Differential model of biaxial hysteresis with coupled principal strengths and cyclic deterioration for reinforced-concrete elements

Structural analysis often is multidirectional because simultaneous load components are severer than single components. However, current models need improvement to cover various inelastic interactions. Herein a uniaxial hysteretic model of the Bouc–Wen class is extended to two dimensions by double formulation for principal axes, proper to general loading histories, as opposed to one formulation projected from a skewed axis. Coupling of strengths in terms of stress resultants is implemented for arbitrary degree of interaction, also different between principal directions. Coupling of cyclic deterioration of stiffness and strength is incorporated consistently with phenomenological application of the model at the element scale. The proposed model is assessed by fibre analysis of symmetric and asymmetric cross-sections, and by experimental outcome in the literature. The latter concerns reinforced-concrete square columns under constant axial load and rectangular columns under varying axial load, each subjected to cyclic square and rhombic displacement paths. Based on residual displacement, final energy, and transverse force, the proposed biaxial model is reasonably less accurate than the background uniaxial model. However, it proves to be adequate to simulate force-displacement loops and hysteretic energy of columns and piers.