9.0 15 30 11.0 20 19 9.0 20 31 10.0 25 20 8.5 25 33 9.5 30 21 8.0 30 35 9.0 35 22 10.5 35 37 8.5 40 23 10.0 40 39 8.0 87 KAHN SYSTEM OF REINFORCED CONCRETE On page 87 will be found table of design of culvert tops of various spans and depth of fill, computed on the above basis. The design for side walls are determined by local conditions of soil, drainage, etc., and for this reason cannot be conveniently tabulated. When a floor slab is used continuous between side walls, its design is merely the invert of the culvert cover. ARCH BRIDGES The arch bridge of reinforced concrete is built either in the form of a continuous section arch ring, or as an arch rib. The reinforcement for arches is placed in two layers, one near the intrados, the other near the extrados with the diagonals interlacing. Attention is called to the perfect lattice girder effect produced by the interlacing of the diagonals, making the entire structure act as a monolith, under any condition of loading. The reinforce- ment being curved into an arch form, its first tendency when under stress is to straighten, and this will occur unless it is restrained from doing so by rigidly attached diagonals extending well into the concrete. This makes the Kahn Trussed Bar especially adaptable for work of this kind. The continuous section arch has the same thickness of rib throughout its width. The thickness is a minimum at the center increasing in thickness to a maximum at the abutments. It is frequently possible and advantageous to build these abutments hollow instead of a solid block of concrete. The hollow abutment consists of a series of buttresses carried down to a good foundation ana usually connected at the base by a thick reinforced slab. The earth fill between the buttresses tends to insure stability. As the strength of the arch is based on the immobility of its abutments, these abutments must be carefully designed and carried to a foundation of unquestioned value or founded on piles. Usually the earth fill is built directly on the arch ring. Occasionally in long spans, a complete superstructure of rein- forced^'concrete columns, girders and slabs is built on the arch ring to 'carry the roadway. The advantage of this design is the greatly reduced loading to be carried and the consequent reduction in the thickness of the arch ring. This is an important consider- ation in long span work. The arch rib design consisting of a series of ribs of rein- forced concrete is especially adapted for long span work and is usually built supporting a reinforced concrete superstructure. Otherwise these ribs may consist of a series of spandrel sections TRUSSED CONCRETE STEEL COMPANY with reinforced beams or slabs, spanning between the tops of them, such as the I^ake Park Bridge and the Nelson Street Viaduct. There is no doubt that the best guides to the design of arch bridges are existing structures that have proven satisfactory. The use of empirical formulae giving results that agree with current practice is therefore justifiable. One method of designing an arch giving approximate results, is to determine the crown thickness (C) by the use of an empirical formula: make the thickness of the ring at the quarter points equal from to l^C, and place steel near both intrados and extrados. The total net section of which is equal to of the area of the crown section of the arch ring. The following formula for crown thickness proposed by F. F. Weld, C. E., in Engineering Record, November 4th, 1905, based on a study of many existing arches and original designs is inserted for the use of those who do not care to make a more thorough investigation of the proposed arch. It will also be found useful in determining a trial arch ring for the more rigorous methods. C T T? C=^/s- 10 200 ' 400 C=Crown thickness in inches, >S=Clear span in feet, L=Live load per square foot, F=Weight of fill at