Biaxial hysteretic model for the characterization of quasi

Given that the biaxial hysteretic model of shear-critical reinforced concrete columns is usually developed by incorporating with the single-degree-of-freedom system to write its expression in differential equation of motion control, it is unfeasible to match with the experimental data of the biaxial quasi-static testing in terms of force-displacement relationship. Therefore, a simple and effective biaxial hysteretic model is proposed in this study based on the Bouc–Wen–Baber–Noori model for characterizing the biaxial quasi-static testing of shear-critical reinforced concrete columns. An incremental numerical algorithm is then proposed to solve the pair of coupled differential equations based on the backward Euler discretization method and Newton–Raphson iteration scheme. Moreover, the influence of critical model parameters affecting the typical hysteretic characteristics of shear-critical reinforced concrete columns, such as strength deterioration, stiffness degradation, pinching phenomena, and biaxial coupling effect, is investigated, respectively, to demonstrate the capability of the biaxial hysteretic model developed. Finally, a parameter calibration procedure using the differential evolution algorithm is introduced to calibrate the magnitude of involved model parameters by comparing with the experimental data of the biaxial quasi-static testing. According to the investigation, it is found that the developed biaxial hysteretic model can reasonably describe the typical hysteretic characteristics of shear-critical reinforced concrete columns under biaxial quasi-static excitation. Following the proposed parameter calibration procedure, the biaxial hysteretic model developed produces the biaxial hysteretic loops of shear-critical reinforced concrete columns, which is in good agreement with the experimental data once the magnitude of involved model parameters is calibrated