基于非线性静力分析的地震强度直接计算方法
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摘要
依据给定延性系数下地震强度和伪加速度响应之间的正比规律,提出了根据非线性静力分析得到的结构响应求解特定地震波形下相应地震强度的直接计算方法。建议的直接计算方法基于非线性静力分析得到的能力曲线,通过建立弹塑性体系伪加速度动力放大系数与延性系数之间的函数关系,快速求解曲线上各点对应的地震强度,建立可用于新一代基于性态抗震能力分析的结构响应函数。与已有寻求特定地震强度下结构响应性态点的计算方法不同,所提出的计算方法从能力曲线上的任一点出发,求解过程中仅有一个未知量,避免了迭代或试算。它既适用于平滑的设计谱,也适用于针对特定地震波的实际反应谱。在求得的结构响应曲线上,根据特定的地震强度,可以准确地反求性态点。针对实际反应谱和设计谱,通过算例分别与采用非线性时程分析和Chopra的算例进行对照。结果表明:建议的计算方法不仅准确,而且过程直接、计算快捷。
The proportional relationship between seismic intensity and pseudo acceleration response under a given ductility factor was revealed.A procedure,which directly calculates the seismic intensity of a determined ground wave corresponding to the structural response from non-linear static analysis,was proposed.Based on the capacity curve obtained from the non-linear static procedure,the direct procedure was derived by establishing the relationship between the pseudo acceleration scale factor and the ductility factor of inelastic system.The procedure is efficient to generate the structural response function under the analytical frame of 'Next-generation performance-based seismic design procedures'.Different from conventional methods which search the performance point under a certain seismic intensity,the proposed procedure starts from an arbitrary point on the capacity curve.Since the proposed procedure has only one unknown parameter,iteration or trial calculation can be avoided.The procedure is suitable for the actual response spectrum of a determined ground wave,as well as the smooth design spectrum.The non-linear history analysis and a numerical example of Chopra,using actual and design spectrum,are adopted respectively to calibrate the procedure.The results show that the proposed procedure is exact and fast.
The proportional relationship between seismic intensity and pseudo acceleration response under a given ductility factor was revealed.A procedure,which directly calculates the seismic intensity of a determined ground wave corresponding to the structural response from non-linear static analysis,was proposed.Based on the capacity curve obtained from the non-linear static procedure,the direct procedure was derived by establishing the relationship between the pseudo acceleration scale factor and the ductility factor of inelastic system.The procedure is efficient to generate the structural response function under the analytical frame of 'Next-generation performance-based seismic design procedures'.Different from conventional methods which search the performance point under a certain seismic intensity,the proposed procedure starts from an arbitrary point on the capacity curve.Since the proposed procedure has only one unknown parameter,iteration or trial calculation can be avoided.The procedure is suitable for the actual response spectrum of a determined ground wave,as well as the smooth design spectrum.The non-linear history analysis and a numerical example of Chopra,using actual and design spectrum,are adopted respectively to calibrate the procedure.The results show that the proposed procedure is exact and fast.
引文
[1]ATC-58 50%Draft Guidelines for seismicperformance assessment of buildings[S].WashingtonDC:Federal Emergency Management Agency,2009.
[2]FEMA 445 Next-generation performance-based seismicdesign guidelines program plan for new and existingbuildings[S].Washington DC:Federal EmergencyManagement Agency,2006.
[3]Vamvatsikos D,Cornell C A.Incremental dynamicanalysis[J].Earthquake Engineering and StructuralDynamics,2002,31(3):491-514.
[4]FEMA 350 Recommended seismic design criteria fornew steel moment-frame buildings[S].WashingtonDC:Federal Emergency Management Agency,2000.
[5]GB 50011—2010建筑抗震设计规范[S].北京:建筑工业出版社,2010.(GB 50011—2010 Code forseismic design of buildings[S].Beijing:ChinaArchitecture&Building Press,2010.(in Chinese))
[6]ATC-40 Seismic evaluation and retrofit of concretebuildings[S].Washington DC:Federal EmergencyManagement Agency,1996.
[7]FEMA 356 Prestandard and commentary for theseismic rehabilitation of buildings[S].WashingtonDC:Federal Emergency Management Agency,2000.
[8]Akkar S,Metin A.Assessment of improved nonlinearstatic procedures in FEMA-440[J].Journal ofStructural Engineering,2007,133(9):1237-1246.
[9]Krawinkler H.New trends in seismic designmethodology[C]//Proceedings of 10th EuropeanConference on Earthquake Engineering.Rotterdam:Balkema,1995:821-830.