crown per sq. ft. Among the more elaborate methods for determining the stresses in an arch without hinges may be mentioned the graphical, of which an excellent discussion is given in Prof. Cain's **Steel Concrete Arches & Domes," and also in a slightly modified form, in ^'Reinforced Concrete," by Chas. F. Marsh. The analytical method which follows is condensed from the chapter on "Parabolic Ribs with Fixed Ends," in Prof. Chas. E. Greene's "Trusses and Arches," Part III. 89 KAHN SYSTEM OF REINFORCED CONCRETE TYPICAL HIGHWAY ARCH BRIDGES Rise = Span CLEAR CROWN Thickness STEEL IN INTRADOS AND EXTRADOS Concrete in Arch Cu. Feet IN FEET JVclIill JJcirb Spacing Concrete in Abutments Cu. Feet 20 ^"X2j;\" 16" c. to c. 700 2000 30 10'' K''x2A" 14" " 1050 2800 40 12'' K"x2i3^" 12" " 1600 3400 50 13K'' l"x3" 18 " 2250 4000 60 15" l"x3" 16" " 3000 5000 70 16K" i xo iO 3800 6000 80 18" l"x3" 14" " 4800 7000 90 20" l"x3" 13" " 5800 8000 100 22" l"x3" 12" " 6900 9000 110 24" l"x3" 11" " 8200 10000 120 26" l"x3" 10" " 9500 11000 Note: — This table is designed for low arch bridges with a rise of 1-lOth of the span, a live load of 150 lbs. per square foot and a fill of not less than 12 inches. Width of roadway — 16'0" in the clear for all spans. Spandrel walls to be reinforced with ^ "x2 " Kahn Bars spaced 2'0" c. to c. Amounts of concrete in abutments are rough ap- proximations as local conditions govern. 90 TRUSSED CONCRETE STEEL COMPANY DESIGNS OF PARABOLIC ARCHES WITHOUT HINGES. Let the span be divided into ten equal panels and points of division numbered from one to nine. u'==load in pounds at point under consideration. c=one-half span (in feet), A'=rise of arch (in feet), m=ratio between load (w) and bending moment, taken from table, M=bending moment due to load at point under consideration =m c w. /i=ratio between load and thrust produced, taken from table. — indicates tension in extrados, + indicates tension in intradoes. In order to make plain this method of calculation, and the use of the table let it be assumed that it is desired to design a high- way bridge having a clear span of 60 feet and a rise of 6 feet to carry a live load of 100 pounds per sq. ft. The weight of the fill at the crown is assumed to be 200 pounds per sq. ft. Substituting these values in the empirical formula for crown thickness, gives 14.7''. SPAN TO BE DIVIDED INTO lO EQUAL PANEL5 1 1 \ ] 1 1 i r~ c J 91 KAHN SYSTEM OF REINFORCED CONCRETE ARCHES— TABLE No. 1 Parabolic Rib Fixed At Ends. Values Of "m" At Points. POSITION OF LOAD 'o 9 8 7 6 5 4 3 2 1 U + .022 + .064 + .095 -f .096 + .062 0 — .073 — .128 — .121 -1 i + .006 + .016 + .019 + .011 — .006 — .026 — .036 — .018 + .051 o — .005 — .017 — .031 — .040 — .037 — .017 + .028 + .107 + .028 6 — .012 — .035 — .054 — .056 — .031 + .026 + .119 + .048 + .011 A 4 —.013 —.037 —.050 —.037 + .012 + .104 + .036 + .004 _.002 5 .UiU — .uzu -j- .UiO -f- .uy4 —I- ni f\ 1 .UiD — .uzu .{JZi^ ni n .UlU 6 —.002 + .004 + .036 + .104 + .012 —.037 —.050 —.037 —.013 7 -h.oii + .048 + .119 + .026 —.031 —.056 —.054 —.035 —.012 8 + .028 + .107 + .028 —.017 —.037 —.040 —.031 —.017 —.005 9 + .051 —.018 —.036 — .026 —.006 + .011 + .019 + .016 + .006 10 .121 —.128 —.073 0 + .062 + .096 + .095 4- 099 VALUES OF "/^" FOR VARIOUS POSITIONS OF LOAD 'W 1 Points 1 9 8 7 6 5 4 3 2 1 .061 .192 .331 .432 .469 .432 .331 .192 .061 From Prof. C. E. Greene's 'Trusses and Arches. " Part III. 92 TRUSSED CONCRETE STEEL COMPANY Lay out the center line of the proposed arch for the given span and rise, divide it into ten equal parts, numbering them as shown in the figure. 