关于能力谱方法收敛性的讨论

给出了ATC-40迭代求解方法A收敛性的一个数学解释。分析了ATC-40迭代求解方法A和改进的能力谱方法在迭代上的差异,并从数学上证明了改进的能力谱方法有收敛的结果。     

Comparison of displacement coefficient method and capacity spectrum method with experimental results of RC columns

For the performance‐based seismic design of buildings, both the displacement coefficient method used by FEMA‐273 and the capacity spectrum method adopted by ATC‐40 are non‐linear static procedures. The pushover curves of structures need to be established during processing of these two methods. They are applied to evaluation and rehabilitation of existing structures. This paper is concerned with experimental studies on the accuracy of both methods. Through carrying out the pseudo‐dynamic tests, cyclic loading tests and pushover tests on three reinforced concrete (RC) columns, the maximum inelastic deformation demands (target displacements) determined by the coefficient method of FEMA‐273 and the capacity spectrum method of ATC‐40 are compared. In addition, a modified capacity spectrum method which is based on the use of inelastic design response spectra is also included in this study. It is shown from the test specimens that the coefficient method overestimates the peak test displacements with an average error of +28% while the capacity spectrum method underestimates them with an average error of ‐20%. If the Kowalsky hysteretic damping model is used in the capacity spectrum method instead of the original damping model, the average errors become ‐11% by ignoring the effect of stiffness degrading and ‐1.2% by slightly including the effect of stiffness degrading. Furthermore, if the Newmark–Hall inelastic design spectrum is implemented in the capacity spectrum method instead of the elastic design spectrum, the average error decreases to ‐6.6% which undervalues, but is close to, the experimental results. Copyright © 2003 John Wiley & Sons, Ltd.     

An improved capacity spectrum method for ATC‐40

In order to account for the non‐linear behavior of structures via non‐linear static procedure, the capacity spectrum method has been adopted by ATC‐40 for evaluation and retrofit of reinforced concrete buildings. For elastic‐perfectly‐plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo‐acceleration response spectrum (PS_a) is used to create the demand diagram. It is found that the ATC‐40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S0._a) instead of the PS_a to establish the demand diagram. The step‐by‐step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake‐induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC‐40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (μ) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when μ>4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright © 2003 John Wiley & Sons, Ltd.     

基于改进能力谱方法的位移反应估计

本文阐述了Pushover分析中改进能力谱方法的概念和实施步骤；对不同场地条件下四个中、低层框架结构采用改进能力谱方法估计的目标位移和非线性时程反应分析结果进行了比较，分析，并提供了不同场地条件下两种方法的相对误差，为该方法的实际应用提供了一些参考依据。     

Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona

Conceptual aspects related to seismic vulnerability, damage and risk evaluation are discussed first, together with a short review of the most widely used possibilities for seismic evaluation of structures. The capacity spectrum method and the way of obtaining seismic damage scenarios for urban areas starting from capacity and fragility curves are then discussed. The determination of capacity curves for buildings using non-linear structural analysis tools is then explained, together with a simplified expeditious procedure allowing the development of fragility curves. The seismic risk of the buildings of Barcelona, Spain, is analyzed in the paper, based on the application of the capacity spectrum method. The seismic hazard in the area of the city is described by means of the reduced 5% damped elastic response spectrum. The information on the buildings was obtained by collecting, arranging, improving and completing a broad database of the dwellings and current buildings. The buildings existing in Barcelona are mainly of two types: unreinforced masonry structures and reinforced concrete buildings with waffled-slab floors. The ArcView software was used to create a GIS tool for managing the collected information in order to develop seismic risk scenarios. This study shows that the vulnerability of the buildings is significant in Barcelona and, therefore, in spite of the low-to-moderate seismic hazard in the region, the expected seismic risk is considerable.     

