Deformation dependent equivalent modal damping ratios for the performance-based seismic design of plane R/C structures

Abstract

A performance-based seismic design method is proposed for three types of plane R/C structures, i.e., moment resisting frames, infilled moment resisting frames and wall-frame dual systems. It is a force-based design method using the concept of the equivalent viscous damping ratio ξ to account for inelastic energy dissipation instead of that of the behavior (or strength reduction) factor q (or R). More specifically, it uses equivalent modal damping ratios ξk defined for the equivalent linear multi-degree-of-freedom system to the original non-linear multi-degree-of-freedom system. This equivalent system has the same mass and the elastic stiffness of the non-linear one. Furthermore, these equivalent modal damping ratios ξk are constructed as functions of the periods of the structure, the target non-structural and structural deformation (both expressed in terms of inter-storey drift ratio and member plastic rotation) and soil type. Thus, the proposed method is more rational and leads to more accurate results in one step (only strength checking) than code-based design methods requiring two steps (strength and deformation checkings). In addition, it can be used as a performance-based seismic design method with two or more performance levels. Explicit expressions of these ξk for the first few significant modes are proposed. These expressions have been obtained through extensive parametric studies involving non-linear dynamic analysis of 76 frames under 100 far-fault ground motions (corresponding to four soil types of EC8) for different deformation targets. These ξk can be used for seismic design through linear analysis in conjunction with an elastic acceleration design spectrum modified for high amounts of damping. The proposed method is illustrated and validated by numerical examples which demonstrate its advantages over the Eurocode 8 seismic design method.