92. In these formulas, V is taken as the proportion of total shear assumed as carried by the reinforcement.
93. The longitudinal spacing of stirrups shall not exceed three-fourths the depth of the beam in the por tion of the beam where the shearing stresses exceed the allowable shearing value of the concrete.
94. It is important that adequate bond strength be provided to fully develop the assumed strength of all shear reinforcement.
95. Inasmuch as small deformation in the horizontal reinforcement tends to prevent the formation of diagonal cracks, a beam will be strengthened against diagonal tension failure by so arranging the horizontal reinforce ment that the unit-stresses at points of large shear shall be relatively low.
96. Columns. It is recommended that the ratio of unsupported length of column to its least width be lim ited to fifteen.
97. The effective area of the column shall be taken as the area within the protective covering, as defined in paragraph 3. Or, in the case of hooped columns or columns reinforced with structural shapes, it shall be taken as the area within the hooping or structural shapes.
98. Columns may be reinforced by means of longi tudinal bars; by bands or hoops; by bands or hoops together with longitudinal bars; or by means of struc tural forms which in themselves are sufficiently rigid to act as columns. The general effect of bands or hoops is greatly to increase the "toughness" of the column and its ultimate strength; but hooping has little effect upon its behavior within the limit of elasticity. It thus renders the concrete a safer and more reliable material, and should permit the use of a somewhat higher working stress. The beneficial effects of "toughening" are inade quately provided by a moderate amount of hooping, a larger amount serving mainly to increase the ultimate strength and the possible deformation before ultimate failure.
99. The following recommendations are made for the relative working stresses in the concrete for the several types of columns : (a) Columns with longitudinal reinforcement only, the unit-stress recommended in paragraph 58.
(b) Columns with reinforcement of bands or hoops, as specified below, stresses 20 per cent higher than given for a.
(c) Columns reinforced with not less than 1 per cent and not more than 4 per cent of longitudinal bars, and with bands or hoops, stresses 45 per cent higher than given for a.
(d) Columns reinforced with structural steel column units which thoroughly encase the concrete core, stresses 45 per cent higher than given for a.
100. In all cases, in addition to the stress borne by the concrete given above, longitudinal reinforcement is assumed to carry its proportion of stress in accordance with the ratio of its elasticity to concrete. For example,
with a working stress in concrete of 450 pounds per square inch, the longitudinal reinforcement may be as sumed to carry 15 X 450 -=- 6,750 pounds per square inch.
101. The hoops or bands are not to be counted upon directly as adding to the strength of the column.
102. Bars composing longitudinal reinforcement shall be straight, and shall have sufficient lateral support to be securely held in place until the concrete is set.
103. Where bands or hoops are used, the total amount of such reinforcement shall be not less than 1 per cent of the volume of the column enclosed. The clear spacing of such bands or hoops shall be not greater than one-fourth the diameter of the enclosed column. Adequate means must be provided to hold bands or hoops in place so as to form a column the core of which shall be straight and well-centered.
104. Bending stresses due to eccentric loads must be provided for by increasing the section until the maximum stress does not exceed the values above specified.
105. Splicing of Bars. Wherever in tension rein forcement it is necessary to splice the reinforcing bars, the length of lap shall be determined on the basis of the safe bond stress and the stress in the bar at the point of splice; or a connection shall be made between the bars of sufficient strength to carry the stress. Splices at points of maximum stress should be avoided. In columns, large bars should be properly butted and spliced; small bars may be treated as indicated for tension reinforce ment, or their stress may be taken off by being embedded in large masses of concrete. At foundations, bearing plates should be provided for large bars or structural forms.
106. Reinforcing for Shrinkage and Temperature Stresses. Where large areas of concrete are exposed to atmospheric conditions, the changes of form due to shrinkage (resulting from hardening) and to action of temperature, are such that large cracks will occur in the mass, unless precautions are taken so to distribute the stresses as either to prevent the cracks altogether or to render them very small. The size of the cracks will be directly proportional to the diameter of the reinforcing bars, and inversely proportional to the percentage of reinforcement and also to its bond resistance per unit of surface area. To be most effective, therefore, reinforce ment should be placed near the exposed surface and well distributed, and a form in reinforcement used which will develop a high bond resistance.