[10]汪梦甫,周锡元.高层建筑结构抗震弹塑性分析方法及抗震性能评估研究[J].土木工程学报,2003,36(11):44-48.(Wang Mengfu,Zhou Xiyuan.Modified pushover analysis and seismic performanceevaluation for tall building[J].China Civil EngineeringJournal,2003,36(11):44-48.(in Chinese))
[11]杨溥,李英民,王亚勇,等.结构静力弹塑性分析(push-over)方法的改进[J].建筑结构学报,2000,21(1):44-50.(YANG Pu,LI Yingmin,WANGYayong,et al.A study on improvement of push-overanalysis[J].Journal of Building Structures,2000,21(1):44-50.(in Chinese))
[12]孙爱伏,欧进萍.高层钢结构抗震Pushover分析的侧向力分布模式及其影响[J].地震工程与工程振动,2008,28(4):88-93.(Sun Aifu,Ou Jinping.Lateral action patterns and their effects on pushoverseismic analysis of steel tall buildings[J].Journal ofEarthquake Engineering and Engineering Vibration,2008,28(4):88-93.(in Chinese))
[13]卢文胜,吕西林.模态静力非线性分析中模态选择的研究[J].地震工程与工程振动,2004,24(6):32-38.(Lu Wengsheng,Lu Xilin.Study on the modeselection in the modal pushover analysis[J].Journal ofEarthquake Engineering and Engineering Vbration,2004,24(6):32-38.(in Chinese))
[14]沈蒲生,龚胡广.多模态静力推覆分析及其在高层混合结构体系抗震评估中的应用[J].工程力学,2006,23(8):69-73.(Shen Pusheng,GongHuguang.Multi-mode pushover analysis and seismicevaluation in hybrid structures[J].EngineeringMechanics,2006,23(8):69-73.(in Chinese))
[15]毛建猛,谢礼立,翟长海.模态Pushover分析方法的研究和改进[J].地震工程与工程振动,2006,26(6):50-55.(Mao Jianmeng,Xie Lili,Zhai Changhai.Studies on and improvements in modal pushoveranalysis[J].Journal of Earthquake Engineering andEngineering Vibration,2006,26(6):50-55.(inChinese))
[16]Chopra A K,Goel R K.A modal pushover analysisprocedure for estimating seismic demands for buildings[J].Earthquake Engineering and Structural Dynamics,2002,31(3):561-582.
[17]Kalkan E,Kunnath S K.Adaptive modal combinationprocedure for nonlinear static analysis of buildingstructures[J].Journal of Structural Engineering,2006,132(11):1721-1731.
[18]Fragiacomo M,Amadio C,Rajgelj S.Evaluation of thestructural response under seismic actions using non-linear static methods[J].Earthquake Engineering andStructural Dynamics,2006,35(12):1511-1531.
[19]Gencturk B,Elnashai A S.Development andapplication of an advanced capacity spectrummethod[J].Engineering Structures,2008,30(11):3345-3354.
[20]Fajfar P.Capacity spectrum method based on inelasticdemand spectra[J].Earthquake Engineering andStructual Dynamics,1999,28(9):979-993.
[21]Chopra A K,Goel R K.Capacity demand diagrammethod for estimating seismic deformation of inelasticstructures:SDOF system[R].Berkeley,California:University of California.Pacific Earthquake EngineeringResearch Center,1999:40-45.
[22]屈成忠,谢礼立.性态点的数值解法[J].世界地震工程,2003,19(1):21-24.(Qu Chengzhong,XieLili.A numerical solution for determining performancepoint[J].World Earthquake Engineering,2003,19(1):21-24.(in Chinese))
[23]叶列平.基于性能/位移的能力-需求曲线设计方法[J].工程抗震与加固改造,2009,31(3):50-55.(Ye Lieping.Capacity-demand curves method forperformance/displacement-based seismic design[J].Earthquake Resistant Engineering and Retrofitting,2009,31(3):50-55.(in Chinese))
[24]叶献国.多层建筑结构抗震性能的近似评估-改进的能力谱方法[J].工程抗震,1998,20(4):11-15.
[25]Sung Y C,Liao W I,Yen W P.Performance-basedconcept on seismic evaluation of existing bridges[J].Earthquake Engineering and Engineering Vibration,2009,8(1):127-135.
[26]Newmark N M,Hall W J.Earthquake spectra anddesign[R].Oakland,California:EarthquakeEngineering Research Institute,1982.
[27]Chopra A K.结构动力学[M].谢礼力,吕大刚,译.北京:高等教育出版社,2007.(Chopra A K.Dynamics of structures[M].Translated by Xie Lili,LüDagang.Beijing:Higher Education Press,2007.(inChinese))
[2]FEMA 445 Next-generation performance-based seismicdesign guidelines program plan for new and existingbuildings[S].Washington DC:Federal EmergencyManagement Agency,2006.
[3]Vamvatsikos D,Cornell C A.Incremental dynamicanalysis[J].Earthquake Engineering and StructuralDynamics,2002,31(3):491-514.
[4]FEMA 350 Recommended seismic design criteria fornew steel moment-frame buildings[S].WashingtonDC:Federal Emergency Management Agency,2000.
[5]GB 50011—2010建筑抗震设计规范[S].北京:建筑工业出版社,2010.(GB 50011—2010 Code forseismic design of buildings[S].Beijing:ChinaArchitecture&Building Press,2010.(in Chinese))
[6]ATC-40 Seismic evaluation and retrofit of concretebuildings[S].Washington DC:Federal EmergencyManagement Agency,1996.
[7]FEMA 356 Prestandard and commentary for theseismic rehabilitation of buildings[S].WashingtonDC:Federal Emergency Management Agency,2000.
