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1、【精品文档】如有侵权，请联系网站删除，仅供学习与交流DOC-高层结构建筑外文翻译-框架横向刚度估计和横向刚度线性与非线性的连续模型的静力分析-其他专业.精品文档. 中文2597字Lateral stiffness estimation in frames and its implementation to continuum modelsfor linear and nonlinear static analysis Tuba Eroglu Sinan AkkarAbstract：Continuum model is a useful tool for approximate analysis
2、 of tall structures including moment-resisting frames and shear wall-frame systems. In continuum model, discrete buildings are simplified such that their overall behavior is described through the contributions of flexural and shear stiffnesses at the story levels. Therefore, accurate determination o
3、f these lateral stiffness components constitutes one of the major issues in establishing reliable continuum models even if the proposed solution is an approximation to actual structural behavior. This study first examines the previous literature on the calculation of lateral stiffness components (i.
4、e. flexural and shear stiffnesses) through comparisons with exact results obtained from discrete models. A new methodology for adapting the heightwise variation of lateral stiffness to continuum model is presented based on these comparisons. The proposed methodology is then extended for estimating t
5、he nonlinear global capacity of moment resisting frames. The verifications that compare the nonlinear behavior of real systems with those estimated from the proposed procedure suggest its effective use for the performance assessment of large building stocks that exhibit similar structural features.
6、This conclusion is further justified by comparing nonlinear response history analyses of single-degree-of-freedom (sdof) systems that are obtained from the global capacity curves of actual systems and their approximations computed by the proposed procedure.Key words: Approximate nonlinear methods Co
7、ntinuum model Global capacity Nonlinear response Frames and dual systems1 IntroductionReliable estimation of structural response is essential in the seismic performance assessment and design because it provides the major input while describing the global capacity of structures under strong ground mo
8、tions.With the advent of computer technology and sophisticated structural analysis programs, the analysts are now able to refine their structural models to compute more accurate structural response. However, at the expense of capturing detailed structural behavior, the increased unknowns in modeling
9、 parameters, when combined with the uncertainty in ground motions, make the interpretations of analysis results cumbersome and time consuming. Complex structural modeling and response history analysis can also be overwhelming for performance assessment of large building stocks or the preliminary des
10、ign of new buildings. The continuum model, in this sense, is an accomplished approximate tool for estimating the overall dynamic behavior of moment resisting frames (MRFs) and shear wall-frame (dual) systems. Continuum model, as an approximation to complex discrete models, has been used extensively
11、in the literature. Westergaard (1933) used equivalent undamped shear beam concept for modeling tall buildings under earthquake induced shocks through the implementation of shear waves propagating in the continuum media. Later, the continuous shear beam model has been implemented by many researchers
12、(e.g. Iwan 1997; Glkan and Akkar 2002; Akkar et al. 2005; Chopra and Chintanapakdee 2001) to approximate the earthquake induced deformation demands on frame systems. The idea of using equivalent shear beams was extended to the combination of continuous shear and flexural beams by Khan and Sbarounis
