考虑地震空间效应的大跨度空间结构抗震分析与设计方法
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摘要
近年来,我国陆续建成了一批形式新颖、规模宏大的大跨度空间建筑。与传统建筑结构相比,大跨度空间建筑结构尺度大,地震空间效应的影响不容忽视,而现行设计规范无法考虑、难以满足抗震安全性要求,因此针对大跨度空间结构的特点,建立考虑地震空间效应的大跨度空间结构抗震设计方法,已经成为工程界和学术界迫切需要解决的关键科学问题。
本文基于随机振动理论,系统研究了大跨度空间结构随机地震响应分析的相关算法、地震动场模型以及地震空间效应的影响,建立了考虑地震空间效应的大跨度空间结构抗震设计方法。主要研究工作与创新成果包括以下几个方面:
(1)在原有虚拟激励算法的基础上,改进了多点激励虚拟激励算法,提高了大跨度空间结构随机地震响应分析的计算效率,使算法更便于在实际抗震设计中应用,并根据改进后的算法编制了结构随机地震响应分析程序。
(2)针对现有Ritz向量叠加法的不足,建立了一种带Rayleigh商偏移的Ritz向量叠加法。分析了现有Ritz向量截断标准存在的问题,提出了相应的修正建议。引入本征正交分解法(POD法)求解统计占优的前几阶本征模态作为计算Ritz向量的地震荷载空间分布向量,将Ritz向量叠加法与虚拟激励法结合起来,提高了多点激励下大跨度空间结构随机地震响应分析的计算效率。
(3)建立了相对位移谱与结构相对位移响应峰值均值之间的联系,参考《建筑抗震设计规范》(GB50011-2001)中地震反应谱曲线的分段表示方法,给出了地面加速度分段功率谱密度曲线。在现有随机地震动场模型的基础上,同时考虑地震动的三维平动分量和空间变化特性,建立了多维、多点输入的随机地震动场模型。
(4)通过理论分析和数值模拟,研究了行波效应、部分相干效应和局部场地效应对大跨度空间结构地震响应的影响。给出了结构地震响应峰值随地面视波速变化的规律,部分相干效应随结构跨度和激励频率的变化规律以及局部场地效应对城市大跨度空间结构地震响应的影响程度,为大跨度空间结构抗震设计提供了参考依据。
(5)通过理论分析和数值模拟,研究了地震空间效应影响大跨度空间结构地震响应的一般规律,提出了考虑地震空间效应的大跨度空间结构抗震设计的一般步骤及建议。
In the recent years, a number of long-span spatial structures with novel patterns and large scale have been built in China. Compared with traditional structures, the long-span spatial structures are more characterized by large spatial dimensions, which inevitably induces that it is inaccurate to ignore the influence of spatial variation of ground motion. However, the spatial effect of long-span spatial structures is not included in the current seismic design code, so it is quite urgent to establish a seismic design method for long-span spatial structures, in which the spatial variation of ground motion should be taken into account.
In this dissertation, based on the theories of random vibration, algorithms for analyzing the random seismic response of long-span spatial structures are improved, and a model of earthquake ground motion is established, in which the spatial seismic effects is taken into account. Moreover, a practical method for long-span spatial structures with general consideration of spatial seismic effects is proposed in this dissertation. The outline of the main work and achievements are concluded as follows:
(1) Based on the existing pseudo-excitation method, the algorithms for multi-excitation seismic analysis are improved. The improved algorithms are more efficient for random seismic analysis of long-span spatial structures and more practical for practical seismic design. Moreover, according to the improved algorithms, computer programs are compiled.
(2) For the defects of the existing Ritz vector superposition method, a new method with Rayleigh quotient shift is proposed. Problems of the cut-off criteria for Ritz vectors are discussed and some correction measures are given. Proper orthogonal decomposition (POD) technique is applied to compute the first several statistically dominant POD modes which are regarded as spatial distributions vectors of earthquake loadings for the generation of Ritz vectors. Then, the Ritz vector superposition method and the proper orthogonal decomposition technique are combined to improve the efficiency of multi-input seismic analysis for long-span spatial structures.
(3) A relationship between relative displacement spectrum and the mean peak value of relative displacement responses is established. According to the piecewise curves of response spectrum given by the code for seismic design of buildings, the PSD piecewise curves of ground acceleration are provided. And based on the existing stochastic models of ground motions, a multi-dimensional, multi-input stochastic model of ground motion is established, and three-dimensional translational motion components and spatial variation of the ground motion are taken into account as well.
(4) The influences of wave passage effect, partial coherence effect and local site effect on seismic responses of long-span spatial structures are studied in both theoretical analysis and numerical simulation. Conclusions are given on the variation of the peak response due to different apparent wave velocities, the variation of partial coherence effect due to different span and excitation frequency, and the influence extent of local site effect on response of urban long-span spatial constructions. These conclusions provide directions to seismic design of long-span spatial structures.