[8]Akkar S,Metin A.Assessment of improved nonlinearstatic procedures in FEMA-440[J].Journal ofStructural Engineering,2007,133(9):1237-1246.
[9]Krawinkler H.New trends in seismic designmethodology[C]//Proceedings of 10th EuropeanConference on Earthquake Engineering.Rotterdam:Balkema,1995:821-830.
[10]汪梦甫,周锡元.高层建筑结构抗震弹塑性分析方法及抗震性能评估研究[J].土木工程学报,2003,36(11):44-48.(Wang Mengfu,Zhou Xiyuan.Modified pushover analysis and seismic performanceevaluation for tall building[J].China Civil EngineeringJournal,2003,36(11):44-48.(in Chinese))
[11]杨溥,李英民,王亚勇,等.结构静力弹塑性分析(push-over)方法的改进[J].建筑结构学报,2000,21(1):44-50.(YANG Pu,LI Yingmin,WANGYayong,et al.A study on improvement of push-overanalysis[J].Journal of Building Structures,2000,21(1):44-50.(in Chinese))
[12]孙爱伏,欧进萍.高层钢结构抗震Pushover分析的侧向力分布模式及其影响[J].地震工程与工程振动,2008,28(4):88-93.(Sun Aifu,Ou Jinping.Lateral action patterns and their effects on pushoverseismic analysis of steel tall buildings[J].Journal ofEarthquake Engineering and Engineering Vibration,2008,28(4):88-93.(in Chinese))
[13]卢文胜,吕西林.模态静力非线性分析中模态选择的研究[J].地震工程与工程振动,2004,24(6):32-38.(Lu Wengsheng,Lu Xilin.Study on the modeselection in the modal pushover analysis[J].Journal ofEarthquake Engineering and Engineering Vbration,2004,24(6):32-38.(in Chinese))
[14]沈蒲生,龚胡广.多模态静力推覆分析及其在高层混合结构体系抗震评估中的应用[J].工程力学,2006,23(8):69-73.(Shen Pusheng,GongHuguang.Multi-mode pushover analysis and seismicevaluation in hybrid structures[J].EngineeringMechanics,2006,23(8):69-73.(in Chinese))
[15]毛建猛,谢礼立,翟长海.模态Pushover分析方法的研究和改进[J].地震工程与工程振动,2006,26(6):50-55.(Mao Jianmeng,Xie Lili,Zhai Changhai.Studies on and improvements in modal pushoveranalysis[J].Journal of Earthquake Engineering andEngineering Vibration,2006,26(6):50-55.(inChinese))
[16]Chopra A K,Goel R K.A modal pushover analysisprocedure for estimating seismic demands for buildings[J].Earthquake Engineering and Structural Dynamics,2002,31(3):561-582.
[17]Kalkan E,Kunnath S K.Adaptive modal combinationprocedure for nonlinear static analysis of buildingstructures[J].Journal of Structural Engineering,2006,132(11):1721-1731.
[18]Fragiacomo M,Amadio C,Rajgelj S.Evaluation of thestructural response under seismic actions using non-linear static methods[J].Earthquake Engineering andStructural Dynamics,2006,35(12):1511-1531.
[19]Gencturk B,Elnashai A S.Development andapplication of an advanced capacity spectrummethod[J].Engineering Structures,2008,30(11):3345-3354.
[20]Fajfar P.Capacity spectrum method based on inelasticdemand spectra[J].Earthquake Engineering andStructual Dynamics,1999,28(9):979-993.
[21]Chopra A K,Goel R K.Capacity demand diagrammethod for estimating seismic deformation of inelasticstructures:SDOF system[R].Berkeley,California:University of California.Pacific Earthquake EngineeringResearch Center,1999:40-45.
[22]屈成忠,谢礼立.性态点的数值解法[J].世界地震工程,2003,19(1):21-24.(Qu Chengzhong,XieLili.A numerical solution for determining performancepoint[J].World Earthquake Engineering,2003,19(1):21-24.(in Chinese))
[23]叶列平.基于性能/位移的能力-需求曲线设计方法[J].工程抗震与加固改造,2009,31(3):50-55.(Ye Lieping.Capacity-demand curves method forperformance/displacement-based seismic design[J].Earthquake Resistant Engineering and Retrofitting,2009,31(3):50-55.(in Chinese))
[24]叶献国.多层建筑结构抗震性能的近似评估-改进的能力谱方法[J].工程抗震,1998,20(4):11-15.
[25]Sung Y C,Liao W I,Yen W P.Performance-basedconcept on seismic evaluation of existing bridges[J].Earthquake Engineering and Engineering Vibration,2009,8(1):127-135.
[26]Newmark N M,Hall W J.Earthquake spectra anddesign[R].Oakland,California:EarthquakeEngineering Research Institute,1982.
[27]Chopra A K.结构动力学[M].谢礼力,吕大刚,译.北京:高等教育出版社,2007.(Chopra A K.Dynamics of structures[M].Translated by Xie Lili,LüDagang.Beijing:Higher Education Press,2007.(inChinese))
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