13、(1964).Heidebrecht and Stafford Smith (1973) defined a continuum model (hereinafter HS73) for approximating tall shear wall-frame type structures that is based on the solution of a fourthorder partial differential equation (PDE). Miranda (1999) presented the solution of this PDE under a set of later
14、al static loading cases to approximate the maximum roof and interstory drift demands on first-mode dominant structures. Later, Heidebrecht and Rutenberg (2000) showed a different version of HS73 method to draw the upper and lower bounds of interstory drift demands on frame systems. Miranda and Tagha
15、vi (2005) used the HS73 model to acquire the approximate structural behavior up to 3 modes. As a follow up study, Miranda and Akkar (2006) extended the use of HS73 to compute generalized drift spectrum with higher mode effects. Continuum model is also used for estimating the fundamental periods of h
16、igh-rise buildings (e.g. Dym and Williams 2007). More recently, Gengshu et al. (2008) studied the second order and buckling effects on buildings through the closed form solutions of continuous systems. While the theoretical applications of continuum model are abundant as briefly addressed above, its
17、 practical implementation is rather limited as the determination of equivalent flexural (EI) and shear (GA) stiffnesses to represent the actual lateral stiffness variation in discrete systems have not been fully addressed in the literature. This flaw has also restricted the efficient use of continuu
18、m model beyond elastic limits because the nonlinear behavior of continuum models is dictated by the changes in EI and GA in the post-yielding stage This paper focuses on the realistic determination of lateral stiffness for continuum models. EI and GA defined in discrete systems are adapted to contin
19、uum models through an analytical expression that considers the heightwise variation of boundary conditions in discrete systems. The HS73 model is used as the base continuum model since it is capable of representing the structural response between pure flexure and shear behavior. The proposed analyti
20、cal expression is evaluated by comparing the deformation patterns of continuum model and actual discrete systems under the first-mode compatible loading pattern. The improvements on the determination of EI and GA are combined with a second procedure that is based on limit state analysis to describe
21、the global capacity of structures responding beyond their elastic limits. Illustrative case studies indicate that the continuum model, when used together with the proposed methodologies, can be a useful tool for linear and nonlinear static analysis.2 Continuum model characteristicsThe HS73 model is
22、composed of a flexural and shear beam to define the flexural (EI) and shear (GA) stiffness contributions to the overall lateral stiffness. Themajor model parameters EI and GA are related to each other through the coefficient (Eq.1). As goes to infinity the model would exhibit pure shear deformation
23、whereas = 0 indicates pure flexural deformation. Note that it is essential to identify the structural members of discrete buildings for their flexural and shear beam contributions because the overall behavior of continuum model is governed by the changes in EI and GA. Equation 2 shows the computatio
24、n of GA for a single column member in HS73. The variables Ic and h denote the column moment of inertia and story height, respectively. The inertia terms Ib1 and Ib2 that are divided by the total lengths l1 and l2, respectively, define the relative rigidities of beams adjoining to the column from top
25、 (see Fig. 3 in the referred paper).Equation 2 indicates that GA (shear component of total lateral stiffness) is computed as a fraction of flexural stiffness of frames oriented in the lateral loading direction. Accordingly, the flexural part (EI) of total stiffness is computed either by considering
