基于MPA和IDA的偏心结构性态评估分析方法
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摘要
基于性态的地震工程及其相关设计理论、方法等都是目前地震工程学术界和工程界广泛关注的课题。其主要的研究内容为如何依据设防水准合理确定设计参数,使结构的抗震能力最优,并使结构在不同强度的地震作用下,达到预计的性态水平,以减少生命财产损失。在性态抗震理论中,采用何种方法高效、精确地分析结构的性态反应,是基于性态的地震工程中的重要基础课题之一。同时,近年来我国大、中型城市中土木工程建设日渐增多,其中不乏偏心和不规则结构,如何科学合理地分析这些偏心或不规则结构在地震作用下的抗震性能、评估其性态反应,已成为目前性态反应分析研究中的关键问题之一。
针对基于等效单自由度体系和单向地震动输入的能力谱方法无法反映偏心结构平扭耦联反应特性的问题,本文利用偏心结构模态信息,通过建立模态等效多自由度体系,并拓展模态Pushover分析方法在偏心结构中的应用,对偏心结构进行简化分析、性态反应评估。改进了考虑平扭耦联效应的结构性态评估方法,使其进一步完善,也为偏心结构基于性态的抗震设计等工作提供了新思路。本文的研究内容主要包括以下几个方面:
(1)针对模态静力非线性分析中,基于顶点位移的能力曲线存在失稳现象,分析了这种失稳现象发生的机理,认为实际结构振动中这种失稳现象并不存在,而是由推覆过程造成的。通过在模态Pushover中利用基于结构变形能的等效变形替代基于顶点位移的变形,解决了高阶模态能力曲线失稳的问题。通过与顶点位移计算变形的方法进行比较,结果表明本文方法稳定、精度好,且不增加计算量。能力曲线稳定性问题的解决,也为模态能力谱在偏心结构中的应用奠定了基础。
(2)结构楼层平面内偏心且受到单向地震作用的情况较为常见,单向偏心结构模型也是研究平扭耦联反应最常用的模型。本文通过将单向偏心结构基底扭矩和顶点扭转角转化成扭转能力曲线,考虑了平扭耦联效应,拓展了模态Pushover分析方法和能力谱方法。通过将等效单自由度体系构造单向偏心特性,引入扭转自由度,提出等效二自由度简化模型,可以快速、可靠地求解单向偏心结构的非线性反应,进行性态评估。
(3)平面双向偏心结构受到双向地震作用时,其非弹性反应十分复杂,本文基于模态分解理论,将结构按模态简化成含有三个自由度的简化体系,提出了等效三自由度简化模型,并依照平动、扭转的模态能力曲线考虑其非线性特性,解决了双向偏心结构性态评估问题,使能力谱方法能够更好的分析双向偏心结构。进一步地,通过引入等位移原理简化了本文提出的性态评估分析方法。分析表明,本文方法计算精度好,效率高。
(4)静力非线性分析中,加载模式的选取将直接影响到性态评估的结果。自适应加载模式能够合理的考虑结构体系非线性的发展,但自适应加载的能力曲线也存在失稳现象。在分析总结多种加载模式的基础上,为了全面的考虑偏心结构进入非线性阶段的性态反应,本文通过将结构变形能等效为两个平动变形和一个扭转变形指标,来代替顶点位移和扭转角变形,解决了三维能力曲线失稳的问题,提出了自适应三维能力谱方法,并用双向地震作用下复杂偏心结构进行了验证。
(5)等效多自由度简化模型可以较好的考虑偏心结构的空间耦合反应,且具备计算效率高、峰值反应精度好的优点;增量动力分析方法可以全面的评估结构的抗震性能,但需对结构进行大量的非线性时程分析,计算量巨大。本文方法将两者结合在一起,通过将等效二自由度和等效三自由度简化模型引入增量动力时程分析中,提出偏心结构的简化增量动力分析方法:2D-IDA和3D-IDA方法,使增量动力分析方法分别应用于单向偏心结构受单向地震动作用以及双向偏心结构受双向地震动作用的性态评估之中,解决了偏心结构的可靠性和失效概率等性态评估问题。结果表明,本文方法对偏心结构在受到强地震动作用下的结构性态评估有较高的精度,可以追踪结构从弹性阶段到防止倒塌各阶段的性态变迁全过程,并进行定量评估。
The Performance-Based Earthquake Engineering (PBEE), including the theory and method of design, are issues paid attentions extensively by earthquake engineering academia and engineers at present. The contents of PBEE include the evaluation of the seismic behavior of structures, optimization of the structural performance based on capacity criterions and design of different seismic intensity rationally to reduce possible loss of life and property. The performance of structures should be evaluated accurately and efficiently according to PBEE theory, which is one of the most important subjects in PBEE. On the other hand, there are more and more complicated structures were built up in the cities of China, including many asymmetric and irregular buildings. Estimation of the seismic performance of the asymmetric and irregular buildings has become a key issue in the research of performance analysis at present.
