Modelling of R/C members accounting for shear failure localisation: Hysteretic shear model

Reinforced concrete (R/C) frame buildings designed according to older seismic codes represent a large part of the existing building stock worldwide. Their structural elements are often vulnerable to shear or flexure-shear failure, which can eventually lead to loss of axial load resistance of vertical elements and initiate vertical progressive collapse of a building. In this study, a hysteretic model capturing the local shear response of shear-deficient R/C elements is described in detail, with emphasis on post-peak behaviour; it differs from existing models in that it considers the localisation of shear strains after the onset of shear failure in a critical length defined by the diagonal failure planes. Additionally, an effort is made to improve the state of the art in post-peak shear response modelling, by compiling the largest database of experimental results for shear and flexure-shear critical R/C columns cycled well beyond the onset of shear failure and/or up to the onset of axial failure, and developing empirical relationships for the key parameters defining the local backbone post-peak shear response of such elements. The implementation of the derived local hysteretic shear model in a computationally efficient beam-column finite element model with distributed shear flexibility, which accounts for all deformation types, will be presented in a companion paper.