60" 0" SPAN DIVIDED INTO 10 EQUAL PANELS 30 0- 30 'O"- In arch design it is customary to figure the loads and stresses for a section of the bridge one foot wide, for, having determined the necessary section on this basis, the bridge may be made as desired. This of course does not apply to bridges having arch ribs. Here the loads and stresses are determined for each rib. ARCHES— TABLE No. 2 Compute the loads that would come at each of these points for an arch ring one foot wide if the weight of the structure and fill were concen- trated at them, and tabulate as in table No. 2. O C 'o Weight i\rcn rC] Weigh Fill li fin O H 1 1800 6000 7800 2 1600 2400 4000 3 1400 1600 3000 4 1300 1300 2600 5 1200 1200 2400 6 1300 1300 2600 7 1400 1600 3000 8 1600 2400 4000 9 1800 6000 7800 To find the bending moment at any point, as No. 7 proceed as in table No. 3. (Continued on Page 95.) 93 KAHN SYSTEM OF REINFORCED CONCRETE TABLE No. 3 Moments and Thrusts in 60 Ft. Highway Arch — Section One Foot Wide. 1 2 3 — 4 5 6 7 8 9 10 11 12 13 Points c V K Values of Table 1 Dead Loads Live Load On Right Live Load On Left ' Values of "/i" 1 Table No. 1 Total W "S II 0 a u xn 0 H w, m.c.Wi W2 m.c.Wg W., M= m.c.W2 9 a u -f .011 7800 +2570 600 +200 .061 8400 8 ou A + .048 4000 +5760 600 + 860 .192 4600 4420 7 30 6 + .119 3000 + 10710 600 +2140 .331 3600 5960 6 30 6 + .026 2600 +2170 600 + 470 .432 3200 6910 5 30 6 —.031 2400 —2230 300 —280 300 —280 .469 3000 7030 4 30 6 —.056 2600 —4410 600 —1010 .432 3200 6910 3 30 6 —.054 3000 —4860 600 —970 .331 3600 5960 2 30 6 —.035 4000 —4200 600 —630 .192 4600 4420 1 30 6 —.012 7800 —2800 600 —220 .061 8400 2560 +2710 +3390 —3110 46730# +2710 +2710 +6100# — 400;^ Note : — Maximum positive moment at point No. 1= 6100 ft. lbs. Maximum negative moment at point No. 7= —400 ft. lbs. Maximum horizontal thrust of section considered=46730 lbs. 94 TRUSSED CONCRETE STEEL COMPANY In column No. 1 are the points in order. Column No. 4 contains the factors "m" found opposite No. 7 of table No. 1. The half span c and weights W, from table No. 2 are given in columns Nos. 2 and 5 opposite their respective points. The bending moment in foot pounds is given in column No. 6. The algebraic sum of these moments gives the bending moment at point 7 for the unloaded arch. The moments due to the live load are computed in the same way. If a street car loading is specified it may be reduced to an equivalent uniformly distributed load by means of the equivalent load diagram. The live load is usually assumed to extend from one abutment to the center of the span, but may be placed in such positions as would give the greatest stresses at the points under consideration if such loadings are likely to occur when the bridge is actually in use. For example, by an inspection of the signs of the co- efficients in table No. 1 it will be seen that for the maximum negative moments at point 7 the live load should not extend quite to the center of the span. The assumed live load of 100 pounds per sq. ft. extending from the right abutment to the center of the span gives a load of 600 pounds concentrated at each of the points 9, 8, 7 and 6 and 300 pounds at 5. These weights are entered in column 7 of table No. 3, '*m" and "c", remaining the same; column 8 gives the re- sulting moments. This sum added to the moment of the unloaded arches gives a total positive moment due to both dead and live loads at this point. The maximum negative moment is found by placing the live loads upon the other half of the bridge, as in columns 9 and 10, and taking the algebraic sum of the moments due to both live and dead loads. The necessary amount of steel reinforcement may be found by the formula RM — .86 a. d. s.,where — s — is allowed stress in steel, a— area of steel; d — distance from center of steel to opposite surface of arch rib, and R M — Resisting moment of section which must be at least equal to the bending moment produced by the loads. The steel is assumed to take only tension and the concrete only compression. Allowance should be made for the fact that there is no tension in the arch rib unless the line of action of the resultant