The capacity spectrum method adopting single degree of freedom model and considering uni-dimensional ground motions cannot capture the lateral-rotational coupled effect. This work developed multi-degree of freedom systems based on the modal information of asymmetric structures and extended modal pushover analysis method in the performance estimation for asymmetric structures. Fast estimation procedures for the asymmetric structural performance are proposed. The method of performance estimation for asymmetric structures is improved, which provides a new approach to performance-based design for asymmetric structures. The main contents of this dissertation are followed.
(1) The capacity curve deduced from multi-mode nonlinear static procedure (NSP) has showed unstable phenomenon in practice. The mechanism of the unstable phenomenon has been analyzed in this work. The result indicated that the unstable phenomenon do not occur in real structural responses and it is caused by higher-modal pushover analysis. By making utility of the equivalent deformation index deduced from the deformation energy of the structures, the unstable issue of the higher modal capacity curve is solved. Compared with the method based on the roof displacement, the new method is stable and possess favorable precision with relatively computational cost. Furthermore, the unstable capacity curve prevented can pave the way for the extension utility of the modal capacity spectrum for asymmetric buildings.
(2) One-way asymmetric structural model subjected to uni-directional seismic excitation is common and widely used in the research of asymmetric structures responses. By calculating the rotational capacity curve from the base torque and top rotational angle including the lateral-rotational coupled effect, the modal pushover analysis and capacity spectrum method is extended for asymmetric structures. The Equivalent Dual-Degree of Freedom (EDDOF) system is proposed by offsetting the mass at the top of the SDOF model for construction of the eccentric property. The NSP provides the hysteretic rules for the nonlinear property of EDDOF model, and the coupled effect is considered in NSP. The issue of performance estimation of one-way asymmetric structures including lateral-rotational coupled effect can be solved fast and reliable.
(3) The two-way asymmetric structures subjecting dual-directional seismic excitation will generate complicate nonlinear responses. Based on the modal decoupled operation, the problem is simplified by decoupling the responses into lateral responses and rotational response. The Equivalent Triple-Degree of Freedom (ETDOF) model is proposed based on the decoupled modal equations. The performance evaluations issue of two-way asymmetric structures is solved with high precision and efficiency. In addition, the equal displacement rule is adopted to determine the target displacement of NSP, which simplified the procedure and improved the robustness for three dimensional issues.
(4) For many NSP methods, the loading distribution takes effect on the performance evaluation results directly. Considering the nonlinear development of the structures, the adaptive load pattern is accepted as the most reasonable formula at present. However, the adaptive load distribution algorithm is with poor stability. Firstly, the study summarizes and discusses different load patterns. By transforming the deformation energy into three equivalent deformation indexes, the stability issue is solved and the adaptive algorithm is improved. The adaptive modal combination procedure (three dimensional capacity spectrum method) is proposed and the method is verified with a complicated asymmetric structure subjecting two-way seismic excitation.
