| As one of the earthquake-resilient structures,self-centring steel frames have achieved the higher seismic fortification criterion.Because they can not only prevent structural systems from collapsing but also mitigate post-earthquake residual deformations,self-centring steel frames have been widely focused.The design philosophy of the self-centring steel frames is concentrating the deformation on the self-centring members.Therefore,the main structures besides the self-centring members in the self-centring steel frames will keep elastic under the earthquake motions.Currently,the design and evaluation of self-centring steel frames are mostly based on the assumption,in which the deformation of the structures completely follows the typical bilinear flag-shaped hysteresis.However,studies have shown that due to the unpredictability of the earthquake the deformation of the main structures in the self-centring steel frames may also progress into the plastic stage under the action of strong earthquake motions.In this case,the hysteretic curve of the self-centring steel frames will show multiple yielding stages owing to the interaction of inelasticity of self-centring fuses and ductile structural members.Thus,the typical bilinear flag-shaped hysteresis may be not accurate enough to describe the mechanical behaviour of the self-centring steel frames.Therefore,the steel frame equipped with self-centering energy dissipation bays is chosen to analyse the true seismic response of the self-centring steel frame.Firstly,an equivalent single-degree-of-freedom(SDOF)system consisting of two parallel springs is proposed to describe the steel frames equipped with self-centering energy dissipation bays.Based on the SDOF system and the hysteretic curve of an analytical structure,a trilinear self-centring hysteretic law considering multiple yielding stages is proposed.Then,the nonlinear dynamic analysis of the SDOF system under the trilinear self-centring hysteretic law with different hysteretic parameters is carried out.The influence of each hysteretic parameter on the key indices under the near-field earthquake motions and the far-field earthquake motions is investigated respectively.The key indices include the ductility factor and nonlinear displacement ratio.According to the analysis results,a set of empirical expressions for quantifying the ductility factor and nonlinear displacement ratio of trilinear self-centring hysteretic oscillators are developed via nonlinear regression analysis.Finally,utilising the above empirical expressions and based on the concept of energy balance,a seismic performance evaluation procedure considering multiple indices and multiple stages is proposed to efficiently evaluate the seismic performance of self-centring steel frames.Several conclusions can be reached as follows: 1)it is reasonable to utilise the SDOF system consisting of two parallel springs to represent the mechanical properties of the steel frames equipped with self-centering energy dissipation bays.The trilinear self-centring hysteretic law can be obtained by paralleling the bilinear flag-shaped hysteretic model and ideal elastic-plastic hysteretic model,which can be divided into elastic stage,self-centring stage and ultimate stage.2)the ductility factor and nonlinear displacement ratio of the trilinear self-centring hysteretic oscillators are sensitive to the hysteretic parameters.Particularly,increasing the first yielding stiffness ratio,the second yielding stiffness ratio,the energy dissipation coefficient and the yielding displacement ratio can reduce the ductility factor.The nonlinear displacement ratio decreases with the increasing of the first yielding stiffness ratio,the second yielding stiffness ratio and the energy dissipation coefficient.The effect of the yielding displacement ratio on the nonlinear displacement ratio is not clear.In addition,the interactive effect of the influential parameters on the ductility factor and nonlinear displacement ratio is evident.3.The data calculated from the empirical expressions are close to the results of the inelastic spectral analyses,and the discrepancies are generally within 10%.Thus,the proposed empirical expressions can be used to effectively estimate the ductility factor and nonlinear displacement ratio of the SDOF system under the trilinear self-centring hysteretic law.4)the seismic performance evaluation procedure based on the multiple indices and multiple stages can be used to determine the deformation stages of self-centring steel frames under the given earthquake motions.The peak roof displacement of the self-centring steel frame whose deformation has progressed into the ultimate stage can also be estimated. |