thrust passes outside of the middle third of the section; in other words, unless M~H^d~6. The horizontal thrust is a maximum when the arch is fully loaded and is found by means of the factors given at the foot of table No. 1. The results are tabulated in the last 95 KAHN SYSTEM OF REINFORCED CONCRETE TRUSSED CONCRETE STEEL COMPANY three columns of table No. 3. The sum gives the maximum horizontal thrust exerted upon the abutments by the loaded arch. This combined graphically with the dead weight of the half span and fill gives a resultant thrust which is in turn combined with the weight of the abutment and superimposed earth. This hvtter resultant gives the amount and direction of the thrust of the abutment upon its foundation. In order that there may be no overturning tendency this resultant should pass within the middle third of the base. If the assumed abutment does not meet these conditions a new length of base should be assumed and the new position of the resultant determined. In case the arch ring is not parabolic in form, but does not depart widely from the parabola, this method of computation may be employed by determining a new span for the arch, which with the given rise will give the same area between the springing line and the neutral surface curve as- would be included between the same elements if the curve was a parabola, or recourse may be had to one of the graphical methods where the description of the curve is of less consequence. 97 KAHN SYSTEM OF REINFORCED CONCRETE NOTES REGARDING ERECTION [Note. — The following is a brief outline of construction methods. For detailed information see "Instructions to Superintendents", and "Specifi- cations for Reinforced Concrete Work", two booklets i)ublished by The Trussed Concrete Steel Co.] The erection of a reinforced structure is similar to the making of a casting in a large foundry. Forms or patterns are built to correspond exactly with the lines of the finished work, the reinforcing steel is set in place, and the concrete is poured into the forms. The whole structure is thus built as a monolith and moulded into the finished form. The concrete is allowed to set a requisite length of time, the forms are removed, and the building stands complete, — a structure carved, as it were, out of solid rock. It is thus seen that the erection work consists primarily of four distinct operations. 1st. The erection of the centering or false work. 2nd. The placing of the reinforcing steel. 3rd. The mixing and placing of the concrete, and 4th., the removal of the centering. ERECTION As the forms represent the mould from which the OF finished structure is made, great care is used to make CENTER- these exact and true to line. They are built rigid ING and thoroughly braced so as to bear the weight of the plastic concrete without deflection. In order to give a smooth ri4'-/Z'BATT£:NS -ABOUT z o oc 2'xQ'JOI5T5-to support SHCflTH/NO^ I'x/O'SHCflTH/NG 4"x4'0y£ff POSTS Zx4'6UPPdR T5 BOTTOM Of BEAM BOX POSTS TO BE BRACED IN BOTH DIRECTIONS Z\4'-NAILtD TO BATTEN ON BEAM BOX COLUMN SECTION finished surface planed boards are used, and corners of columns and beam boxes are chamfered. All joints are set closely together to make the forms fairly water tight. The steel is set accurately in place in accordance PLACING with detailed drawings prepared for that purpose STEEL and these drawings are followed explicitly. The Engineering Department of The Trussed Concrete Steel Co. prepares such drawings for work in which the Kahn 98 TRUSSED CONCRETE STEEL COMPANY Trussed Bars are used, when desired by, and without charge to the client. Only the best materials are used for the concrete, MIXING and these are thoroughly mixed of the proper pro- AND portions. A rather wet mixture is used. The con- PLACING Crete is poured into the forms and is laid continu- CONCRETE ously over the entire floor