(5) The equivalent multi-degree of freedom models present the lateral-rotational coupled effect and can capture the peak deformation responses very well. On the other hand, the Incremental Dynamic Analysis (IDA) can be used in the performance evaluation for many performance criterions. However, IDA is a computationally extremely work. Based on IDA and the equivalent multi-degree of freedom models, the 2D-IDA method and 3D-IDA method are proposed for one-way asymmetric structures subjected to uni-directional excitation and two-way asymmetric structures subjected to dual-directional excitation, respectively. The 2D-IDA and 3D-IDA methods can evaluate the performance overall stages from elastic phase to collapse prevention level for reliability and collapse fragility consideration with computational simplicity.
针对基于等效单自由度体系和单向地震动输入的能力谱方法无法反映偏心结构平扭耦联反应特性的问题,本文利用偏心结构模态信息,通过建立模态等效多自由度体系,并拓展模态Pushover分析方法在偏心结构中的应用,对偏心结构进行简化分析、性态反应评估。改进了考虑平扭耦联效应的结构性态评估方法,使其进一步完善,也为偏心结构基于性态的抗震设计等工作提供了新思路。本文的研究内容主要包括以下几个方面:
(1)针对模态静力非线性分析中,基于顶点位移的能力曲线存在失稳现象,分析了这种失稳现象发生的机理,认为实际结构振动中这种失稳现象并不存在,而是由推覆过程造成的。通过在模态Pushover中利用基于结构变形能的等效变形替代基于顶点位移的变形,解决了高阶模态能力曲线失稳的问题。通过与顶点位移计算变形的方法进行比较,结果表明本文方法稳定、精度好,且不增加计算量。能力曲线稳定性问题的解决,也为模态能力谱在偏心结构中的应用奠定了基础。
(2)结构楼层平面内偏心且受到单向地震作用的情况较为常见,单向偏心结构模型也是研究平扭耦联反应最常用的模型。本文通过将单向偏心结构基底扭矩和顶点扭转角转化成扭转能力曲线,考虑了平扭耦联效应,拓展了模态Pushover分析方法和能力谱方法。通过将等效单自由度体系构造单向偏心特性,引入扭转自由度,提出等效二自由度简化模型,可以快速、可靠地求解单向偏心结构的非线性反应,进行性态评估。
(3)平面双向偏心结构受到双向地震作用时,其非弹性反应十分复杂,本文基于模态分解理论,将结构按模态简化成含有三个自由度的简化体系,提出了等效三自由度简化模型,并依照平动、扭转的模态能力曲线考虑其非线性特性,解决了双向偏心结构性态评估问题,使能力谱方法能够更好的分析双向偏心结构。进一步地,通过引入等位移原理简化了本文提出的性态评估分析方法。分析表明,本文方法计算精度好,效率高。
(4)静力非线性分析中,加载模式的选取将直接影响到性态评估的结果。自适应加载模式能够合理的考虑结构体系非线性的发展,但自适应加载的能力曲线也存在失稳现象。在分析总结多种加载模式的基础上,为了全面的考虑偏心结构进入非线性阶段的性态反应,本文通过将结构变形能等效为两个平动变形和一个扭转变形指标,来代替顶点位移和扭转角变形,解决了三维能力曲线失稳的问题,提出了自适应三维能力谱方法,并用双向地震作用下复杂偏心结构进行了验证。
(5)等效多自由度简化模型可以较好的考虑偏心结构的空间耦合反应,且具备计算效率高、峰值反应精度好的优点;增量动力分析方法可以全面的评估结构的抗震性能,但需对结构进行大量的非线性时程分析,计算量巨大。本文方法将两者结合在一起,通过将等效二自由度和等效三自由度简化模型引入增量动力时程分析中,提出偏心结构的简化增量动力分析方法:2D-IDA和3D-IDA方法,使增量动力分析方法分别应用于单向偏心结构受单向地震动作用以及双向偏心结构受双向地震动作用的性态评估之中,解决了偏心结构的可靠性和失效概率等性态评估问题。结果表明,本文方法对偏心结构在受到强地震动作用下的结构性态评估有较高的精度,可以追踪结构从弹性阶段到防止倒塌各阶段的性态变迁全过程,并进行定量评估。
The Performance-Based Earthquake Engineering (PBEE), including the theory and method of design, are issues paid attentions extensively by earthquake engineering academia and engineers at present. The contents of PBEE include the evaluation of the seismic behavior of structures, optimization of the structural performance based on capacity criterions and design of different seismic intensity rationally to reduce possible loss of life and property. The performance of structures should be evaluated accurately and efficiently according to PBEE theory, which is one of the most important subjects in PBEE. On the other hand, there are more and more complicated structures were built up in the cities of China, including many asymmetric and irregular buildings. Estimation of the seismic performance of the asymmetric and irregular buildings has become a key issue in the research of performance analysis at present.