Capacity spectrum method based on inelastic demand spectra

By means of a graphical procedure, the capacity spectrum method compares the capacity of a structure with the demands of earthquake ground motion on it. In the present version of the method, highly damped elastic spectra have been used to determine seismic demand. A more straightforward approach for the determination of seismic demand is based on the use of the inelastic strength and displacement spectra which can be obtained directly by time-history analyses of inelastic SDOF systems, or indirectly from elastic spectra. The advantages of the two approaches (i.e. the visual representation of the capacity spectrum method and the superior physical basis of inelastic demand spectra) can be combined. In this paper, the idea of using inelastic demand spectra within the capacity spectrum method has been elaborated and is presented in an easy to use format. The approach represents the so-called N2 method formulated in the format of the capacity spectrum method. By reversing the procedure, a direct displacement-based design can be performed. The application of the modified capacity spectrum method is illustrated by means of two examples. Copyright © 1999 John Wiley & Sons, Ltd.     

有关Kanai-Tajimi模型的统计特征分析

选择金井清过滤白噪声模型,采用留数定理推导出K-T谱激励的自相关函数表达式,并在此基础上利用相关函数法分析出K-T谱激励下的平稳反应,并采用功率谱方法加以验证。这些结果可为结构随机地震反应时域分析和抗震可靠性评估提供基础。     

Strong ground motion record selection for the reliable prediction of the mean seismic collapse capacity of a structure group

How to select a limited number of strong ground motion records (SGMRs) is an important challenge for the seismic collapse capacity assessment of structures. The collapse capacity is considered as the ground motion intensity measure corresponding to the drift‐related dynamic instability in the structural system. The goal of this paper is to select, from a general set of SGMRs, a small number of subsets such that each can be used for the reliable prediction of the mean collapse capacity of a particular group of structures, i.e. of single degree‐of‐freedom systems with a typical behaviour range. In order to achieve this goal, multivariate statistical analysis is first applied, to determine what degree of similarity exists between each selected small subset and the general set of SGMRs. Principal Component analysis is applied to identify the best way to group structures, resulting in a minimum number of SGMRs in a proposed subset. The structures were classified into six groups, and for each group a subset of eight SGMRs has been proposed. The methodology has been validated by analysing a first‐mode‐dominated three‐storey‐reinforced concrete structure by means of the proposed subsets, as well as the general set of SGMRs. The results of this analysis show that the mean seismic collapse capacity can be predicted by the proposed subsets with less dispersion than by the recently developed improved approach, which is based on scaling the response spectra of the records to match the conditional mean spectrum. Copyright © 2010 John Wiley & Sons, Ltd.     

交错桁架多层钢结构推倒分析方法研究

随着基于性能的抗震设计思想的发展,推倒分析开始成为罕遇地震下多、高层结构抗震设计的有力工具。本文以交错桁架多层钢结构为例,采用推倒分析对其在E l Centro波作用下的地震反应进行研究,分别采用位移系数法和能力谱法确定结构目标位移,同时进行结构在相同地震动下的弹塑性时程分析。研究表明,推倒分析能准确地评价交错桁架多层钢结构的抗震性能,采用位移系数法和能力谱法确定的结构顶点侧移均与弹塑性时程分析吻合较好,对层间位移及塑性铰分布的预测,能力谱法比位移系数法更为准确。     

基于易损性的基础隔震结构地震动选取方法研究

对基础隔震结构进行动力弹塑性时程分析时,地震记录的选择是关键.提出基于基础隔震结构弹塑性动力放大系数谱进行地震记录选取的方法:首先采用动力弹塑性时程分析方法对基础隔震结构的两自由度简化模型进行分析,得到结构的动力放大系数谱;然后采用谱匹配的方法选取地震记录,对一8层混凝土框架结构的基础隔震结构进行增量动力分析、地震易损...     

Chaotic dynamics analysis and control of iterative procedure of capacity spectrum method

The capacity spectrum method (CSM), capable of predicting the demands of forces and deformations of the inelastic system, has been applied in the ATC and FEMA guidelines. The deformation of an inelastic system is solved iteratively by using the equivalent linearization for CSM, which actually forms a nonlinear map or discrete dynamical system. However, the iterative procedure of CSM did not converge for some inelastic systems, and the complicated dynamical phenomena for the solutions such as the periodic oscillation, period-doubling bifurcation and chaos may occur, which were shown in the bifurcation plots of iterative map of the simplified CSM in ATC40 and FEMA440. This paper presents a novel method to analyze and control the non-convergence of the iterative procedure of CSM from the perspective of chaotic dynamics. The Lyapunov exponent of the dynamical system is employed to identify the evolutional state and stability of solutions. Finally, the stability transformation method as a simple, versatile and effective chaos feedback control approach is applied to control the convergent failure of CSM in ATC40 and FEMA440. The numerical results illustrate that the stability transformation method can capture the desired fixed points of the dynamical system and obtain the stable convergent solutions of CSM.     