26、the shear-wall members in the loading direction and/or other columns that do not span into a frame in the direction of loading. This assumption works fairly well for dual systems. However, it may fail in MRFs because it will discard the flexural contributions of columns along the loading direction a
27、nd will lump total lateral stiffness into GA. Essentially, this approximation will reduce the entire MRF to a shear beam that would be an inaccurate way of describing MRF behavior unless all beams are assumed to be rigid. To the best of authors knowledge, studies that useHS73model do not describe th
28、e computation of in depthwhile representing discrete building systems as continuum models. In most cases these studies assign generic values for describing different structural behavior spanning from pure flexure to pure shear1. This approach is deemed to be rational to represent theoretical behavio
29、r of different structures. However, the above highlighted facts about the computation of lateral stiffness require further investigation to improve the performance of HS73 model while simplifying an actual MRF as a continuum model. In that sense, it is worthwhile to discuss some important studies on
30、 the lateral stiffness estimation of frames. These could be useful for the enhanced calculations of EI and GA to describe the total lateral stiffness in continuum systems.3 Lateral stiffness approximations for MRFs There are numerous studies on the determination of lateral stiffness in MRFs. The met
31、hods proposed in Muto (1974) and Hosseini and Imagh-e-Naiini (1999) (hereinafter M74 and HI99, respectively) are presented in this paper and they are compared with the HS73 approach for its enhancement in describing the lateral deformation behavior of structural systems. Equation 3 shows the total l
32、ateral stiffness, k, definition of M74 for a column at an intermediate story.The parameters Ic, h, Ib1, Ib2, l1 and l2 have the samemeanings as in Eq. (2). Note that Eq. (2) proposed in HS73 is a simplified version of Eq. (3) for a unit rotation. The former expression assumes that the dimensions of
33、beams spanning into the column from top are the same as those spanning into the column from bottom. However, Eqs. (2) and (3) exhibit a significant conceptual difference: the HS73 approach interprets the resulting stiffness term as the shear contribution whereas M74 considers it as the total lateral
34、 stiffness. The HI99 method defines the lateral stiffness of MRFs through an equivalent simple system that consists of sub-modules of one-bay/one-story frames. Each sub-module represents a story in the original structure and the column inertia (Ic) of a sub-module is calculated by taking half of the
35、 total moment of inertia of all columns in the original story. The relative rigidities of upper (ku) and lower (kl ) beams in a sub-module are calculated by summing all the relative beam rigidities at the top and bottom of the original story, respectively. The total lateral stiffness of a story by H
36、I99 is given in Eq. (5) The parameter kc and h denote the relative rigidity and length of the column in the submodule,respectively. The total lateral stiffness at ground story is computed by assigning relatively large stiffness values to kl to represent the fixed-base conditions. Equation (5) has a
37、similar functional format as Eqs. (2) and (3). Since the lateral stiffness computed stands for the total lateral stiffness, it exhibits a more similar theoretical framework to M74. Discussions presented above indicate that both M74 and HI99 consider the variations in lateral stiffness at the ground