The capacity spectrum method adopting single degree of freedom model and considering uni-dimensional ground motions cannot capture the lateral-rotational coupled effect. This work developed multi-degree of freedom systems based on the modal information of asymmetric structures and extended modal pushover analysis method in the performance estimation for asymmetric structures. Fast estimation procedures for the asymmetric structural performance are proposed. The method of performance estimation for asymmetric structures is improved, which provides a new approach to performance-based design for asymmetric structures. The main contents of this dissertation are followed.
(1) The capacity curve deduced from multi-mode nonlinear static procedure (NSP) has showed unstable phenomenon in practice. The mechanism of the unstable phenomenon has been analyzed in this work. The result indicated that the unstable phenomenon do not occur in real structural responses and it is caused by higher-modal pushover analysis. By making utility of the equivalent deformation index deduced from the deformation energy of the structures, the unstable issue of the higher modal capacity curve is solved. Compared with the method based on the roof displacement, the new method is stable and possess favorable precision with relatively computational cost. Furthermore, the unstable capacity curve prevented can pave the way for the extension utility of the modal capacity spectrum for asymmetric buildings.
(2) One-way asymmetric structural model subjected to uni-directional seismic excitation is common and widely used in the research of asymmetric structures responses. By calculating the rotational capacity curve from the base torque and top rotational angle including the lateral-rotational coupled effect, the modal pushover analysis and capacity spectrum method is extended for asymmetric structures. The Equivalent Dual-Degree of Freedom (EDDOF) system is proposed by offsetting the mass at the top of the SDOF model for construction of the eccentric property. The NSP provides the hysteretic rules for the nonlinear property of EDDOF model, and the coupled effect is considered in NSP. The issue of performance estimation of one-way asymmetric structures including lateral-rotational coupled effect can be solved fast and reliable.
(3) The two-way asymmetric structures subjecting dual-directional seismic excitation will generate complicate nonlinear responses. Based on the modal decoupled operation, the problem is simplified by decoupling the responses into lateral responses and rotational response. The Equivalent Triple-Degree of Freedom (ETDOF) model is proposed based on the decoupled modal equations. The performance evaluations issue of two-way asymmetric structures is solved with high precision and efficiency. In addition, the equal displacement rule is adopted to determine the target displacement of NSP, which simplified the procedure and improved the robustness for three dimensional issues.
(4) For many NSP methods, the loading distribution takes effect on the performance evaluation results directly. Considering the nonlinear development of the structures, the adaptive load pattern is accepted as the most reasonable formula at present. However, the adaptive load distribution algorithm is with poor stability. Firstly, the study summarizes and discusses different load patterns. By transforming the deformation energy into three equivalent deformation indexes, the stability issue is solved and the adaptive algorithm is improved. The adaptive modal combination procedure (three dimensional capacity spectrum method) is proposed and the method is verified with a complicated asymmetric structure subjecting two-way seismic excitation.
(5) The equivalent multi-degree of freedom models present the lateral-rotational coupled effect and can capture the peak deformation responses very well. On the other hand, the Incremental Dynamic Analysis (IDA) can be used in the performance evaluation for many performance criterions. However, IDA is a computationally extremely work. Based on IDA and the equivalent multi-degree of freedom models, the 2D-IDA method and 3D-IDA method are proposed for one-way asymmetric structures subjected to uni-directional excitation and two-way asymmetric structures subjected to dual-directional excitation, respectively. The 2D-IDA and 3D-IDA methods can evaluate the performance overall stages from elastic phase to collapse prevention level for reliability and collapse fragility consideration with computational simplicity.
引文
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