Theory of the Stresses Induced in Reinforced Concrete by Applied Two-Dimensional Stress
Bruce H. Falconer
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This paper presents a theory of the stresses which are induced in concrete, reinforced in up to two directions, when under applied two-dimensional stress. It is based on convenient simplifying assumptions of the modes of failure. These assumptions are that failure will occur when either redistributions of internal stress cannot relieve tensions greater than yield in the reinforcement, or when induced compressions in the concrete exceed the ultimate compressive strengths of plain concrete. Although the actual stresses within reinforced concrete are, in general, indeterminate under given loadings, it is shown that the stresses lie within computable regions of magnitude. Consequently, the theory can be used for the computation of quantities and orientations of reinforcement which are consistent with desired ultimate strengths. This application should prove useful in planning the reinforcement of shear walls, deep beams, and normal beams. As a particular and illustrative case of the theory, consideration is given to the reinforcement of concrete to carry shear plus axial load. An explanation is offered for the experimentally observed high shear strengths of lightly stirruped beams. In an appendix the theory is applied to a consideration of the strengths of normal or "shallow" reinforced concrete beams, in which the longitudinal reinforcement is customarily located only near the top and bottom of the cross sections. The theory, as applied, purports to predict the shear strengths of "ideally reinforced" beams with given percentages of web reinforcement, presuming that the reinforcement has marked yield stresses. A comparison is given with the results of tests conducted at the University of Illinois.