Investigation on residual displacements for SDOF systems with various initial viscous damping models

Abstract Nonlinear time history analysis (NTHA) is widely used in estimation of post-earthquake residual displacement demands. However, the choice of initial viscous damping models in NTHA has attracted insufficient attention in study of residual displacements. The more versatile viscous damping model similar to the tangent-stiffness proportional Rayleigh damping commonly used in multi-degree-of-freedom (MDOF) systems is utilized in NTHA of single-degree-of-freedom (SDOF) systems. With different combinations of mass proportional and tangent-stiffness proportional damping terms, the significance of the choice of initial damping models is examined in terms of energy dissipation and residual displacement demands. The residual displacement ratio, defined as the ratio of residual displacements to elastic spectral displacements, is computed for constant-strength SDOF systems when subjected to an ensemble of 240 earthquake ground motions. The results are statistically organized to investigate the effect of initial viscous damping models on residual displacement demands. The difference in residual displacement ratios for various damping models is found to be significant, and dependent on natural periods, relative lateral strength, post-yield stiffness, unloading stiffness degradation and initial damping ratios. The effect of these factors on residual displacement demands of SDOF systems with tangent-stiffness proportional damping, which is confirmed to be most appropriate for nonlinear analysis, is also examined. Finally, the constant-strength residual displacement response spectra are constructed for seismic assessment of structures.