Equivalent Viscous Damping for Dual Frame-Wall Resilient System

A resilient dual frame-wall lateral force-resisting system, designed to mitigate frame-expansion challenges in self-centering structures, has been introduced. One notable obstacle encountered when applying direct displacement-based design (DDBD) to this dual frame-wall system is the ductility-damping relationship that can be used for estimating nonlinear structural responses. To address this issue, more than 3.5 million damping data points were generated through nonlinear time-history (NLTH) analyses by creating the linearized substitute system. These analyses span a broad range of parameters, including the fundamental period of the original system, ductility, normalized subsystem stiffness ratio, and post-yielding stiffness ratio of the subsystems. The results reveal that the equivalent viscous damping ratio (EVDR) exhibits significant period dependency for a wide range of periods. Both ductility and the subsystem stiffness ratio, which govern the hysteresis response area, exert a substantial influence on EVDR, except for the post-yielding stiffness ratio. Consequently, an EVDR model that takes into account the effective period, ductility, and normalized subsystem stiffness ratio was formulated and was validated using an additional data set of over 0.2 million data points. Ductility-period design displacement spectra were also proposed to illustrate the implementation of the proposed EVDR model and provide an easy way to understand the equivalent procedure.