Novel Lower-Bound Solution for Bearing Capacity of Reinforced Concrete Deep Beams

Abstract

The present study proposes a novel yet straightforward method for calculating the bearing capacity of deep beams using the theory of lower-bound limit analysis. The equations of the proposed method are obtained from the evaluation of the stresses induced in concrete and reinforcements of deep beams. The modified Mohr-Coulomb yield criterion is utilized to constrain the concrete stress states. Because the proposed method and relevant equations are simple and noniterative, they can be easily employed for design purposes. Moreover, the equations can be applied to beams with and without shear reinforcement. However, the method is limited to deep beams with rectangular cross sections and without openings. In order to assess the accuracy of results, the shear strengths of deep beams obtained by the proposed method are compared with experimental results and the results obtained by the strut-and-tie model. The evaluations of 225 tested deep beams show that the mean ratio of calculated strength to the strength obtained from the test result is 0.94, and the coefficient of variation is 0.22. The variations in results of the proposed method are also investigated for various components, such as the compressive concrete strength, the shear span-to-depth ratio, and the reinforcement ratio. This study shows that the trend of changes in the strength of a deep beam with respect to these components agrees with experimental results. The simplicity of the method is illustrated by an example.