基于能量平衡的建筑结构非线性静力方法及分灾设计谱的研究
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摘要
近年来世界各地频发大地震,造成了重大的工程结构破坏、人员伤亡和经济损失。随着我国城市化水平的不断提高,多数大中型城市都建设了大量的高层建筑,且不少地区属于地震易发区域。目前由于地震尚不能准确预测,因此着力提高工程结构的抗震能力仍具有重要的社会、经济意义。基于国家自然科学基金重大研究计划“重大工程的动力灾变”中重点项目“超高层建筑的动力失效模式及抗灾-分灾优化设计研究(90815023)”,本文主要开展了地震作用下建筑结构简化的非线性分析方法、全寿命造价优化设计和分灾设计等相关的研究工作,为高层建筑结构的抗震设计提供理论方法依据。
首先,本文概要地总结了工程结构抗震设计的方法,及非线性静力方法、全寿命造价优化设计和结构分灾设计的近期发展；系统地整理了建筑结构地震响应分析的基本理论,包括了地震作用下运动方程、弹性的模态时程分析及反应谱分析方法、非弹性静力分析方法；重点回顾了4种经典的非线性静力方法,包括等效线性化方法、位移系数法、N2方法和模态Pushover方法。
基于性能的结构抗震设计所面临的一个巨大挑战就是研究、发展高效可行的评估结构抗震性能的方法。非线性静力Pushover分析方法目前正在被越来越多的规范指南推荐使用,并逐渐成为认可的标准方法。为了避免传统Pushover曲线的翻转,本文提出了基于能量平衡的多模态Pushover分析方法,可以有效地捕捉高阶模态效应。与能力谱方法一致,该方法结合了模态的能量能力和需求的概念,并保持了不变的侧力加载分布的优势。在使用近断层地震动作用下平面结构对该方法进行数值评估时,本文采用了高阶模态能量需求为弹性的假定,通过数值评估表明提出的方法可以有效地估计地震响应需求。然后,本文着重考察了基于能量平衡的多模态Pushover分析方法对单向偏心结构的适用性,包括TS (Torsionally-stiff)、TSS (Torsionally-similarly-stiff)和TF (Torsionally-flexible)结构系统。研究表明对于弹性模态弱耦合的TS、TF系统,本文提出的方法能够有效地估计结构的地震响应；但对于弹性模态强耦合的TSS系统,会严重低估TSS系统的地震响应。此外,随着激励的增强,该方法的评估精度逐渐降低。本质上,该方法是地震反应谱分析方法在非弹性域的一个推广。
此外,本文开展了基于改进的模态Pushover分析方法的结构全寿命造价优化设计。本文采用了基于模糊评判技术的损失评估策略,且使用了能够较好地考虑结构高阶模态效应的改进的模态Pushover方法。需要指出的是,在优化过程中进行结构抗震分析时,本文采用基于地震反应谱的实用的模态Pushover方法,主要是为了方便地考虑设计地震的位移需求。通过自适应的模拟退火算法进行优化求解,不但得到了全寿命造价优的设计,而且最优设计的结构鲁棒性也显著地提高。
最后,本文详细研究了含金属结构保险丝的分灾系统。结构分灾设计将整个结构系统从概念上分为两个部分：主体功能结构和分灾元件(或结构保险丝)。强地震作用下分灾元件开始发挥分灾作用,通过损伤耗能甚至完全牺牲破坏以保护主体功能结构。根据三线性单自由度系统的延性方程,本文提出了结构分灾设计谱,并对其进行了参数化分析,得到了满足结构保险丝概念的有效参数集。本文还分别给出了含金属结构保险丝的分灾系统的周期约束条件和分灾系统屈服力的需求公式,以及基于力的结构分灾设计和加固的基本步骤,并通过设计算例来验证提出的设计方法的有效性。
Recently severe earthquakes hit the world frequently, which have caused significant engineering structure damage, calsualities and economic loss. As the level of urbanization increasingly improving in China, a great number of tall buildings have been built at most of large-and medium-sized cities, and some of them belong to earthquake-prone regions. Currently, it is still socially and economically worthwhile to improve the seismic capacity of engineering structures due to the unpredictable earthquake. Based on the key project "Investigation on the dynamic failure modes and damage-resistant/reduction optimum design for the super-high-rise buildings under the hazards (90815023)" in the major project "Damage evolution of civil infrastructure under strong earthquake and wind" funded by National Natural Science Foundation of China, this paper primarily focuses on the study of the simplified nonlinear analysis procedures, life-cycle cost optimum design and damage-reduction design for buildings under the earthquakes, which may provide the theoretic and methodological insights on seismic design for tall buildings.