area. It is placed care- fully around the steel work, so as not to disturb the location of the bars and to thoroughly cover them at all points. The concrete is puddled in the form so as to allow no voids to occur. The hardening of concrete is not a "Drying out" process, as some suppose, but is a chemical action caused by the addition of the water to the cement. The concrete takes its "Initial set" in a short time and therefore should be deposited in place as quickly after mixing as possible. Concrete work is often carried on in the winter months and will freeze if precautions are not taken. The freezing retards the setting of the concrete and often completely ruins it. It is usually best to remove any concrete known to have been frozen. Simple precautions can be taken to prevent such freezing such as heating the materials, adding salt to the water (less than a 10 per cent, solution), keeping the building heated by charcoal grates and covering the concrete after being laid with some good insulating material such as cement bags, straw, manure, etc. After the concrete has thoroughly set and hardened, REMOVAL the forms are carefully taken down. This is done OF FORMS gradually and evenly so as to cause no undue shocks on the concrete work. The length of time necessary to leave the forms in place depends very largely on the atmospheric conditions, the season of the year, the thickness of the concrete work, and the kind of cement used. With the removal of the forms the structural portion of the building is complete and ready for use. The concrete, however, will continue to grow harder and stronger every day. FINISH ON CONCRETE WORK The most common finish for floors is the ordinary cement finish. This is a cement mortar composed of one part Portland cement and two parts clean sharp sand. It is preferably laid at the same time as the main body of the concrete work in order to pro- cure adhesion to the same. If for any reason this cannot be done, the old concrete should be thoroughly cleaned before the finish is laid, and the finish should be ra-ide at ka-^t one imfti m thickness. ; A less thickness will ^rack off: The ctnieot finish should be 99 KAHN SYSTEM OF REINFORCED CONCRETE marked off in squares, the line of the marking being so arranged as to bring them over all beams and girders. Where finished wood floors are laid on concrete, bevelled wood sleepers are used as nailing strips. These sleepers are about 2x3'' in size, and are placed usually 16'' on centers. Between the sleepers a filling of weak cinder concrete is used to hold them in place. Marble, tile, mosaic and similar floors are laid on concrete construction by imbedding them in a cement mortar. Where a cement finish is desired on concrete walls, the finish should be placed while the wall is being built. The rough con- crete is spaded back from the forms and the rich mortar placed in front of it. A cement finish plastered on concrete after the wall is built will usually crack and not give the best results. After the forms are removed the concrete should be rubbed smooth and given a coat of cement wash mixed and applied as a paint. There are many other ways of obtaining pleasing appearances to finished concrete work, such as bush hammering, pebble dash, Quimby process and a large variety of patented processes, all of which have been used with more or less success. WATERPROOFING . For all ordinary purposes the use of a rich wet mixture with a cement finish will be as waterproof as necessary. In some cases, however, special provision must be made. The use of asphalt and tar and felt combinations are old methods and always give good results. A number of methods to make concrete waterproof in itself have been used. The following method has been employed in some very large work and with good results: The "Waterproof mortar" is made of 1 part Portland Cement and two parts of sand. Add M pound pulverized alum, for each cu. ft. of sand and mix dry. Then add the proper quantity of water in which has been dissolved H pound soft soap per gallon of water and mix thoroughly. This mortar is applied as a plaster 1" in thickness and is also useful in preventing efflorescence. Besides this there are a large number of waterproof cements, compounds and patented processes upon the market, which give more or less satisfactory results. 