Study On Elastic-Plastic Response Spectra Of SDOF With Different Hysteretic Models

The study on the seismic force modification factor based on the displacement ductility is an important branch of the seismic force theory. The number of the earthquake records used in the early research was much less, and the influence of the frequency property and two characteristic periods on the seismic force modification factor was not taken into consideration either. The results are distorted. Studies on dynamic response of single degree of freedom (SDOF) hysteretic system are smaller in amount.Based on C++program, this paper analyzed the seismic force modification factor R of bilinear elastic-plastic (BIL) model and shear-slipped elastic-plastic (SSP) model for different site and oil condition and ductility. The dynamic P-A effect is considered. The results are compared with those of elastic-perfectly plastic (EPP) models. Results reveal that the equal-energy rule is valid only for BIL model in the range of Tga<T<TgR. For EPP and SSP, the R spectra are greater than for BIL, indicating the importance of energy dissipation capacity in the period range of Tga<T<TgR. With T>2TgR, the R spectra are similar for all models. P-A effect has almost no influence on the R spectra of BIL model, but for EPP and SSP models, its influence increases with the ductility factor and cannot be neglected. For the R spectra with90%assurance, R is very small for BIL model in the period of Tga<T<TgR, the SSP has only minor improvement, the R spectra of EPP model is the greatest. The practical applications of the above findings are:(ⅰ) for SSP systems when the structural period is within Tga<T<TgR, additional requirements must be posted on frames;(ⅱ) for seismic design based on high ductility, the P-A effect must be considered.The seismic force modification factor R of strength degrading modified elastic-perfectly plastic (EPP) model, bilinear elastic (BIL) model and shear-slipped elastic-plastic (SSP) model for different site and ductility factor is calculated. The system coefficient spectra of base shear αEK were constructed to analyze the influence of the degradation of strength on seismic force modification factors. An ideal elastic-plastic model is proposed which is equivalent to the degradation model. Results reveal that the strength degradation has almost no influence on the R spectra of BIL and SSP model, but for modified EPP model, its influence increases with the degradation and cannot be neglected. When taking the strength degradation to define the ductility factor in practice in modified EPP model, it is necessary to adopt a ductility-definition-related strength reduction factor. For the strength degrading system, the strength demand and the deformation-capacity demand are found to be αEK times of the ideal elastic-perfectly plastic model.Dynamic response of SSP, BIL hysteretic system are analyzed. The influence of site types, natural vibration periods, displacement ductility, damping ratios and P-Δ effect coefficients are taken into account. Results indicate that damping ratio and P-Δ effect coefficient all have obvious effect on β.β produces more ideal effect. than R on elastic-plastic seismic force calculation.In order to investigate the curvature ductility in the actual projects and classify the steel cross-sections oriented, this paper uses theoretical methods to study the seismic performance of the steel structure system in the elastic-plastic stage. Push-over analysis of cantilever mast and frame with ANSYS was made to get the relation between curvature ductility and displacement ductility. Compare with displacement ductility, the curvature ductility will suddenly increase so that it is not suitable for the use of design. Curvature ductility in the same seismic force is greater than the displacement ductility. Curvature ductility of cantilever mast is the least, followed by frame without and with uniform load.This paper also analyzed the seismic force modification factor R of dual lateral force resisting system combined with elastic-perfectly plastic (EPP) model and modified Clough (MC) model for different site, ductility factor and degradation of strength. The results are normalized using two characteristic periods and compared with those of EPP and MC models. Results reveal that for dual lateral force resisting system, R spectra are greater than for EPP, slightly larger for MC model. The influence of degradation increases with the degradation and cannot be neglected.