大跨度结构多点抗震分析及程序研制
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摘要
由于行波效应、非相干性效应以及局部场地效应等空间效应的影响,大跨度结构各地面支承点在地震过程中的地面运动是不同的。不同的支承点运动可使结构产生较大的内力,因此有必要对大跨度桥梁结构进行多点激励地震响应分析。目前,大跨度结构地震响应分析方法主要有:反应谱方法、时程分析方法和功率谱方法。本文对这三种分析方法进行了比较详细的介绍,分析了它们的优缺点和目前存在的问题。在多点功率谱方法(虚拟激励法)研究工作的基础上,重点研究了多点输入反应谱方法和多点输入地震波的生成,并在有限元程序BPEM的基础上进行了程序实现。本文的主要工作包括:
1)介绍了大跨度结构在多支承激励作用下反应谱分析(MSRS)的数值过程,重点关注了该方法在大型有限元程序中的实现策略。在有限元程序BPEM的基础上,实现了大跨度结构在多支承激励作用下的反应谱分析功能。通过对互功率谱密度函数进行线性插值,探讨了求解互相关系数的积分表达式的简化计算方法。将MSRS法推广应用于沿水平方向传播的这三种类型的地震波(P波、SH波和SV波),推导了相应的计算公式。作为例子,对一两跨简支梁桥进行了多支承激励作用下的反应谱分析。该模型受到峰值地面加速度(PGA)值为0.5g的地震荷载作用,对三种荷载条件下的地震响应进行说明和比较,揭示了多支承激励作用下大跨度结构地震响应的一些特点。
2)总结了多支承点输入的地震动合成的理论和方法,并且采用工程常用的三角级数方法编写地震动合成程序。在合成过程中,通过互功率谱密度函数考虑地面运动的空间相关性,将互功率谱密度函数矩阵分解成一个下三角阵,从而获得幅值表达式,最终合成具有非平稳性的地震动时程。最后,通过一个实例合成地震动,并且利用生成的地震动进行反应谱拟合来验证地震动的正确性。
3)针对一个具体大跨度桥梁,在BPEM程序中使用三种方法(即功率谱方法、反应谱方法和时程分析方法)分别进行多点抗震分析,比较这三种方法所计算出来的响应结果,分析不同方法的特点,从而考核了所编制的程序。
It is known that,under realistic conditions,there are differences among supports of long span structures due to variations of the ground motion,including the wave passage, incoherence and local effects.The differences in the support motions can significantly influence the internal forces generated in the structure.It is necessary to investigate seismic responses of long-span structures subjected to multi-support excitations.Presently,a seismic analysis can be performed either by the response spectrum method,the time history method or by the power spectrum method.This paper introduces these three methods in detail and discusses their advantages and disadvantages.Based on the power spectrum method of multi-support excitation(Pseudo Excitation Method),the multi-support response spectrum method and the multi-point ground motion time histories are investigated especially,and the finite element based program BPEM is developed.This paper is mainly includes three aspects as following:
1) A numerical procedure is described for the response spectrum analysis of long-span structures subjected to multi-support excitations,attention is devoted to the programming strategy of this algorithm.Based on a finite element program BPEM,it has been implemented to make response spectrum analysis of long-span structures under multi-support excitations. Additionally,a simplified method is developed to obtain the cross correlation coefficients by line interpolating of the cross power spectral densities.The MSRS method is extended to deal with three different types of earthquake wave propagating along horizontal direction(i.e.,P wave,SH wave and SV wave),the corresponding formula are also developed.An example of an application is shown regarding the seismic responses of a FE model of a two-span beam for multi-supported excitations.The model is subjected to an extreme multiple-support seismic loading having a PGA equal to 0.5g.The seismic behavior in the three loading situations is illustrated and compared,showing some facets,especially in terms of multi-support excitations for long-span structures.
2) The multi-points ground motion simulation method is introduced and a corresponding program is developed using the common trigonometric series method to synthesis seismic waves.The cross power spectral density function is used for consider the spatially varying ground motions.The cross power spectral density matrix is a Hermitian matrix,which can be decomposed into the product of a lower triangular matrix and a upper triangular matrix,so the amplitudes can be expressed by lower triangular matrix,and non-stationary time history is synthesized.Finally,an example is verified to fit a standard response spectrum by generating the acceleration time histories.
