Research On Seismic Performance Of PC Frame Based On Damage Model Of Stiffness Degradation And Fiber-beam Elements

As cast-in-situ prestressed concrete(PC)frame structure is widely promoted and used in Chinese seismic zones,it’s necessary to carry out seismic performance analysis and evaluation on the PC frame structure.In addition,as the performance-based seismic design method become the research focus of scholars,how to effectively quantify the performance goals has become one of the core issues of the method,more and more researchers tend to adopt damage models.In the paper,based on the the bonded cast-in-situ PC frame designed according to our country codes and standards,the fiber element analysis model and damage model for PC frame structure were established.The HRB400 bar and PC beam test were carried out.The established numerical analysis model and damage model were verified by experiments,and the damage index values were determined.Based on the vulnerability analysis method of the incremental dynamic analysis(IDA),the seismic performance of the PC frame was analyzed and evaluated.The low cycle fatigue tests of HRB400 steel bars were carried out,and the ReinforcingSteel constitutive parameters related to HRB400 steel bars were obtained.The quasi-static tests of three unbonded prestressed concrete(PC)beams and one reinforced concrete(RC)were accomplished.The results show that simply increasing the reinforcement ratio of longitudinal reinforcement can improve the yield strength of PC beam,but its ductility may decrease.When the longitudinal reinforcement ratio is the same,the smaller the applied prestressing force is,the fuller the hysteretic curve of the beam is,but the ultimate bearing capacity of the beams is not changed,and the ductility improvement is not obvious.The hysteresis curve of RC beam is fuller than PC beam,but its ductility decreases obviously because of its wide crack.Taking OpenSees as analysis platform the PC component combined model using fiber beam column element were established.The established model included Simplified Chang and Mander concrete model,ReinforcingSteel model and Hysteretic model embodies Initial Strain or Initial Stress model.The numerical analysis model was used to analyze the PC beam test.The results show that the finite element model including the smooth bearing element and the zero length element embodying Elastic PPGap material can not only accurately describes the hysteretic characteristics of PC beam under cyclic loading,but also can accurately simulate the mechanical behavior of prestressed tendons and the deformation behavior of sections.A damage model was established based on material damage(stiffness degradation and fiber beam-column elements)in Matlab.In the established model,concrete fiber damage was defined by the degradation of the initial reloading modulus,reinforcing steel fiber damage was defined by the low-cycle fatigue law,and prestressing tendon fiber damage was defined by the plastic strain.Then,section damage,member damage,story damage and structure damage were defined by the degradation of the sectional bending stiffness,the degradation of the rod-end bending stiffness,the degradation of the story lateral stiffness and structure lateral stiffness,respectively.Three RC columns,a PC beam,a RC frame and a PC frame tested by quasi-static method were analysed to verify the established model.The results indicate that the damage model can determine their damage states accurately,and a close connection between damage indices at various level by using the direct stiffness method and static condensation method.Additionally,the established damage model layed a solid foundation for damage estimation at various levels of a large-scale structure subjected to seismic loading.Finally,differences between near-fault ground motions and far-fault ground motions were identified by comparing the response spectras of a single degree of freedom elastic system.One three-story three-span 2nd grade PC frame and one six-story three-span 1st grade PC frame were designed according to the current codes and standards,and the response characteristics of the PC frames subjected to near-fault pulse-like ground motions and near-fault no pulse-like ground motions were analyzed.Then,the seismic performance of the designed PC frames was evaluated by using the established damage model and the vulnerability analysis based on IDA.The results show that two PC frames can meet the seismic requirements of frequent earthquakes and rare earthquakes under the action of pulse-like ground motions,but the maximum story drift of the six-story PC frame is very close to the limit.The three-story PC frame and the six-story PC frame can accomplish the "mixed energy dissipation mechanism" under the action of near-fault ground motion,and the energy dissipation mechanism of the PC frames don’t change under near-fault pulse-like ground motions.The two PC framework designed according to the current codes and standards will not collapse under rare earthquakes and meet the requirement of life safety.The pulse components of near-fault pulse-like ground motions were extracted,and the influence of the pulse component parameters on the response of the PC frames was analyzed.The results show that Sap(T1,ξ)has a strong correlation with the damage of PC frame,and it is suggested that Sap(T1,ξ)should be used as the parameters of ground motion adjustment.The correlation between the damage of PC framework and Vp is weak.The damage of PC frame is greater under seveal Tp/T1 values(2.8,4.8,10.5).Therefore,it is suggested that the effect of pulse effect should be taken into account in the process of structural design,so that the designed structure can not exceed the specified performance level.