Reinforced concrete (RC) columns exhibit cyclic damage, such as strength degradation, under cyclic lateral loading, such as earthquakes. Considering the cyclic damage, the nonlinear load-deformation response of RC columns can be simulated using a lumped plasticity model. Based on an experimental database, this study calibrates lumped plasticity model parameters for 371 rectangular and 290 circular RC columns. The model parameters for adequate flexural rigidity, plastic rotation capacity, post-capping rotation capacity, moment strength, and cyclic strength degradation parameter are adjusted to match each experimentally observed load-deformation response. We have developed predictive equations that accurately relate the model parameters to the design characteristics of RC columns through regression analyses, providing a reliable tool for engineers and researchers. To demonstrate their application, the proposed and existing models numerically simulate the earthquake response of a bridge pier in a metropolitan railway bridge. The pier is subjected to several ground motions, increasing intensity until collapse occurs. The proposed lumped plasticity model showed about 41% less vulnerable to collapse.

For a member model in nonlinear structural analysis, a lumped plastic model that idealizes its flexural bending, shear, and axial behaviors by springs with the nonlinear hysteretic model is widely adopted because of its simplicity and transparency compared to the other rigorous finite element methods. On the other hand, a challenging task in its numerical solution is to satisfy the equilibrium condition between nonlinear flexural bending and shear springs connected in series. Since the local forces between flexural and shear springs are not balanced when one or both springs experience stiffness changes (e.g., cracking, yielding, and unloading), the additional unbalanced force due to overshooting or undershooting each spring force is also generated. This paper introduces an iterative scheme for numerical solutions satisfying the equilibrium conditions between flexural bending and shear springs. The effect of equilibrium iteration on analysis results is shown by comparing the results obtained from the proposed method to those from the conventional scheme, where the equilibrium condition is not perfectly satisfied.