A numerical critical shear crack model and its application to post‐peak behavior assessment of RC and SFRC beams

Abstract

In this paper, a numerical critical shear crack model, in which the shear‐flexural coupling effect is considered and the full process of stress and strain is captured, is proposed to evaluate the post‐peak behavior of reinforced concrete (RC) and steel fiber reinforced concrete (SFRC) beams. The shape of critical shear crack is identified by combining the modified compression field theory considering the bridge effect of steel fibers and the section analysis method. Based on the shape of critical shear crack, the shear capacity of beam members is provided by the shear tension zone and the shear compression zone. The shear capacity of the shear tension zone is calculated by the modified compression field theory and that of the shear compression zone is determined by multiaxial strength criterion of concrete. The vertical displacements caused by the flexure deformation and shear deformation are deduced by the moment area method and integration of shear strain. To verify the proposed numerical approach, a test database of 486 RC beams and 313 SFRC beams was established to predict the shear strength, and the force‐displacement relationships of twelve beam members are used to validate the feasibility for full process analysis. The stochastic analysis of beams with different failure modes is conducted via GF‐discrepancy‐based point selection method and probability density evolution method. The limitation between different failure modes is defined according to the degradation percent of shear capacity and it is taken as threshold value of failure domain, and the failure probability analysis indicates that the designed flexure beam member suffered severe degradation of shear capacity, resulting in a significant decline in safety probability.