100 TRUSSED CONCRETE STEEL COMPANY BRIEF SPECIFICATIONS OF MATERIALS FOR REIN- FORCED CONCRETE WORK* Steel for reinforced concrete shall be made by the REINFORC- Open Hearth process. This steel shall have an ING STEEL ultimate tensile strength of from 60,000 to 70,000 pounds per sq. ft. and an elastic limit of at least half that amount, with an elongation of at least ^0 per cent. A bar shall bend cold through an angle of 180 degrees and close down on itself without cracking. High carbon steel or steel with an elastic limit greater than 45,000 pounds per sq. in. shall not be used in reinforced concrete work. Reinforcing steel shall provide for shearing stresses. These shear members shall be rigidly attached to the main tension member and preferably be part of the same bar.. Cement shall be of such requirements as to satisfy CEMENT the standard specifications for cement adopted by The American Society for Testing materials Nov. 14th, '04. Sand shall be clean, and sharp, and not contain over SAND, 3 per cent. loam. Broken stone and gravel shall be STONE, hard and close grained and free from dust and dirt. GRAVEL They shall be of such size as to pass through a ring one inch in diameter. Concrete for beams and slabs shall be proportioned PROPORT- of one part Portland cement, two parts sand, 4 parts IONS broken stone or gravel, concrete for columns shall be al :1>2 :3 mixture. *For detailed requirements see * 'Specifications for Reinforced Concrete Work," published by the Trussed Concrete Steel Co. 101 KAHN SYSTEM OF REINFORCED CONCRETE QUANTITIES OF MATERIAL FOR ONE CUBIC YARD OF RAMMED PLAIN AND REINFORCED", PERCENT Proportions by Parts Proportions by Volume Volume of Mortar in Terms of Percentage of Volume oi oLone 50% Broken Stone Screened to Cement Packed Cement Uniform Size Sand Stone Loose Sand Loose Stone 1 CO ID Ul. Cu. Ft. Cu. Ft. Bbl. Cu. Yd. Cu. Yd. 1 1 1.5 1 3.8 5.7 99 Q 1 Q U.40 U.D / 1 1 2 1 3.8 7.6 75 9 ftp; U.oU 1 1 2.5 1 3.8 9.5 61 u. oo u.yu 1 1 3 1 3.8 11.4 51 9 Q/1 U.oo n QQ u.yy 1 1.5 2 1 5.7 7.6 93 9 zLQ U.»J0 0 70 1 1.5 2.5 1 5.7 9.5 76 9 97 U.40 U.oU 1 1.5 3 1 5.7 11.4 64 9 HQ u.oo 1 1.5 3.5 1 5.7 13.3 55 1 QzL n QA u.yo 1 1.5 4 1 5.7 15.2 49 1 .oU U. Oo 1 .U i 1 1.5 4.5 1 5.7 17.1 44 1 AQ n QA U. OD 1 07 1 .U/ 1 1.5 5 1 5.7 19.0 40 1 p;q i .oy U.o4 119 i . iZ 1 2 3 1 7.6 11.4 75 1 .oy u.oo O SO U.oU 1 2 3.5 1 7.6 13.3 65 1 7P, 1 . / D n ziQ O 87 U.o / 1 2 4 1 7.6 15.2 57 i .DO n Af\ O Q*^ U.yo 1 2 4.5 1 7.6 17.1 51 1 U.44 O Qft u.yo 1 2 5 1 7.6 19.0 47 1.4/ U.4i 1 o*^ 1 .Uo 1 2 5.5 1 7.6 20.9 43 i .oy u. oy 1 Oft i .Uo 1 2 6 1 7.6 22.8 40 1 Q9 n Q7 U.o/ 111 I 2.5 3 9.5 11.4 87 1 79 i . / z U.D i O 7Q U. / o 1 2.5 3.5 1 9.5 13.3 75 1 A9 1 .DZ n p;7 u.o / O ftO U.oU 2.5 4 9.5 15.2 66 1 f^9 i .OZ U.04t O ftA U.oD 2.5 4.5 9.5 17.1 60 1.44 0.51 0.91 2.5 5 9.5 19.0 54 1.37 0.48 0.96 2.5 5 '5 9.5 20.9 49 1.30 0.46 1.01 2.5 6 9.5 22.8 46 1.24 0.44 1.05 2.5 6.5 9.5 24.7 42 1.18 0.42 1.08 2.5 7 9.5 26.6 40 1.13 0.40 1.11 3 4 11.4 15.2 76 1.42 0.60 0.80 3 4.5 11.4 17.1 68 1.34 0.57 0.85 3 5 11.4 19.0 61 1.28 0.54 0.90 3 5.5 11.4 20.9 56 1.22 0.52 0.94 3 6 11.4 __22.8 52 1.16 0.49 0.98 3 6.5 11.4 24.7 48 1.12 0.47 1.02 102 TRUSSED CONCRETE STEEL COMPANY CONCRETE BASED ON A BBL. OF 3.8 CU. FT. FROM ^XONCRETE, TAYLOR & THOMPSON. AGE OF VOIDS IN BROKEN STONE OR GRAVEL 45% Average Conditions 40% Gravel 30% Scientifically Gr aded 20% Mixtures Cement m 0 Cement m