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1、宁波工程学院毕业设计（论文）-外文翻译 外文原文： Lateral stiffness estimation in frames and its implementation to continuum modelsfor linear and nonlinear static analysisTuba Eroglu Sinan AkkarReceived: 23 April 2010 / Accepted: 17 November 2010 Springer Science+Business Media B.V. 2010Abstract Continuum model is a useful
2、 tool for approximate analysis 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. There
3、fore, accurate determination of 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 la
4、teral stiffness components (i.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
5、then extended for estimating the 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
6、 similar structural features. 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.Keywords Appr
7、oximate nonlinear methods Continuum model Global capacity Nonlinear response Frames and dual systemsT. ErogluDepartment of Civil Engineering, Akdeniz University, 07058 Antalya, Turkeye-mail: etubametu.edu.trS. Akkar (B)Department of Civil Engineering, Middle East Technical University, 06531 Ankara,
8、Turkeye-mail: sakkarmetu.edu.tr1 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 motions.With the advent of computer technol
9、ogy 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 parameters, when combined with the uncer
10、tainty 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 design of new buildings. The continuum model
11、, 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 in the literature. Westergaard (1933) use
12、d 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 (e.g. Iwan 1997; Glkan and Akkar 2002; Ak
13、kar 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 (1964).Heidebrecht and Stafford Smith (19
14、73) 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 lateral static loading cases to approximate th
15、e 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 Taghavi (2005) used the HS73 model to acquire
16、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 high-rise buildings (e.g. Dym and Williams
17、 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 practical implementation is rather limit
18、ed 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 continuum model beyond elastic limits because the
19、 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 continuum models through an analytical expressi
20、on 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 analytical expression is evaluated by comparing
21、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 the global capacity of structures respond
22、ing 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 characteristics The HS73 model is composed of a flexural and shear beam to
23、 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 whereas = 0 indicates pure flexural defo
24、rmation. 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 computation of GA for a single column member in HS
25、73. 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 (see Fig. 3 in the referred paper). Equ
26、ation 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 the shear-wall members in the loading d
27、irection 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 and will lump total lateral stiffness in
28、to 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 the computation of in depthwhile represen
29、ting 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 behavior of different structures. However, the
30、 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 the lateral stiffness estimation of fr
31、ames. 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 methods proposed in Muto (1974) and Hossei
32、ni 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 lateral stiffness, k, definition of M74
33、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 beams spanning into the column from to
34、p 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 stiffness. The HI99 method defines th
35、e 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 total moment of inertia of all column
36、s 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 HI99 is given in Eq. (5) The parameter
37、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 similar functional format as Eqs. (2)
38、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 story due to fixed-base boundary condi
39、tions. 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 only consist of ground and top floors but
40、 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 expression that accounts for the stiffn
41、ess 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 of existing buildings: ASCE standard, re
42、port no. ASCE/SEI 41-06. Reston, Virginia3、Applied Technology Council (ATC) (2004) FEMA-440 Improvement of nonlinear static seismic analysis procedures, ATC-55 project report. prepared by the Applied Technology Council for the Feeral Emergency Management Agency, Washington, DC4、Blume JA (1968) Dynam
43、ic characteristics of multi-story buildings. J Struct Div ASCE 94(2):3774025、Borzi B, Pinho R, Crowley H (2008) Simplified pushover-based vulnerability analysis for large-scale assessmentof RC buildings. Eng Struct 30:804820中文翻译：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 吐哈埃尔奥卢思南阿卡尔 收到日期：2010年4月23日/发表日期：2010年11月
44、17日 施普林格科学商业媒体B.V.2010+ 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
45、性表明其对大型建筑表现出类似的结构特征，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、框架和双系统吐哈埃尔奥卢目前留在中东技术大学研究生学院。T. Erog lu土木工程系，Akdeniz大学，07058土耳其安塔利亚电子邮件：etubametu.edu.trS. Akkar (B)土木工程系，中东技术大学，06531安卡拉，土耳其电子邮件：sakkarmetu.edu.tr1、 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，
46、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
47、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
48、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，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的一系列计算。变量Ic和H分别表示的惯性和层高。Ib1的