Development of inelastic displacement ratio using constant energy-based damage index for performance-based design

In this study, the inelastic displacement ratio (IDR) for far-field earthquake ground motions is statistically evaluated by the modified energy damage indices, known as hys-teresis energy to input energy ratio, to estimate the target displacement in performance-based design theory with an energy approach. The suggested damage model can consider the effect of the frequency content, earthquake amplitude, and ground motion duration by accounting for whole energy aspects, including kinematic energy, damping energy, hys-teresis energy, and input energy, without complex parameters in its structure. The IDR is statistically determined in six damage levels, four hysteresis models, and 30 periods of vibration by performing 216,000 dynamic analyses on 300 far-field ground motions. More-over, the effect of the period, magnitude, source-to-site distance, and soil classes are inves-tigated. Hence, a simplified mathematical equation is proposed based on the C-DI-T-DIfunction to estimate the target displacement in different damage levels for performance-based design. Finally, the proposed method and formula are verified by target inelastic displacements gained from dynamic time history analysis. Statistical results showed that the coefficient of variation (COV) is not too high, and the influence of record-to-record characteristics on the IDR ratio is negligible. Additionally, the proposed equation could estimate the inelastic target displacement in different damage levels and periods of vibra-tion appropriately.