3) Multi-support excitation seismic response analysis of a long-span bridge is fulfilled by all the three methods(the power spectrum method,response spectrum and time history analysis method) in the program BPEM.The results are compared as well as the program is verified.
1)介绍了大跨度结构在多支承激励作用下反应谱分析(MSRS)的数值过程,重点关注了该方法在大型有限元程序中的实现策略。在有限元程序BPEM的基础上,实现了大跨度结构在多支承激励作用下的反应谱分析功能。通过对互功率谱密度函数进行线性插值,探讨了求解互相关系数的积分表达式的简化计算方法。将MSRS法推广应用于沿水平方向传播的这三种类型的地震波(P波、SH波和SV波),推导了相应的计算公式。作为例子,对一两跨简支梁桥进行了多支承激励作用下的反应谱分析。该模型受到峰值地面加速度(PGA)值为0.5g的地震荷载作用,对三种荷载条件下的地震响应进行说明和比较,揭示了多支承激励作用下大跨度结构地震响应的一些特点。
2)总结了多支承点输入的地震动合成的理论和方法,并且采用工程常用的三角级数方法编写地震动合成程序。在合成过程中,通过互功率谱密度函数考虑地面运动的空间相关性,将互功率谱密度函数矩阵分解成一个下三角阵,从而获得幅值表达式,最终合成具有非平稳性的地震动时程。最后,通过一个实例合成地震动,并且利用生成的地震动进行反应谱拟合来验证地震动的正确性。
3)针对一个具体大跨度桥梁,在BPEM程序中使用三种方法(即功率谱方法、反应谱方法和时程分析方法)分别进行多点抗震分析,比较这三种方法所计算出来的响应结果,分析不同方法的特点,从而考核了所编制的程序。
It is known that,under realistic conditions,there are differences among supports of long span structures due to variations of the ground motion,including the wave passage, incoherence and local effects.The differences in the support motions can significantly influence the internal forces generated in the structure.It is necessary to investigate seismic responses of long-span structures subjected to multi-support excitations.Presently,a seismic analysis can be performed either by the response spectrum method,the time history method or by the power spectrum method.This paper introduces these three methods in detail and discusses their advantages and disadvantages.Based on the power spectrum method of multi-support excitation(Pseudo Excitation Method),the multi-support response spectrum method and the multi-point ground motion time histories are investigated especially,and the finite element based program BPEM is developed.This paper is mainly includes three aspects as following:
1) A numerical procedure is described for the response spectrum analysis of long-span structures subjected to multi-support excitations,attention is devoted to the programming strategy of this algorithm.Based on a finite element program BPEM,it has been implemented to make response spectrum analysis of long-span structures under multi-support excitations. Additionally,a simplified method is developed to obtain the cross correlation coefficients by line interpolating of the cross power spectral densities.The MSRS method is extended to deal with three different types of earthquake wave propagating along horizontal direction(i.e.,P wave,SH wave and SV wave),the corresponding formula are also developed.An example of an application is shown regarding the seismic responses of a FE model of a two-span beam for multi-supported excitations.The model is subjected to an extreme multiple-support seismic loading having a PGA equal to 0.5g.The seismic behavior in the three loading situations is illustrated and compared,showing some facets,especially in terms of multi-support excitations for long-span structures.
2) The multi-points ground motion simulation method is introduced and a corresponding program is developed using the common trigonometric series method to synthesis seismic waves.The cross power spectral density function is used for consider the spatially varying ground motions.The cross power spectral density matrix is a Hermitian matrix,which can be decomposed into the product of a lower triangular matrix and a upper triangular matrix,so the amplitudes can be expressed by lower triangular matrix,and non-stationary time history is synthesized.Finally,an example is verified to fit a standard response spectrum by generating the acceleration time histories.
3) Multi-support excitation seismic response analysis of a long-span bridge is fulfilled by all the three methods(the power spectrum method,response spectrum and time history analysis method) in the program BPEM.The results are compared as well as the program is verified.
引文
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[3]潘旦光,楼梦麟,范立础.多点输入下大跨度结构地震反应分析现状[J].同济大学学报,2001,29(6):1213-1219.
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