Study On Seismic Performance And Analysis Method Of Multi-yield-stage Steel Structures Subjected To Multiple Earthquake Motions

The probability of the structures subjected to isolated earthquakes is low.The case that multiple earthquake motions occur during the event is pretty high.Multiple earthquakes result in further damages to structure,which means more serious damage to structures.But,in most current codes all over the world,the seismic design methods do not consider the effects of multiple earthquake motions.The requirement of seismic resilience plays an important role in the recovery of society and economy,after the structures subjected to earthquake.An effective approach to enhance seismic resilience is to install the structures with energy dissipation components.It suggests that such structures show multi-yielding stages.The seismic responses of these structures under repeated earthquake are significantly different from those under a single earthquake.In this paper,the seismic performance and analysis methods of multi-yield steel structures under repeated earthquake are studied,and the main contents and results are presented as follows:（1）Eighteen hysteretic models were introduced and compared.An artificial ground motion database composed of repeated near-field earthquake motions is developed in this study.A statistical examination of a database with more than eighty-four million（84,048,000）energy factor demands of multi-yield-stage oscillators representing multi-yield-stage steel structures responding in different yielding stages is conducted.The cascading effect among the hysteretic parameters and repeated seismic events on the energy factor is examined in detail.The research findings show that whenδ<δ₂,the energy factor demand of a multi-yield-stage steel structure is not sensitive to repetition of earthquake motions and the hysteretic parameter.In contrast,a remarkable elevation of the energy factor is observed for multi-yield-stage oscillators progressing into the stage ofδ>δ₂.A nonlinear regression model quantifying the mean energy factor demand of the system under repeated near-field earthquake motions is proposed to facilitate performance-based seismic design of multi-yield-stage structures.By comparing with the predictions based on the Newmark and Hall design spectra,the mathematical model proposed in this paper is proved to have better applicability and accuracy.（2）Based on one hundred pulse-like near-fault earthquake events,the definition of the energy factor demand of modified-Clough oscillators was clarified.Then,oscillators covering a reasonable range of nonlinear parameters and dynamic properties were analysed with a constant-ductility-based method,and a ground motion database characterising pulse-like near-fault ground earthquake motions was used as seismic excitations.The practical range of hysteretic parameters was covered by more than 210 thousand inelastic spectral analyses.The influence of the hysteretic quantities on the energy factor demand of the modified-Clough oscillators was discussed based on the statistical results.Comparison between the energy factor demand from the analysis database and the counterparts computed based on the widely used Newmark-Hall model was made.As a general remark,the mean energy factor demand evidently increases with increasing ductility factor for short-period systems（i.e.T≤0.3s）,but the opposite trend was observed for the modified-Clough oscillators with a longer period.As for the effect of the post-yielding stiffness ratio,it was seen that this parameter only has a slight effect on the mean energy factor demand for very short period systems（i.e.T=0.1s）,and increasing post-yielding stiffness ratio results in a reduction of the mean energy factor demand.To clarify the effect of the ductility factor,the energy factors of oscillators with variedμ_s were compared,and the mean energy factor of short-period systems（i.e.T≤0.3s）and the counterparts with longer period withμ_s=2 were plotted against the counterparts with larger ductility factors,as shown in this paper,and the aforementioned observation can be demonstrated.It can be seen that the variation of the post-yielding stiffness only results in slight fluctuation of the energy factor of systems with T=0.1s.Comparing the energy factor spectra with varied ductility levels,it was also seen that increasing the ductility factor correspondingly increases the data scatteration considering all ground motion samples.The energy factor spectra determined from the classical Newmark and Hall design spectra are also indicated in this paper for comparison.In general,the Newmark and Hall spectra produced reasonable estimates of the mean energy factor demand on the conservative side when the ductility factor was not significant,i.e.μ_s=2.With the ductility factor increasing,the direct application of the Newmark and Hall spectra may underestimate the mean energy factor demand of the modified-Clough oscillators from the short-to-moderate period region.Recognising the limitations of the current design model,an alternative design equation for estimating the mean energy factor demand of oscillators with the modified Clough hysteretic model was proposed using nonlinear regression analyses.The improved accuracy of the developed model was demonstrated.（3）The paper commenced with clarification of the hysteretic behaviour of steel structures exhibiting multi-yielding stages,and recent experimental findings were also revisited.An effective finite element model for replicating the cyclic response of a multi-yield-stage steel structure was proposed and verified by the test data.The finite element（FE）programme ABAQUS was used to develop numerical models of the specimens in the four test programmes.Specifically,a SSW was discretised by shell elements.The beam elements were utilised to model the frame members.Intersecting elastic beam elements were used to simulate the connection between the SSW with the adjacent girders,The energy dissipation beams are discretised by five I-section beam elements with varied flange widths.The applicability of a multi-yielding stages model for idealising the hysteretic response of the systems was examined.It is seen that reasonable correlation between the FE predictions and the test results was obtained,and the predicted curves by‘case A’were in better agreement with the test results because the behaviour deterioration of the SSWs induced by distortional buckling of the flexural links was simulated reasonably.In contrast,fuller hysteretic curves were achieved in‘case B’,in which the lateral distortional buckling of the flexural links was avoided.In practical cases,available buckling restrained devices can ensure the stable hysteretic performance of SSWs.This part provides a basis for the study below.（4）The nonlinear response history analysis was applied to two prototype multi-yield-stage steel structures under 2 groups of repeated earthquakes（i.e.160earthquake events）.Based on the requirement for seismic shear-gravity ratio,the calculating results about basic structural period satisfied with the base shear factor issued in the code were attained.It can be easy to determine if basic structural period satisfied with the base shear factor issued in the code by using this table.The research findings show that whenδ<δ₂,the seismic response of a multi-yield-stage steel structure is not sensitive to repetition of earthquake motions and the hysteretic parameter.In contrast,a remarkable elevation of the seismic response is observed for multi-yield-stage structures progressing into the stage ofδ>δ₂.（5）This part aims to develop a nonlinear static procedure for estimating seismic demands of steel structures exhibiting multi-yielding stages under seismic actions.Numerical models were also developed and verified b y revisiting the four previous test programmes.Then,a multi-stage-based nonlinear static procedure governed by the energy-balance concept was proposed,which enables practitioners to quantify the seismic demands of a multi-yield-stage steel structure.The multi-stage-based nonlinear static procedure was subsequently applied to two prototype multi-yield-stage steel structures under design basis earthquakes and maximum considered earthquakes（i.e.forty earthquake events）.The predictions by the multi-stage-based nonlinear static procedure were compared with nonlinear response history analysis to examine the effectiveness of the method.The lateral load distributions documented in FEMA-356 were also included in the work for comparison.The observations from this part suggests that the proposed multi-stage-based nonlinear static procedure offers a promising tool for estimating the peak seismic response of steel structures showing multi-yielding stages.（6）Based on the proposed equation for estimating the energy factor demand of oscillators,this part aims to develop a nonlinear static procedure for estimating seismic demands of steel structures exhibiting multi-yielding stages under repeated earthquake.The multi-stage-based nonlinear static procedure was subsequently applied to a prototype multi-yield-stage steel structures under repeated earthquakes.The predictions by the multi-stage-based nonlinear static procedure were compared with nonlinear response history analysis to examine the effectiveness of the method.The observations from this part suggests that the proposed multi-stage-based nonlinear static procedure offers a promising tool for estimating the peak seismic response of steel structures showing multi-yielding stages under repeated earthquakes.