Nonlinear Numerical Simulation of Reinforced Concrete Columns Under Cyclic Biaxial Bending Moment and Axial Loading

A nonlinear finite element algorithm is proposed to analyze the reinforced concrete (RC) columns subjected to cyclic biaxial bending moment and axial loading. In the proposed algorithm, the following parameters are considered: uniaxial behavior of concrete and steel elements, the pseudo-plastic hinge produced in the critical sections, and global behavior of the columns. In the proposed numerical simulation, the column is discretized into two macro-elements located between the pseudo-plastic hinges at critical sections and the inflection point. The critical sections are discretized into fixed rectangular finite elements. The basic equilibrium is justified over a critical hypothetical cross section assuming the kinematics Navier’s hypothesis with an average curvature. The method used qualifies as a “strain plane control process” that requires the resolution of a quasi-static simultaneous equation system using a triple iteration process over the strains in each section. To reach equilibrium, three main strain parameters (the strains in the extreme compressive point, the strains in the extreme tensile point and the strains in another corner of the section) are used as the three main variables. The proposed algorithm has been validated by the results of tests carried out on full-scale RC columns. The application of the components effects combination method is also compared with the proposed simultaneous direct method. The results obtained show the necessity of applying SDM for the post-elastic phase, which occurs frequently during earthquake loading.