o a 0-) o m s 0 Cement 0 0 m m m m m J j; 5 rJDl . Til Yd. Til Yd. Bbl. Cu. Yd. Cu. Yd. Bbl. Cu. Yd. Cu. Yd. 0 Dl. Til Yd. Til Yd. 3.08 0.43 0.65 2 97 0.42 0.63 2.78 0.39 0.59 2.62 0.37 0.55 2.73 0.38 0.77 2 62 0.37 0.74 2.43 0.34 0.68 2.26 0.32 0.64 2.45 0.34 0.86 2 34 0.33 0.82 2.15 0.30 0.76 1.99 0.28 0.70 2.22 0.31 0.94 2 12 0.30 0.90 1.93 0.27 0.82 1.77 0.25 0.75 2.40 0.51 0.68 2 31 0.49 0.65 2.16 0.46 0.61 2.03 0.43 0.57 / 2.18 0.46 0.77 .v2 09 0.44 0.74 ''1I.94 0.41 0.68 1.80 0.38 0.63 2.00 0.42 0.84 .91 0.40 0.81 1.76 0.37 0.74 1.63 0.34 0.64 1.84 0.39 0.91 1 .76 0.37 0.87 1.61 0.34 0.79 1.48 0.31 0.73 1.71 0.36 0.96 1 .63 0.34 0.92 1.48 0.31 0.83 1.36 0.29 0.77 1.60 0.34 1.01 1 .51 0.32 0.96 1.37 0.29 0.87 1.25 0.26 0.79 1.50 0.32 1.06 1 .42 0.30 1.00 1.28 0.27 0.90 1.17 0.25 0.82 1.81 0.51 0.76 1 .74 0.49 0.74 1.61 0.45 0.68 1.50 0.42 0.63 AJ 1.68 0.47 0.83 .1 .61 0.45 0.79 -91.48 0.42 0.73 1.38 0.39 0.68 L57 0.44 0.88 -1 .50 0.42 0.84 ^1.38 0.39 0.78 1J7 0.36 0.72 1.48 0.42 0.94 1 .41 0.40 0.89 1.28 0.36 0.81 1.18 0.33 0.75 1.39 0.39 0.98 1 .32 0.37 0.93 1.20 0.34 0.84 1.10 0.31 0.77 1.31 0.37 1.01 1 .25 0.35 0.97 1.13 0.32 0.87 1.03 0.29 0.80 1.25 0.35 1.06 1 .18 0.33 1.00 1.06 0.30 0.89 0.97 0.27 0.82 1.66 0.58 0.70 1 .60 0.56 0.68 1.49 0.52 0.63 1.40 0.49 0.59 1.55 0.55 0.76 1 .49 0.52 0.73 1.38 0.49 0.68 1.29 0.45 0.64 1.46 0.51 0.82 1 .40 0.49 0.79 1.29 0.45 0.73 1.19 0.42 0.67 1.37 0.48 0.87 1 .31 0.46 0.83 c;1.20 0.42 0.76 1.11 0.39 0.70 J. 30 0.46 0.92 1 .24 0.44 0.87 ^il.l3 0.40 0.80 1.04 0.37 0.73 1.23 0.44 0 U. t/U 1 .17 0.41 0 Ql 1 07 yj . 00 u . 00 0.98 n u . 0^ u. < u 1.17 0.41 0.99 1 .11 0.39 0.94 1.01 0.36 0.85 0.92 0.32 0.78 1.12 0.39 1.02 1 .06 0.37 0.97 0.96 0.34 0.88 0.88 0.31 0.80 1.07 0.37 1.05 1 .01 0.36 0.99 0.91 0.32 0.90 0.83 0.29 0.82 1.36 0.36 0.77 1 .30 0.55 0.73 1.21 0.51 0.68 1.12 0.47 0.63 1.28 0.55 0.81 1 .23 0.52 0.78 1.13 0.48 0.72 1.05 0.44 0.66 1.22 0.52 0.86 1 .17 0.49 0.82 1.07 0.45 0.75 0.99 0.42 0.70 A/ 1.16 0.49 0.90 : 1 .11 0.47 0.86 1.01 0.43 0.78 0.93 0.39 0.72 1.11 0.47 0.94 . 1 05 0.44 0.89 0.96 0.41 0.81 0.88 0.37 0.74 1.06 0.45 0.97 1 .01 0.43 0.92 0.92 0.39 0.84 0.84 0.35 0.77 103 KAHN SYSTEM OF REINFORCED CONCRETE MATERIALS FOR ONE CUBIC YARD COMPACT PLASTIC MORTAR BASED ON BARREL OF 3.8 Cu. Ft. FROM CONCRETE PLAIN AND REINFORCED" By Taylor & Thompson Relative Proportions by Parts Relative Proportions by Volume Cement l-/00se Sand Cement Sand Cement bbl. Sand cu. ft. bbl. cu. yd. 0 8.31 1.9 6.73 0.47 1 3.8 5.01 0.71 5.7 4.00 0.84 1 2 I 7.6 3.32 0.93 9.5 2.84 1.00 3 11.4 2.48 1.05 sy2 13.3 2.20 1.08 4 15.2 1 Oft 111 4>^ 17.1 1.80 1.14 5 19.0 1.65 1.16 20.9 1.52 1.18 6 22.8 1.41 1.19 6K 24.7 1.32 1.21 7 26.6 1.23 1.21 8 28.5 30.4 1.16 1.10 1.22 1.24 NOTE: — Variation in the fineness of the cement and the sand. and in the consistency of the mortar, may affect the values by 10% in either direction. Cement- — as packed by manufacturer. Sand — loose. 104 TRUSSED CONCRETE STEEL COMPANY INDEX Page Allowable stresses 20 Arch Bridges 88 Arch Bridges, Table for Highway 90 Arch Bridges, Table for Parabolic 92 Bending Moments 40 Beams, Explanation of Tables for Kahn Bar 58 Beams, Tables for carrying capacities of concrete 59 Beams, Moments of Resistance 32 Beams, Shear in Reinforced Concrete 84 Beams, Concrete, Safe Loads 59-62 Bin Design, Ex])lanation of Tables for 72 Bins, Tables for Pressure in Vertical 73 Bins, Grain Piessure in 77 Building Laws of Various Cities for different classes of Buildings 79 Building Laws Governing Reinforced Concrete 80 Bridges, Reinforced Concrete 81 Bridge, Table for Slab Highway 84 Bridge, Table for Girder Highway 8.5 Centering, Erection of 98 Compression in Concrete Limits Design in Beams 31 Concrete Columns, Tables for Reinforced 63 Culverts, Highway Box 81 Culverts, Railroad Box 86 Covers for Railway Box Culverts 87 Columns, Tables