AbstractThe commonly-used viscous damping approach, Rayleigh damping, has been shown to develop excessive damping forces in the nonlinear response history analysis (RHA) of fixed-base structural systems. These forces are referred to as the initial stiffness. While the incorporation of foundation flexibility plays an important role on the seismic performance of the structures, this effect has been ignored in past studies that examined Rayleigh damping. In this study, the elastic and inelastic RHA were applied on fixed- and flexible-base structural systems to (1) address the effect of foundation flexibility on the resulting Rayleigh damping ratios; and (2) evaluate the effect of various damping formulations on the structural response. A structural analysis was performed on 10-story steel special moment-resisting frames. The results showed that the incorporation of the flexibility of the foundation increased the stiffness proportional ratio of Rayleigh damping, which, in turn, increased the total damping ratio compared to the fixed base condition ratios. Mass proportional damping was not affected by foundation flexibility. Consequently, initial stiffness-based proportional damping resulted in the largest dynamic response compared to the other damping approaches for the fixed base systems. Per contra, the structure was heavily damped when stiffness proportional damping was in control for the flexible-base system. In contrast, mass proportional damping produced the largest lateral deflection and interstory drift for the flexible-base systems. The flexible-base story shear was not significantly affected for the different components of Rayleigh damping.