Seismic force modification factors for modified-Clough hysteretic model: Fid-Bau Portal

Seismic force modification factors for modified-Clough hysteretic model

Genshu, Tong / Yongfeng, Zhao

AbstractBased 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 $T / T_{g}$ to maintain the peak characteristics of the $R$ spectra near the characteristic periods $T_{g}$ for different earthquake records. The dramatic increase of $R$ values at the site period $T_{g}$ 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 $T / T_{g} = 1$ 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 $0.6 < T / T_{g} < 3$ . 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.