基于矩法的结构非线性整体抗震可靠性分析
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摘要
建立了基于极限基底剪力的结构非线性整体承载能力极限状态方程。为了从概率的角度评估结构的整体抗震能力,分别提出了基于Nataf变换的点估计法(PEM)和基于点估计法的随机Pushover分析方法(RPA)。在此基础上,提出了一种将点估计法、Pushover分析和矩法(MM)相结合进行结构整体非线性抗震可靠性分析的统计矩半解析法。将该方法应用于钢筋混凝土框架结构,得到了此类结构整体抗震可靠度随地震作用变异系数变化的规律。算例分析表明,本文提出的方法简单、实用、有效,模拟次数很少,且具有与蒙特卡罗模拟法(MCS)相当的计算精度。
In this paper,a global limit state equation for load-carrying capacity of structural systems is firstly set up,in which the safety margin is defined as the difference between the base shear limit of structural system and the total horizontal seismic action.To probabilistically assess the global seismic capacity of a structure,a new point estimation method(PEM) based on Nataf transformation for analyzing statistical moments of complex random functions is put forward,and then,it is combined with deterministic finite element analysis to produce the so-called 'random pushover analysis(RPA)'.On the basis of these new methodologies,a semi-analytical approach which integrates the improved point estimation method,pushover analysis and moment method(MM) is developed to analyze the nonlinear seismic reliability of a structure as a global system.By applying the proposed approach to a RC frame structure,the variation rules of the global seismic reliability of the structure with the coefficients of variation of the seismic action are derived.It is demonstrated by the numerical example that the developed method in this paper is simple,practical and efficient compared with MCS,and with fewer samples,it has the same accuracy as MCS.
In this paper,a global limit state equation for load-carrying capacity of structural systems is firstly set up,in which the safety margin is defined as the difference between the base shear limit of structural system and the total horizontal seismic action.To probabilistically assess the global seismic capacity of a structure,a new point estimation method(PEM) based on Nataf transformation for analyzing statistical moments of complex random functions is put forward,and then,it is combined with deterministic finite element analysis to produce the so-called 'random pushover analysis(RPA)'.On the basis of these new methodologies,a semi-analytical approach which integrates the improved point estimation method,pushover analysis and moment method(MM) is developed to analyze the nonlinear seismic reliability of a structure as a global system.By applying the proposed approach to a RC frame structure,the variation rules of the global seismic reliability of the structure with the coefficients of variation of the seismic action are derived.It is demonstrated by the numerical example that the developed method in this paper is simple,practical and efficient compared with MCS,and with fewer samples,it has the same accuracy as MCS.
引文
[1]董聪.现代结构系统可靠性理论及其应用[M].北京:科学出版社,2001.
[2]Zhao Y G,Ono T.System reliability evaluation ofductile frame structures[J].Journal of StructuralEngineering,ASCE,1998,124(6):678-685.
[3]Zhao Y G,Alfredo H S.System reliability assessmentby method of moments[J].Journal of StructuralEngineering,ASCE,2003,129(10):1341-1349.
[4]Onoufriou T,Forbes V J.Developments in structuralsystem reliability assessments of fixed steel offshoreplatforms[J].Reliability Engineering and SystemSafety,2001,71:189-199.
[5]Li G Q,Li J J.Asemi-analytical simulation method forreliability assessments of structural systems[J].Reliability Engineering and System Safety,2002,78:275-281.
[6]Li J J,Li G Q.Reliability-based integrated design ofsteel portal frames with tapered members[J].Structural Safety,2004,26(2):221-239.
[7]李国强,李进军.基于整体承载极限状态的钢结构可靠度设计方法及其在门式钢刚架设计中的应用[J].建筑结构学报,2004,25(4):94-99.
[8]李国强,刘玉姝,赵欣.钢结构框架体系高等分析与系统可靠度设计[M].北京:中国建筑工业出版社,2006.
[9]欧进萍,侯纲领,吴斌.概率Pushover分析方法及其在结构体系抗震可靠度评估中的应用[J].建筑结构学报,2001,22(6):81-86.
[10]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.
[11]Liu P L,Der Kiureghian A.Multivariate distributionmodels with prescribed marginals and covariances[J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[12]Zhao Y G,Ono T.New point estimates for probabilitymoments[J].Journal of Engineering Mechanics,ASCE,2000,126(4):433-436.
[13]Zhao Y G,Ono T.Moment methods for structuralreliability[J].Structural Safety,2001,23(1):47-75.
[14]王超.结构非线性整体抗震可靠度与动力可靠度分析[D].哈尔滨:哈尔滨工业大学,2005.
[2]Zhao Y G,Ono T.System reliability evaluation ofductile frame structures[J].Journal of StructuralEngineering,ASCE,1998,124(6):678-685.
[3]Zhao Y G,Alfredo H S.System reliability assessmentby method of moments[J].Journal of StructuralEngineering,ASCE,2003,129(10):1341-1349.
[4]Onoufriou T,Forbes V J.Developments in structuralsystem reliability assessments of fixed steel offshoreplatforms[J].Reliability Engineering and SystemSafety,2001,71:189-199.
[5]Li G Q,Li J J.Asemi-analytical simulation method forreliability assessments of structural systems[J].Reliability Engineering and System Safety,2002,78:275-281.
[6]Li J J,Li G Q.Reliability-based integrated design ofsteel portal frames with tapered members[J].Structural Safety,2004,26(2):221-239.
[7]李国强,李进军.基于整体承载极限状态的钢结构可靠度设计方法及其在门式钢刚架设计中的应用[J].建筑结构学报,2004,25(4):94-99.
[8]李国强,刘玉姝,赵欣.钢结构框架体系高等分析与系统可靠度设计[M].北京:中国建筑工业出版社,2006.
[9]欧进萍,侯纲领,吴斌.概率Pushover分析方法及其在结构体系抗震可靠度评估中的应用[J].建筑结构学报,2001,22(6):81-86.
[10]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.
[11]Liu P L,Der Kiureghian A.Multivariate distributionmodels with prescribed marginals and covariances[J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[12]Zhao Y G,Ono T.New point estimates for probabilitymoments[J].Journal of Engineering Mechanics,ASCE,2000,126(4):433-436.
[13]Zhao Y G,Ono T.Moment methods for structuralreliability[J].Structural Safety,2001,23(1):47-75.
[14]王超.结构非线性整体抗震可靠度与动力可靠度分析[D].哈尔滨:哈尔滨工业大学,2005.
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