Abstract
In order to predict inelastic displacement response without nonlinear dynamic analysis, the equal displacement rule can be used for the structures with longer natural periods than the characteristic period, $T_g$, of earthquake record. In the period range longer than $T_g$, peak displacement responses of elastic systems are equal or larger than those of inelastic systems. In the period range shorter than $T_g$, opposite trend occurs. In the equal displacement rule, it is assumed that peak displacement of inelastic system with longer natural period than $T_g$ equals to that of elastic system with same natural period. The equal displacement rule is very useful for seismic design purpose of structures with longer natural period than $T_g$. In the period range shorter than $T_g$, the peak displacement of inelastic system can be simply evaluated from the peak displacement of elastic system by using the inelastic displacement ratio, which is defined as the ratio of the peak inelastic displacement to the peak elastic displacement. Smooth hysteretic behavior is more similar to actual response of real structural system than a piece-wise linear hysteretic behavior such as bilinear or stiffness degrading behaviors. In this paper, the inelastic displacement ratios of the smooth hysteretic behavior system are evaluated for far-fault and near-fault earthquakes. The simple formula of inelastic displacement ratio considering the effect of $T_g$ is proposed.
