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 R 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 R. 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 R is the ductility. The damping and post-yield stiffness only have a secondary effect in the short period range. The R 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 R spectra are correlated with the normalized system period T/Tg to maintain the peak characteristics of the R spectra near the characteristic periods Tg for different earthquake records. The dramatic increase of R values at the site period Tg is explained through constructing similar R spectra for the EPP (elastic–perfectly plastic) SDOF model under sinusoidal excitation. Simple formulae are proposed for the R spectra which are expressed as multiplication of functions of the ductility, damping and post-yield stiffness. The peak characteristics of the R spectra at T/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 R 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<T/Tg<3. Comparisons between R factors for EPP and BILE or SSP models show that the effect of energy-dissipating capacity on R spectra is statistically evident only in the short period range, and the maximum decrease in R values for the latter two models is by 50% at most. With increasing period, the effect of energy-dissipating capacity is negligible. This suggests that the effect of the energy-dissipating capacity is not so great as we expected even in the low period range, and it has nearly no effect on the R spectra in the middle and long period range.