79. In the case of beams and slabs continuous for two spans only, or of spans of unusual length, more exact calculations should be made. Special consideration is also required in the case of concentrated loads.
80. Bonding Strength and Spacing of Bars. In direct pull or direct compression a bar must be embedded a length sufficient to give a working strength in bond equivalent to the working strength of the steel in tension or compression. For 2,000-pounds concrete, in which 80 pounds per square inch is permitted in bond, and a work ing strength of 16,000 pounds per square inch in the steel, plain round bars thus require an embedded length of fifty diameters.
81. The bond stress in the horizontal bars in a beam may be represented by the formula: u= . V (7) jcM) 82. With the unit-bond of 80 pounds per square inch (assuming d), the total circumference of tension rods at any section of the beam should be at least: V ."° (8)70d 83. For T-beams, b' is substituted for b, and jd may be taken as approximately the distance from center of slab to steel.
84. Where high bond resistance is required, the de formed bar is a suitable means of supplying the necessary strength. Adequate bond strength throughout the length of a bar is preferable to end anchorage; but such anchor age may properly be used in special cases. Anchorage furnished by short bends at a right angle is less effective than hooks consisting of turns through 180 degrees.
85. The lateral spacing of bars should not be less than two and one-half diameters, center to center, nor should the distance from the side of the beam to the center of the nearest bar be less than two diameters.
The clear spacing between two layers of bars should be not less than 1/2 inch.
86. Shear and Diagonal Tension. Calculations for web resistance shall be made on the basis of maxi mum shearing stress as determined by the formulas here inafter given. When the maximum shearing stresses exceed the value allowed for the concrete alone, web reinforcement must be provided to carry the diagonal tensile stresses involved. This web reinforcement may consist of bent bars, or inclined or vertical members attached to or looped about the horizontal reinforcement. When inclined members are used, the connection to the horizontal reinforcement shall be such as to insure against slip.
87. Experiments bearing on the design of details of web reinforcement are not yet complete enough to allow more than general and tentative recommendations to be made. It is well established, however, that a very mod erate amount of reinforcement, such as is furnished by a few bars bent up at small inclination, increases the strength of a beam against failure by diagonal tension to a considerable degree ; and that a sufficient amount of web reinforcement can readily be provided to increase the shearing resistance to a value three or more times that found when the bars are all horizontal and no web reinforcement is used.
88. The Joint Committee recommend the following allowable values for maximum shearing stresses for con crete whose crushing strength is 2,000 pounds at 28 days : (a) For rectangular beams with horizontal bars only, V i web reinforcement is necessary when is greater than kid 40, or (assuming distance between centers of tension and V i compression to be when — is greater than 35.
bd (b) For rectangular beams in which a part of the horizontal reinforcement is used in the form of bent-up bars arranged with due respect to shearing stresses, a higher value may be allowed, but not to exceed 60 pounds per square inch. In this case (assuming stir rups will be required when is greater than 52.
(c) In any case, no matter how thoroughly rein forced for diagonal tension, the total shear should not exceed 120 pounds per square inch, that is (assuming jd d), bd must never be less than 105 89. For T-beams the same rules apply, except that only the web of the beam is effective; hence b' must be substituted for b.
90. In the calculation of web reinforcement to pro vide a strength of 120 pounds per square inch, the con crete may be counted upon as carrying one-third of the shear, or, for 2,000-pound concrete, 40 pounds per square inch. The remainder may be provided for by means of metal reinforcement consisting of bent bars or stirrups, but preferably both. The area of a stirrup, acting in tension, must be proportioned to the force equal to the whole horizontal shear produced between the two adja cent stirrups, less the amount to be carried by the con crete. This total horizontal shear may be found by multi plying the distance between stirrups by the average hori zontal unit-shear, which is equal to the vertical unit shear, and is represented by the expression:— V , jd 91. In accordance with this method the stress in a d s ' vertical stirrup will be equal to -7 and in a stirrup j .7 or bent rod at 45 degrees, it will equal 0 s in which s = horizontal spacing—that is, the distance apart, of stirrups or bent rods.