38、story due to fixed-base boundary conditions. However, they ignore the free end conditions at the top story. As a matter of fact, Schultz (1992) pointed that lateral stiffness changes along the building height might be abrupt at boundary stories. The boundary stories defined by Schultz (1992) not onl
39、y consist of ground and top floors but also the 2nd story because the propagation of fixed-base conditions above the ground story level is prominent at the 2nd story as well. Although Schultz (1992) proposed correction factors for boundary stories of some specific cases, he does not give a general e
40、xpression that accounts for the stiffness changes at boundary stories.References1.Akkar S, Yazgan U, Glkan P (2005) Drift estimates in frame buildings subjected to near-fault ground motions. J Struct Eng ASCE 131(7):101410242.American Society of Civil Engineers (ASCE) (2007) Seismic rehabilitation o
41、f existing buildings: ASCE standard, report no. ASCE/SEI 41-06. Reston, Virginia3.Applied Technology Council (ATC) (2004) FEMA-440 Improvement of nonlinear static seismic analysis pro-cedures, ATC-55 project report. prepared by the Applied technology Council for the Federal Emergency Management Agen
42、cy, Washington, DC. 4.Blume JA (1968) Dynamic characteristics of multi-story buildings. J Struct Div ASCE 94(2):377402 5.Borzi B, Pinho R, Crowley H (2008) Simplied pushover-based vulnerability analysis for large-scale assessment of RC buildings. Eng Struct 30:804820框架横向刚度估计和横向刚度线性 与非线性的连续模型的静力分析 吐哈
43、埃尔奥卢思南阿卡尔摘要： 连续模型是高层结构的近似分析，包括抗弯框架剪力墙系统都是非常有用的工具。在连续介质模型，离散的建筑物被简化，这样他们的整体性能可以通过楼层层面的弯曲和剪切刚度来描述。因此，这些组件横向刚度的准确测定，是建立可靠的连续模型的主要问题之一，即提出的解决方案是一个实际的近似结构。本研究首先探讨通过与精确结果的比较，通过对横向刚度组件（即弯曲和剪切刚度）以往文献的计算来获得离散模型。基于这些比较，一种适用于横向刚度连续模型变化的新方法被提出来。建议的方法是进行延伸来估计非线性抗弯矩框架的整体能力。该核查是比较与建议的过程，而估计的实际系统的非线性特性表明其对大型建筑表现出类似
44、的结构特征，并被有效利用。这一结论是通过比较，来进一步说明单自由度的非线性特性历史分析（单自由度），它们从实际系统和拟议的程序的近似计算来得到系统的整体能力曲线。关键词：近似非线性方法 连续模型 整体能力 非线性特性 框架和双系统1 介绍结构特性的可靠估计是抗震性能评估和设计必不可少，因为它提供主要数据在描述在强地震时结构的整体能力。随着计算机技术和先进的结构分析程序的出现，分析家现在能够改进其结构模型来计算更准确的结构反应。然而，在捕捉详细的结构性能为前提，模型参数未知的增加与地面运动相结合的不确定性，会使分析结果繁琐与解释费时。复杂的结构模型和反应历史分析，也可用于大型建筑群性能评估或新建
45、筑物的初步设计的确定。连续模型，在这个意义上，是估计抗弯矩框架（MRFs）和剪力墙框架（dual）系统近似整体动态反应的工具。连续模型，近似的作为一种复杂的离散模型，已被广泛使用在文献中。Westergaard（1933）是用于地震引起的冲击下，高层建筑模型通过连续介质传播横波方式的等效阻尼剪切梁的概念。后来，连续剪切梁模型由许多研究者实现了（如伊万1997年古坎和阿卡尔2002;阿卡尔等人，2005年。普拉和柴可珀达2001）模拟地震引起的变形对框架体系的作用。可翰和 贝冉斯 (1964)采用等效剪切梁的理念扩展到连续剪切和弯曲梁的组合。黑布瑞去和斯塔福德史密斯（1973）所界定连续的结构模
46、型（以下简称HS73），是用一个四阶偏微分方程（PDE）来解决高层剪力墙框架模型，虽然连续介质模型的理论应用建立在简要讨论上，其实际执行情况是相当有限，因为等效弯曲测定和剪刚度测定，代表的实际离散系统横向刚度变化在文献里没有得到充分处理。这一缺陷也限制了，因为超出弹性极限的非线性行为的连续模型的有效利用，连续模型是取决于在后阶段EI和GA的变化。本文的重点是横向刚度连续模型的定义。EI和GA在离散系统中的定义，是边界条件下离散系统的变化模型的解析表达式。该HS73模型作为基础连续模型，是因为它表现了纯弯曲和剪切行为，能代表结构反应的能力。建议的解析表达式是通过比较在第一个模式兼容加载模式下的，
47、连续模型和实际离散系统的变形模式。在EI和GA测定的改善，在结合了第二个过程的极限状态分析的基础上，描述了结构承载超出其弹性极限后的整体能力。说明案例研究表明，连续模型，使用时与所建议的方法一起，可以成为线性和非线性静力分析的有用工具。2 连续模型的特点该HS73模型是由弯曲和剪切梁组成，来定义弯曲（EI）及剪切（GA）刚度的，从而确定整体刚度横向刚度。主要的模型参数EI和GA有关，通过彼此的（公式1）系数相互联系。以趋于无穷模型将展出纯剪切变形而= 0表示纯弯曲变形。注意的事，必须查明离散建筑物的结构构件的弯曲和剪切，因为连续模型的整体行为是受在EI和GA的变化而决定。公式2表示在HS73的
48、一系列计算。变量Ic和H分别表示的惯性和层高。Ib1的惯性和由L1和L2，分别确定相对僵化的总长度除以Ib2，梁毗邻自顶柱（见图。在3提到文件）。 公式2表明，GA（占总数的横向刚度剪切组件）是一个横向载荷方向框架抗弯刚度的计算分数。弯曲部分（EI）的总刚度计算或者考虑在剪力墙加载方向/或不成为一个框架中其它柱跨度方向的负荷载。这个假设对双系统效果非常好。但是，它可能会失败，因为它会在抗弯矩框架上沿载荷方向，将柱并到GA横向刚度。事实上，这种近似将减少整个抗弯矩框架到剪力梁，将会不准确的描述抗弯矩框架反应，除非所有的梁被认为是刚性的。就作者的所知，研究使用HS73模型不仅详细描述了的计算，而且
49、把离散建筑系统作为连续模型。在大多数情况下，这些研究不同结构分配过程，从纯弯曲跨越到纯剪通用的值。这种方法被认为是合理的，是代表不同结构理论的行为。不过，以上强调的事实，即有关的横向刚度计算需要进一步调查，以提高模型的性能，同时简化HS73实际抗弯矩框架作为一个连续模型。在这个意义上说，的关于框架侧向刚度估计的一些重要研究是值得讨论的。这可能是关于GA和EI有用的增强计算方法，用于描述连续系统的总横向刚度。3 抗弯矩框架的近似横向刚度这里有很多研究关于抗弯矩框架横向刚度的测定。Muto (1974) 和 Hosseini 和Imagh-e-Naiini (1999) 所提出的方法（以下分别简称M74和HI99）基于本文件和他们相对于HS73途径提高了其在描述系统结构的侧向变形。公式3显示总横向刚度K的M74，是一根柱在一