Seismic force modification factors for modified-Clough hysteretic model

Based on the elastic–plastic time-history earthquake analysis of SDOF (single degree of freedom) systems, this paper describes an investigation of the seismic force modification factor RR for the modified-Clough hysteretic model. In total 370 earthquake records belonging to 4 site conditions, with each containing 74 to 106 records, are used to calculate the structural response and finally the factor RR. The structure periods vary from 0.1 to 6 s and the displacement ductility is taken to be 2, 3, 4, 5 and 6 respectively. Damping ratios of 0.0, 0.035 and 0.05 and post-yield stiffness ratios of 0.0, 0.05, 0.1 and 0.2 are used in the analysis. It is found that the most important factor determining the RR is the ductility. The damping and post-yield stiffness only have a secondary effect in the short period range. The RR spectra values increase with system periods, from 1 to the maximum value when the system has the same period as the site, and then decrease rapidly, close to the ductility in the long period range. The RR spectra are correlated with the normalized system period T/TgT/Tg to maintain the peak characteristics of the RR spectra near the characteristic periods TgTg for different earthquake records. The dramatic increase of RR values at the site period TgTg is explained through constructing similar RR spectra for the EPP (elastic–perfectly plastic) SDOF model under sinusoidal excitation.Simple formulae are proposed for the RR spectra which are expressed as multiplication of functions of the ductility, damping and post-yield stiffness. The peak characteristics of the RR spectra at T/Tg=1T/Tg=1 are maintained. Both the averaged spectra and the spectra with 90% probability are presented.Three other hysteretic models: elastic–perfectly plastic (EPP), shear–slipped (SSP) and bilinear elastic (BILE), are analyzed to separate the effects of ductility, energy-dissipating capacity and stiffness degradation in the modified-Clough model on RR spectra. Their results are compared with each other. It is found that structures with the modified-Clough model will experience lateral strength demands typically (5%–25%) smaller than those of the EPP models with periods 0.6