Influence of hysteretic behavior on equivalent period and damping of structural systems

Relations for the equivalent period T-eq and equivalent damping ratio zeta(eq) for the equivalent linear system approach for seismic design are proposed. These relations are based on optimal T-eq and zeta(eq) values derived from extensive time-history analyses of single-degree-of-freedom systems with six types of hysteretic behavior and a period range of 0.1 to 1.5 s. The proposed relations are more general (in their applicability to a wide range of hysteretic systems) and have stronger ties to physical behavior compared to existing empirical methods for evaluating T-eq and zeta(eq). The proposed relations address differences in equivalent stiffness resulting from different hysteretic behavior. Simulations show that the optimal T-eq, associated with the stiffness of the. partial. load-displacement cycles of a hysteretic system, is the highest for the slip system (with a zero unloading/reloading stiffness) and the lowest for the bilinear elastic system (with an elastic unloading/reloading stiffness). The optimal zeta(eq), associated with the energy dissipation capacity of a hysteretic system, is the highest for the elastoplastic system and the lowest for the bilinear elastic system.