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In this paper, results of  inelastic displacement ratios based on earthquake ground motions of Iran are presented. These ratios are calculated for single degree of freedom systems with elastic perfectly plastic behavior model and various strength reduction factors subjected to 204 earthquake ground motion records. These records are recorded on firm soil sites of Iran and have following characteristics 1) Recorded in earthquakes with seismic moment magnitude larger than 5,  2) At least one of the two horizontal components of records has peak ground acceleration larger than 50 cm/s², 3) Recorded in free field stations so that potential soil-structure interaction effects omitted,  4) Records with hypo central distance larger than 15 km so that near fault effects omitted,  5) Recorded on soil conditions 1, 2 and 3 according to spectral ratio H/V of ground motions,  6) Records in which band pass range in correction process were at least between 0.33 to 20 Hz.  204 acceleration time histories including 70, 30 and 104 acceleration time histories related to soil condition 1, 2 and 3 respectively are used. In this statistical study, 422688 inelastic displacement ratios (related to 204 acceleration time histories, 296 period of vibration and 7 strength reduction factors) from response of SDOF systems with elastic perfectly plastic behavior model are calculated. Mean values of inelastic displacement ratios for each period of vibration and each strength reduction factor subjected to all 204 earthquake records and their dispersions are presented. The influence of period of vibration, strength reduction factor, soil condition, earthquake magnitude and hypocentral distance on inelastic displacement ratios are evaluated. This ratio in short period of vibration is larger than unit (maximum inelastic displacement larger than maximum elastic displacement) and for long period of vibration is close to unit (maximum inelastic displacement nearly equal to maximum elastic displacement). Soil condition effects on inelastic displacement ratio, for period of vibration larger than 1.5 second is very small and neglectable but neglecting of soil condition in periods between 0.4 and 1.5 second cause error up to 20 percent and for periods smaller than 0.4 second cause error up to 40 percent in estimation of inelastic displacement ratio. Neglecting of distance effects to focal of earthquakes in estimation of inelastic displacement ratio, for period of vibration smaller than 1 second, causes error up to maximum 20 percent. This error increase when strength reduction factor increases. For period of vibration larger than 1 second, neglecting of distance effect doesn’t make considerable error. Neglecting of magnitude effects of earthquakes in estimation of inelastic displacement ratio, for period of vibration smaller than 1 second, causes error up to maximum 60 percent. This error increase when strength reduction factor increases. For period of vibration larger than 1 second, neglecting of distance effect doesn’t make considerable error. By using of nonlinear regression analysis, a simplified equation based on mean results is calculated and Maximum inelastic displacement of single degree of freedom systems on Iran firm sites could be estimated using proposed equation and maximum elastic displacement demand. Finally, proposed equation is compared with C₁ coefficient of target displacement in FEMA440.

Keywords: single degree of freedom, inelastic and elastic displacement, elastic perfectly plastic behavior model

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