Firstly, the philosophy of seismic design for engineering structures, and the recent development of nonlinear static procedures (NSP), life-cycle cost oriented optimum design and structural damage-reduction design are briefly reviewed. The basis of the seismic analysis for buildings is systematically summarized, where the motion equations of the buildings under earthquakes, elastic modal time history and response spectrum analysis methods, nonlinear static procedures are covered. And the four classic nonlinear static methods are focused, including the equivalent linearization method, displacement coefficient method, N2method and modal pushover procedure.
A great challenge to performance-based seismic design is to develop an effective and feasible procedure for analyzing and evaluating the seismic demands. Currently, nonlinear static procedure or pushover analysis is accepted by more and more guideline documents and codes, and being viewed as the standard practice. In order to avoid the reversal of the traditional pushover curve, the energy balance based multimode pushover analysis method is developed herein, which can capture the higher mode effects well. Compatiable with the capacity spectrum method, the proposed method has incorporated the concept of modal energy capacity and demand, and retained attractiveness with invariant force distribution. The planar structures under near fault ground motions are utilised to numerically evaluate the proposed approach effectively, and the energy demands of the higher mode are assumed to be elastic, which the proposed method can predict the seismic demands well.
Then the applicability of the proposed method for one-way asymmetric-plan buildings, including Torsionally-stiff (TS), Torsionally-similarly-stiff (TSS), Torsionally-flexible (TF) structural systems, are investigated in this paper. It is shown that the proposed method estimates the seismic responses well for TS and TF systems with elastic modes weak-coupled, while underestimates the seismic demands greatly for TSS system with elastic modes strong-coupled. Additionally, the accuracy of the proposed method decreases as the intensity of the ground motion increases. In essence, the proposed method is an extended version of response spetrum analysis method in the inelastic range.
Besides, the life-cycle cost oriented structural optimization design using the modified modal pushover analysis procedure has been carried out. The damage loss is estimated through the fuzzy-decision technique, and the adopted modified modal pushover method can capture the higher mode effects effectively. It is to be mentioned that the design spectrum based practical modal pushover procedure is utilized as the seismic analysis considering the seismic design displacement demands easily in the process of the optimization. The proposed optimization problem is solved by the adaptive simulated annealing algorithm, in which not only have the cost-effective optimum design achieved, but it is found that the stuctural robustness of the optimum design has been improved greatly as well.
Finally, the building systems with metallic structural fuses are investigetd in detail. In the damage-reduction design the entire structural system is conceptually divided into two parts:the main functional struture and the damage-reduction element (or structural fuse). Under the strong earthquake the damage-reduction elements are damaged through dissipating the energy or even completely sacrificed to protect the main functional structure. The damage-redution spectrum has been formulated through the ductility equation of the trilinear single degree of freedom (SDOF) system, and parameterally studied, in which the effective parameter sets satisfying the structural fuse concept are obtained. Then the period constraint condition and the equations of demanded yield forces are formulated, the force-based design and retrofit procedures are given respectively, and a design example is utilized to show the effectiveness of the proposed procedures.
首先,本文概要地总结了工程结构抗震设计的方法,及非线性静力方法、全寿命造价优化设计和结构分灾设计的近期发展；系统地整理了建筑结构地震响应分析的基本理论,包括了地震作用下运动方程、弹性的模态时程分析及反应谱分析方法、非弹性静力分析方法；重点回顾了4种经典的非线性静力方法,包括等效线性化方法、位移系数法、N2方法和模态Pushover方法。
基于性能的结构抗震设计所面临的一个巨大挑战就是研究、发展高效可行的评估结构抗震性能的方法。非线性静力Pushover分析方法目前正在被越来越多的规范指南推荐使用,并逐渐成为认可的标准方法。为了避免传统Pushover曲线的翻转,本文提出了基于能量平衡的多模态Pushover分析方法,可以有效地捕捉高阶模态效应。与能力谱方法一致,该方法结合了模态的能量能力和需求的概念,并保持了不变的侧力加载分布的优势。在使用近断层地震动作用下平面结构对该方法进行数值评估时,本文采用了高阶模态能量需求为弹性的假定,通过数值评估表明提出的方法可以有效地估计地震响应需求。然后,本文着重考察了基于能量平衡的多模态Pushover分析方法对单向偏心结构的适用性,包括TS (Torsionally-stiff)、TSS (Torsionally-similarly-stiff)和TF (Torsionally-flexible)结构系统。研究表明对于弹性模态弱耦合的TS、TF系统,本文提出的方法能够有效地估计结构的地震响应；但对于弹性模态强耦合的TSS系统,会严重低估TSS系统的地震响应。此外,随着激励的增强,该方法的评估精度逐渐降低。本质上,该方法是地震反应谱分析方法在非弹性域的一个推广。
此外,本文开展了基于改进的模态Pushover分析方法的结构全寿命造价优化设计。本文采用了基于模糊评判技术的损失评估策略,且使用了能够较好地考虑结构高阶模态效应的改进的模态Pushover方法。需要指出的是,在优化过程中进行结构抗震分析时,本文采用基于地震反应谱的实用的模态Pushover方法,主要是为了方便地考虑设计地震的位移需求。通过自适应的模拟退火算法进行优化求解,不但得到了全寿命造价优的设计,而且最优设计的结构鲁棒性也显著地提高。
最后,本文详细研究了含金属结构保险丝的分灾系统。结构分灾设计将整个结构系统从概念上分为两个部分：主体功能结构和分灾元件(或结构保险丝)。强地震作用下分灾元件开始发挥分灾作用,通过损伤耗能甚至完全牺牲破坏以保护主体功能结构。根据三线性单自由度系统的延性方程,本文提出了结构分灾设计谱,并对其进行了参数化分析,得到了满足结构保险丝概念的有效参数集。本文还分别给出了含金属结构保险丝的分灾系统的周期约束条件和分灾系统屈服力的需求公式,以及基于力的结构分灾设计和加固的基本步骤,并通过设计算例来验证提出的设计方法的有效性。