for Reinforced Concrete 63-64 Concrete, Mixing and Placing 99 Design for Utility 13 Design for Economy 14 Double Reinforcement 27 Direct Compression, Pieces Under 38 Earth Pressures, Table for 76 Economy of Kahn Bar 14 Economy of Installation 14 Engineering Department 15 Erection, Notes about 98 Fireproof ness 12 Finish on Concrete Work 99 Floor Construction Framing Between Steel Girders 41 Floor Slabs, Rectangular 43 Floor Loads, Allowable, according to Building Laws 79 Floors, Tables for carrying Capacities of Reinforced Hollow Tile 52 Footing Tables 65 Forms, Removal of 99 Girder Bridges 81 Grain Pressures in Deep Bins 77 Highway Bridges 81-84-85 Hooped Columns 38 Hollow Tile Construction, Reinforced 44 Hollow Tile Floors, Tables 52-56 Hooped Columns, Tables for Safe Loads carried by 64 Internal Stress Action 11 Kahn Trussed Bar 8 Kahn Bars, Shearing of 16 Kahn Bars, Sections of 17 Methods of Reinforced Concrete 9 Methods of Design 20 Monolithic Action • 20 Moments of Resistance of Beams 32 Moments of Thrusts in 60 foot Highway Arch, Table of 94 Notes on Design in General 13 Pieces under Direct Compression 38 Plans for Reinforced Concrete 15 Parabolic Arches without Hinges, Designs of 91 Proportions of Material for Reinforced Concrete Work 101 Pressure in Bins 72-73 105 KAIIN SYSTEM OF REJN FORCED CONCRETE Page Railroad Bridges 86-87 Rectangular Floor Slabs ".*.'.".*.!........!......... . 43 Reinforced Concrete, Definition of 7 Reinforced Concrete, Strength of 20 Reinforced Concrete Work, Theory of 21 Reinforced Concrete Bridges 81 Sections of Kahn Trussed Bar 17 Stirrups for Reinforced Concrete 10 Strength of Kahn Bars . . . . 14 Shearing of Kahn Bars / ] [ 16 Shear in Reinforced Concrete Beams 34 Slab, Solid Conrete Floor 44 Slabs, Tables for carrying Capacities for Solid Concrete 45 Steel Placing 98 Stresses, Allowable, according to Building Laws 79 Specifications of Material for Reinforced Concrete Work .101 Spacing of Bars, Tables 46-50 Theory of Reinforced Concrete Work 21 "T" Beams 27 Table for "T" Beam Design 29 Table of Moments of Resistance of Beams 32 Tables for Solid Concrete Floor Slab, Explanation of 44 Tables for Carrying Capacities of Solid Concrete Slabs 45 Tables for Carrying Capacities of Reinforced Hollow Tile Floors 52 Tables for Kahn Bar Beams, Explanation of 58 Tables for Carrying Capacities of Concrete Beams 59 Tables for Reinforced Concrete Columns 63 Tables for Safe Loads carried by Hooped Columns 64 Tables of Footing ^ 66 Tables for Bin Design, Explanation of 72 Tables for Pressure in Vertical Bins (for Bituminous coal) (for Anthracite coal). -73 Table for Earth Pressures 76 Table for Slab Highway Bridges 84 Table for Girder Highway Bridges 85 Table for Highway Arch Bridges ' 90 Tables for Parabolic Arch Bridges 92 Table of Moments and Thrusts in 60 foot Highway Arch 94 Tables for Quantities of Sand and Cement for 1 cubic yard mortar 102 Table for Quantities of Stone, Sand and Cement for 1 cubic yard of Concrete. 103- 104 Unhooped Columns 38 Vibration, Efifects of 20 Waterproofing 99 INDEX TO ILLUSTRATIONS Anderson Carriage Co 56 Beam Failure by Diagonal Tensions 36 Broadway Warehouse Retaining Wall 76 Cement Storage Bins, Cross Section 33 Charley Creek Viaduct 83 Coal Breaker, Pine Hill, Cross Section 26 Column Detail, Typical 66 Column Footing, Typical Plan 66 Culvert Construction, Application of Kahn Trussed Bar to 84 Distribution of Horizontal and Vertical Shear 34 Diamond Crystal Salt Co., Coal Bin 72 Floor Construction Framing Between Steel Girders 41 Hollow Tile Floor Construction 58 Lines of Stress in Beams under Pressure 35 Percentage of Reinforcement 23 Pierce Garage, Cross Section 58 Round House Grand Trunk Railway 37 Roof Construction 39 Reinforced Hollow Tile Floor, Cross Section 51 Tunnel Missouri Pacific Railway 97 Window Framing into Concrete Lintel Beams 51 106 ^0 B