几种push-over分析方法对比研究

Push-over方法是一种静力非线性计算方法，是近年来在国内外得到广泛研究应用的用于评价结构抗震能力的新方法。采用这种方法计算结构的弹塑性地震反应将会逐渐为广大的工程设计人员所接受，但目前对于这种用静力的方法去预测结构的动力反应，其可靠性如何一直是许多学者所关注的，而且对于现有的几种方法的优劣也没有给出综合的评价。本文在国内外有关理论和方法的基础上，对几种push-over分析方法进行了简要评述，并通过分析计算对其中有代表性的能力谱方法、位移影响系数法和适应谱push-over方法进行了详细的对比研究。指出了其中存在的问题，试图寻找并推荐一种比较好的方法。结果能够实现这一目标，对于push-over方法的发展将会有一定的推动作用。     

基于抗震承载力和改进能力谱法的钢筋混凝土结构耐久性设计

钢筋混凝土结构是一种广泛使用的结构形式,其耐久性设计是一个十分迫切需要解决的问题。在一般大气环境下,混凝土碳化和钢筋锈蚀是钢筋混凝土结构耐久性的重要影响因素,在其作用下结构的抗震承载力发生变化,因此可将结构抗震承载力因素引入结构的耐久性设计中。采用改进能力谱法,以罕遇地震下薄弱层的弹塑性层间位移作为结构承载力指标,研究了一般大气环境下钢筋锈蚀因素对钢筋混凝土结构抗震耐久性的影响,提出了基于抗震承载力和改进的能力谱法的钢筋混凝土结构耐久性设计方法。通过一个五层钢筋混凝土结构的算例说明了验算结构抗震性能耐久行的必要性。     

钢筋混凝土结构抗震能力评估的简化能力谱方法

本文通过对现有能力谱法的研究,在吸收前人研究成果的基础上,探讨了一种简化的能力谱方法。该方法不是根据需求谱与能力谱有无交点(性能点)为评估依据,而是以能力谱为根据求出不同延性状态下既有建筑物相应的抗震能力,并与需求谱相应的谱加速度比较,判断结构的抗震能力是否满足要求。该方法不需要复杂的迭代计算来求结构的性能点,计算过程简单;同时,可以考虑既有建筑物的老化及损伤。最后,本文应用自行编制的计算程序,通过一个工程实例说明了该方法的应用及其特点。     

On the correction of spectra by a displacement reduction factor in direct displacement-based seismic design and assessment

The application of some design and assessment approaches, such as the direct displacement-based design (DDBD) and the capacity spectrum methods, requires the modification of elastic design spectra by some displacement reduction factor, to account for the appropriate energy dissipation capacity of different structures. While several equations to correlate dissipation and hysteresis cycles are available, once the displacement reduction factor has been obtained, the correction of the spectra is operated reducing the displacement demand accordingly and conserving the period of vibration at each point. This procedure is here discussed and proved to be conceptually inappropriate, because the spectral acceleration rather than the period should be kept at each point. The application of this alternative procedure may result in increased shear strength demand in design and in larger required displacement capacity for the same level of strength in assessment, if all other factors are not modified. However, the calibration of the reduction factors applied in DDBD has been extensive, and the method has proved to be effective in predicting displacement demands consistent with those resulting from refined nonlinear time history analysis; therefore, a possible introduction of the proposed correction will require equally extensive studies and possibly compensating corrections in the calculation of the equivalent damping. On the contrary, an appropriate calibration of the factors to be used in the application of the “capacity spectrum” method is still being developed, and the consideration of a constant acceleration may facilitate the derivation of effective equations.     

