Shear Design of Reinforced Concrete Deep Beams: A Numerical Approach

Abstract

A general framework aimed at dealing with the failure analysis of reinforced concrete beam-like structures is presented in this paper. It is based on the yield design theory combined with a “mixed modeling” of this kind of structure, according to which the concrete material is treated as a classical continuum, whereas the longitudinal reinforcements are regarded as elements working predominantly in tension. In addition, shear-reinforced web zones may be incorporated in the analysis through a homogenization procedure. Both lower- and upper-bound methods are then implemented numerically by means of a finite-element formulation, thus producing fairly accurate estimates for the load-carrying capacity of a shear loaded beam, taken as an illustrative application. In particular, it is shown that the shear-span-to-depth ratio, along with the amount of longitudinal reinforcement, play a crucial role in the transition from flexural to shear dominated failure modes of the beam. This conclusion is supported by numerous experimental observations reported in the literature. Numerical predictions even prove to be in good agreement with experimental results provided appropriate reduction factors be assigned to the concrete strength parameters, accounting for its brittleness under tensile loading conditions.