Nonlinear Finite Element Analysis Formulation for Shear in Reinforced Concrete Beams

This study suggests a novel beam-column element formulation that utilizes an equilibrium-driven shear stress function. The beam shear is obtained from the bi-axial states of micro-planes, through matrix condensation and zero vertical traction assumptions. This properly remedies the shear stiffening of a one-dimensional beam-column element, keeping its degrees of freedom to a minimum. For verification of the proposed method, a total of seven shear test results of reinforced concrete (RC) beams were collected from the literature, in which the key variables were the reinforcement ratio, the presence of shear reinforcement, and section shape. The advantages are clearly shown in the shear stresses distributions being accurately described and the global load-displacement relations being successfully obtained and matching well with various test results. The proposed model shows satisfactory descriptions of the monotonic load-displacement response of the RC beams failing in multiple modes that vary from diagonal-tension to flexural-compression. In addition, more accurate and reliable information of sectional responses including sectional shear deformation and stresses is collected, leading to better prediction of a potential shear failure mode. Finally, the advantages of the proposed model are demonstrated by comparing the analysis results of an RCT-beam by using the different shear assumptions that include the constant and parabolic shear strains, constant shear flow, and the proposed shear stress function.