Recently severe earthquakes hit the world frequently, which have caused significant engineering structure damage, calsualities and economic loss. As the level of urbanization increasingly improving in China, a great number of tall buildings have been built at most of large-and medium-sized cities, and some of them belong to earthquake-prone regions. Currently, it is still socially and economically worthwhile to improve the seismic capacity of engineering structures due to the unpredictable earthquake. Based on the key project "Investigation on the dynamic failure modes and damage-resistant/reduction optimum design for the super-high-rise buildings under the hazards (90815023)" in the major project "Damage evolution of civil infrastructure under strong earthquake and wind" funded by National Natural Science Foundation of China, this paper primarily focuses on the study of the simplified nonlinear analysis procedures, life-cycle cost optimum design and damage-reduction design for buildings under the earthquakes, which may provide the theoretic and methodological insights on seismic design for tall buildings.
Firstly, the philosophy of seismic design for engineering structures, and the recent development of nonlinear static procedures (NSP), life-cycle cost oriented optimum design and structural damage-reduction design are briefly reviewed. The basis of the seismic analysis for buildings is systematically summarized, where the motion equations of the buildings under earthquakes, elastic modal time history and response spectrum analysis methods, nonlinear static procedures are covered. And the four classic nonlinear static methods are focused, including the equivalent linearization method, displacement coefficient method, N2method and modal pushover procedure.
A great challenge to performance-based seismic design is to develop an effective and feasible procedure for analyzing and evaluating the seismic demands. Currently, nonlinear static procedure or pushover analysis is accepted by more and more guideline documents and codes, and being viewed as the standard practice. In order to avoid the reversal of the traditional pushover curve, the energy balance based multimode pushover analysis method is developed herein, which can capture the higher mode effects well. Compatiable with the capacity spectrum method, the proposed method has incorporated the concept of modal energy capacity and demand, and retained attractiveness with invariant force distribution. The planar structures under near fault ground motions are utilised to numerically evaluate the proposed approach effectively, and the energy demands of the higher mode are assumed to be elastic, which the proposed method can predict the seismic demands well.
Then the applicability of the proposed method for one-way asymmetric-plan buildings, including Torsionally-stiff (TS), Torsionally-similarly-stiff (TSS), Torsionally-flexible (TF) structural systems, are investigated in this paper. It is shown that the proposed method estimates the seismic responses well for TS and TF systems with elastic modes weak-coupled, while underestimates the seismic demands greatly for TSS system with elastic modes strong-coupled. Additionally, the accuracy of the proposed method decreases as the intensity of the ground motion increases. In essence, the proposed method is an extended version of response spetrum analysis method in the inelastic range.
Besides, the life-cycle cost oriented structural optimization design using the modified modal pushover analysis procedure has been carried out. The damage loss is estimated through the fuzzy-decision technique, and the adopted modified modal pushover method can capture the higher mode effects effectively. It is to be mentioned that the design spectrum based practical modal pushover procedure is utilized as the seismic analysis considering the seismic design displacement demands easily in the process of the optimization. The proposed optimization problem is solved by the adaptive simulated annealing algorithm, in which not only have the cost-effective optimum design achieved, but it is found that the stuctural robustness of the optimum design has been improved greatly as well.
Finally, the building systems with metallic structural fuses are investigetd in detail. In the damage-reduction design the entire structural system is conceptually divided into two parts:the main functional struture and the damage-reduction element (or structural fuse). Under the strong earthquake the damage-reduction elements are damaged through dissipating the energy or even completely sacrificed to protect the main functional structure. The damage-redution spectrum has been formulated through the ductility equation of the trilinear single degree of freedom (SDOF) system, and parameterally studied, in which the effective parameter sets satisfying the structural fuse concept are obtained. Then the period constraint condition and the equations of demanded yield forces are formulated, the force-based design and retrofit procedures are given respectively, and a design example is utilized to show the effectiveness of the proposed procedures.
引文
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