(5) The influences of spatial variation effect on the responses of long-span spatial structures are studied through both theoretical analysis and numerical simulation. According to all of these results, a general design procedure and some suggestions on seismic design of long-span spatial structures with consideration of spatial variation effect are provided.
本文基于随机振动理论,系统研究了大跨度空间结构随机地震响应分析的相关算法、地震动场模型以及地震空间效应的影响,建立了考虑地震空间效应的大跨度空间结构抗震设计方法。主要研究工作与创新成果包括以下几个方面:
(1)在原有虚拟激励算法的基础上,改进了多点激励虚拟激励算法,提高了大跨度空间结构随机地震响应分析的计算效率,使算法更便于在实际抗震设计中应用,并根据改进后的算法编制了结构随机地震响应分析程序。
(2)针对现有Ritz向量叠加法的不足,建立了一种带Rayleigh商偏移的Ritz向量叠加法。分析了现有Ritz向量截断标准存在的问题,提出了相应的修正建议。引入本征正交分解法(POD法)求解统计占优的前几阶本征模态作为计算Ritz向量的地震荷载空间分布向量,将Ritz向量叠加法与虚拟激励法结合起来,提高了多点激励下大跨度空间结构随机地震响应分析的计算效率。
(3)建立了相对位移谱与结构相对位移响应峰值均值之间的联系,参考《建筑抗震设计规范》(GB50011-2001)中地震反应谱曲线的分段表示方法,给出了地面加速度分段功率谱密度曲线。在现有随机地震动场模型的基础上,同时考虑地震动的三维平动分量和空间变化特性,建立了多维、多点输入的随机地震动场模型。
(4)通过理论分析和数值模拟,研究了行波效应、部分相干效应和局部场地效应对大跨度空间结构地震响应的影响。给出了结构地震响应峰值随地面视波速变化的规律,部分相干效应随结构跨度和激励频率的变化规律以及局部场地效应对城市大跨度空间结构地震响应的影响程度,为大跨度空间结构抗震设计提供了参考依据。
(5)通过理论分析和数值模拟,研究了地震空间效应影响大跨度空间结构地震响应的一般规律,提出了考虑地震空间效应的大跨度空间结构抗震设计的一般步骤及建议。
In the recent years, a number of long-span spatial structures with novel patterns and large scale have been built in China. Compared with traditional structures, the long-span spatial structures are more characterized by large spatial dimensions, which inevitably induces that it is inaccurate to ignore the influence of spatial variation of ground motion. However, the spatial effect of long-span spatial structures is not included in the current seismic design code, so it is quite urgent to establish a seismic design method for long-span spatial structures, in which the spatial variation of ground motion should be taken into account.
In this dissertation, based on the theories of random vibration, algorithms for analyzing the random seismic response of long-span spatial structures are improved, and a model of earthquake ground motion is established, in which the spatial seismic effects is taken into account. Moreover, a practical method for long-span spatial structures with general consideration of spatial seismic effects is proposed in this dissertation. The outline of the main work and achievements are concluded as follows:
(1) Based on the existing pseudo-excitation method, the algorithms for multi-excitation seismic analysis are improved. The improved algorithms are more efficient for random seismic analysis of long-span spatial structures and more practical for practical seismic design. Moreover, according to the improved algorithms, computer programs are compiled.
(2) For the defects of the existing Ritz vector superposition method, a new method with Rayleigh quotient shift is proposed. Problems of the cut-off criteria for Ritz vectors are discussed and some correction measures are given. Proper orthogonal decomposition (POD) technique is applied to compute the first several statistically dominant POD modes which are regarded as spatial distributions vectors of earthquake loadings for the generation of Ritz vectors. Then, the Ritz vector superposition method and the proper orthogonal decomposition technique are combined to improve the efficiency of multi-input seismic analysis for long-span spatial structures.
(3) A relationship between relative displacement spectrum and the mean peak value of relative displacement responses is established. According to the piecewise curves of response spectrum given by the code for seismic design of buildings, the PSD piecewise curves of ground acceleration are provided. And based on the existing stochastic models of ground motions, a multi-dimensional, multi-input stochastic model of ground motion is established, and three-dimensional translational motion components and spatial variation of the ground motion are taken into account as well.
(4) The influences of wave passage effect, partial coherence effect and local site effect on seismic responses of long-span spatial structures are studied in both theoretical analysis and numerical simulation. Conclusions are given on the variation of the peak response due to different apparent wave velocities, the variation of partial coherence effect due to different span and excitation frequency, and the influence extent of local site effect on response of urban long-span spatial constructions. These conclusions provide directions to seismic design of long-span spatial structures.
(5) The influences of spatial variation effect on the responses of long-span spatial structures are studied through both theoretical analysis and numerical simulation. According to all of these results, a general design procedure and some suggestions on seismic design of long-span spatial structures with consideration of spatial variation effect are provided.
引文
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