In this study, two new site specific statistical equations are proposed to estimate the inelastic displacement ratio, C-1 of structures subjected to far fault (FF) and near fault (NF) ground motions. The proposed equations consider the effects of fundamental vibration period of the structure, T, lateral strength ratio, R and frequency content of the design earthquake record represented by the A(p)/V-p ratio (or T-0=2/A(p)/V-p), which is a function of the earthquake magnitude, distance to fault, faulting mechanism and site class. It was observed that the C-1 values obtained from the proposed equations are in good agreement with the calculated results. The flare of the plotted C-1 vs. T/T-0 curves enables the proposed equations to cover nearly all the calculated C-1 data range and give satisfactory results. However, the curves obtained using the C-1 equations of several codes and those available in the literature do not cover the whole calculated C-1 data range and generally give unconservative results (smaller C-1 values) especially in the shorter period range. For the longer period range, the predictions of C-1 obtained from the proposed equation and the ones available in the literature are in good agreement with the calculated C-1 data. Copyright (c) 2014 John Wiley & Sons, Ltd.