能力谱方法在桥梁抗震性能评估中的应用研究

位移延性是桥梁抗震性能的重要指标之一,以Pushover分析为基础的能力谱方法能够考察结构在地震下的弹塑性位移响应,是抗震性能评估的一种有效手段.文中阐述了能力谱法的基本原理,说明了基于弹塑性反应谱的能力谱方法在求解性能点时不需要进行迭代计算;基于弹性设计反应谱建立了相对应的弹塑性反应谱,结合某实桥,将能力谱方法和增量动力分析方法进行了对比,并根据不同的地震基本烈度和场地土类型进行了抗震性能评估.分析认为,能力谱方法计算简便,对结构1阶振型的地震响应占主导时,具有较好的精度,并能够基于设计反应谱来考察结构的弹塑性抗震性能,可用于桥梁抗震性能的评估.     

Accuracy of nonlinear static procedures for the seismic assessment of shear critical structures

The nonlinear behavior of reinforced concrete (RC) members represents a key issue in the seismic performance assessment of structures. Many structures constructed in the 1980s or earlier were designed based on force limits; thus they often exhibit brittle failure modes, strength and stiffness degradation, and severe pinching effects. Field surveys and experimental evidence have demonstrated that such inelastic responses affect the global behavior of RC structural systems. Efforts have been made to consider the degrading stiffness and strength in the simplified nonlinear static procedures commonly adopted by practitioners. This paper investigates the accuracy of such procedures for the seismic performance assessment of RC structural systems. Refined finite element models of a shear critical bridge bent and a flexure‐critical bridge pier are used as reference models. The numerical models are validated against experimental results and used to evaluate the inelastic dynamic response of the structures subjected to earthquake ground motions with increasing amplitude. The maximum response from the refined numerical models is compared against the results from the simplified static procedures, namely modified capacity spectrum method and coefficient method in FEMA‐440. The accuracy of the static procedures in estimating the displacement demand of a flexure‐critical system and shear‐critical system is discussed in detail. Copyright © 2015 John Wiley & Sons, Ltd.     

钢筋混凝土结构基于改进能力谱法的地震损伤性能设计

本文基于国内外非线性静力分析方法,阐述了最近由Ｃｈｏｐｒａ和Ｇｏｅｌ提供的改进能力谱法的基本概念和实施步骤;其次,结合文献「１８」中提出的钢筋沸凝土结构地震损伤“三水准”性能目标和改进能力谱法,提出了基于能力谱法的结构地震损伤性能简化设计及验算方法;最后,通过设计例题说明了本文方法的可行性,并将计算结果与时程分析进行了比较,显示了此法的有效性。     

多点激励下结构随机地震反应分析的反应谱方法

基于随机振动理论,提出了多点激励作用下线性系统随机地震反应分析的均值反应谱方法,给出了结构峰值反应的均值、标准差以及反应平均频率的反应谱组合公式。这可以将反应谱方法推广应用到多点激励结构的抗震可靠度分析中。鉴于组合公式中谱参数和相关系数需要由烦琐的数值积分得到,本文进一步针对它们给出合理的简化计算式,从而使得建议的反应谱方法的计算效率大大增加。最后,以一个双塔斜拉桥为例,对本文方法进行了验证。基于建议方法的计算结果与Monte Carlo模拟结果吻合较好。与经典的多点激励反应谱方法(MSRS法)比较,本文方法具有其无法比拟的计算效率。     

地震区居民建筑钢结构极限承载力测试与分析

传统方法一般依据静力检测数据测试居民建筑钢结构的极限承载力,对构件数量的要求较高,无法量测隐蔽构件,测试结果精度低。因此提出基于振动参数以及动力模型修正的地震区居民建筑钢结构极限承载力预测与分析方法,分析建筑钢结构振动参数与极限承载能力的关系,塑造地震区居民建筑钢结构简化以及振动方程,获取其极限载荷与振动参数间的关系。采用基于动力模型修正的极限承载力评估方法,基于动力模型修正理论,采用线性屈曲法、几何非线性法以及双重非线性分析法,对地震区居民建筑钢结构极限承载力进行检测。实验结果说明,所提方法能对居民建筑钢结构立柱轴向性和大钩荷载关系以及荷载-扰度曲线,且实施数值运算效果好,预测获取的极限承载力值精度高,建筑的钢结构状态比较稳定。