Inelastic yielding strength demand coefficient spectra

Currently, earthquake action is obtained by dividing the elastic acceleration spectra by a seismic modification factor, and the latter is also a spectrum actually. The dynamic inelastic response of single-degree-of-freedom (SDOF) systems for modified-Clough hysteretic model with stiffness degradation when subjected to reverse loading were analyzed. Total 370 earthquake records belonging to four site and soil conditions with each containing 74–106 records were used as excitations. The formulae for elastic strength demand coefficient ηe and the seismic force modification factor Rμ were proposed. It is found that the both types of spectra have different characteristic periods, respectively. Two sets of inelastic yielding strength demand coefficients were calculated and compared. The results show that if the elastic ηe and the Rμ spectra were both normalized by the characteristic period TgR, the inelastic ηyμ spectra are not in good agreement with those derived directly from statistical analysis. Therefore, the inelastic ηyμ spectra normalized by the characteristic period Tga were constructed directly, and the obtained curves were quite similar for the four site types. The inelastic ηyμ spectra increase with the period when T<Tga and then descend exponentially with the period. Simple formulae for both the averaged spectra and the spectra with 90% probability guaranty are proposed, and they are in excellent agreement with the statistically obtained curves.