Influence of Hysteretic Behavior on Equivalent Period and Damping of Structural Systems

Relations for the equivalent period Teq and equivalent damping ratio ζeq for the equivalent linear system approach for seismic design are proposed. These relations are based on optimal Teq and ζeq 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 Teq and ζeq. The proposed relations address differences in equivalent stiffness resulting from different hysteretic behavior. Simulations show that the optimal Teq, 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 ζeq, 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.