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1、四层钢筋混凝土框架结构的地震反应对砌体填充的影响一种确定性的评估摘要：四层楼高的钢筋混凝土框架结构的地震响应对砌体填充物的影响研究使用N2的方法。方法是基于塑性分析方法和无弹性谱方法。这是最新扩展，使其适用于填充钢筋混凝土框架结构。文件中总结了该方法并将其应用于四层钢筋混凝土框架结构砌体填充物，并没有他们的确定性地震评估。已经对裸露的框架的性能作出了比较。最常见的分析建模技术，是采用压缩对角支柱砌体填充的建模，和一个组件集中的可塑性元素建模的梁、柱的抗弯性能被应用。分析结果表明，填充物可以彻底改变整个结构的损害分布。填充物对结构响应产生有利的影响，把他们放置于整个结构，并不会导致剪切失效。关键
2、词：地震评估；钢筋混凝土框架；砌体加密；加密钢筋混凝土框架；简化非线性分析引言钢筋混凝土 (RC) 框架砌体在世界许多地区是常用的结构体系。如果填充物适当分布在整个结构和适当考虑在设计中，他们通常对结构的地震反应有一个有益的影响。另一方面，在计划中负面影响可能造成的不规则的定位填充，特别是在竖向。薄弱楼层崩溃是典型的填充结构中填充物的缺失，例如底部层。然而，第一层机制和随后的崩溃也会发现在钢筋混凝土框架结构建筑物的情况下与常规砌体填充物的分布，如果整体延展性的裸露框架和局部塑性的结构要素很低，如果砌体填充物是脆弱和易碎的，如果地面运动是比较强的设计强度。在强烈地震中任何方法的分析或设计的填充墙
3、框架应该适当考虑到高度非线性变形。一个好的关于填充墙框架的设计规定已经被提出。一个全面的概述了建模技术分析的框架填充墙结构准备好了。广泛的用于新型填充面板，单个或多个压缩等效斜压杆。在本文中讨论了四层钢筋混凝土框架结构的地震反应对砌体填充的影响。最近由作者提出的一个简化的抗震性能评估放法，已经被使用。在一个变形，不开口填充（“完全填充墙框架”，第3.1节），而在其他变形有开口门窗填充（“部分填充墙框架”，3.1节）。比较了裸露的变形框架。部分填充墙框架和裸露的框架在埃尔莎实验室进行全面的pseudo-dynamically测试。在分析中，砌体填充板被参照两个对角线的支撑，只可进行压缩的方式。“
4、抗弯性能的梁、柱模型的单组分集中塑性元件，组成一个弹性梁和两根弹性转动铰链（定义为一个弯矩-转角关系）。数学模型的计算结果与实验结果进行比较,验证了非线性动态分析。该opensees计划是用于所有的分析。地震评估讨论，在本文中的应用是确定性的。在文献提出了一种概率评估。1. N2的方法综述卢布尔雅那大学和欧洲规范8(EC8)已经实施的N2方法，最近已扩展到填充墙框架。本文简要总结了框架平面的建筑结构和其扩展名的基本途径。N2方法结合静力弹塑性分析的多自由度（多自由度）模型与反应谱分析的一种等效单自由度（单自由度）模型。荷载横向分布向量，采用弹塑性分析，是有关假定的位移向量(n = 1,n表示屋
5、顶高度) 其中M是对角质量矩阵。这里没有固定位移形状的选择规则。规范性文件可给予一些指导。基底剪力位移关系得到了弹塑性分析是理想化的，通常是由一个双线性（弹塑性）理想化。以这种方式得到力Fy和位移Dy是果断的，该转化为等效单自由度模型是由除以基底剪力和顶层位移的多自由度模型的一个转换因子，定义为其中1是单位向量,m是有效质量。理想化系统的弹性阶段被定义为容量曲线,可以在加速度-位移(AD)格式中绘制和直观地与需求谱中相同的格式绘制相比，确定从理想化的力量变形曲线的等效单自由度体系中除以m。他们之间的关系（光谱）加速度和屈服应力Fy的多自由度系统可以定义为折减系数R由于耗能能力的定义是加速度的比
6、值方面的需求弹性Sae为周期T、光谱加速度、加速度能力上指出(即光谱加速度对应于屈服，式(3)注意折减系数用于抗震规范(例如变形因素q在欧洲规范8中使用)也考虑减少到极限，因此并不能等同于折减系数R的定义式（5）。折减系数R、延展性的和周期T（RT 关系）之间的关系取决于类型的结构体系，并且提供在文献中。最简单的关系是平等的位移规则，通常用于普通结构与时间的中期和长期范围。为了用N2方法填充钢筋混凝土框架结构，在EC8中两种改进需要做出最基本的（简单）版本的实行方法。首先，推覆曲线已经被理想化为线性力位移关系而不是一个简单的弹塑性。一个典型的理想化的力位移曲线包络对应一个填充墙钢筋混凝土框架如
7、图1所示。它可以分为四部分。第一，等效弹性部分代表的初始弹性变形和变形开裂后发生在框架和填充两处。第二部分，点P1和P2之间表示屈服。由于低延性框架填充墙，这部分通常是短暂的。第三部分，这是一个重要的特点，填充墙结构，强度退化治理的结构相应直到达到P3，其填充彻底失败。在这一点后，只有抵抗水平荷载的框架。其次，有弹性的光谱由减少使用特定的因素(即R-T关系)适合填充墙框架，例如那些建议在。结构参数确定的折减系数，这是除了采用参数中使用的常规，例如：弹塑性系统（即初期和整体延展性），延性之初,强度退化s = D2 / D1(图1),以及填充失败后强度减少ru= F3/F1（图1）。折减系数还取决
8、于角的弹性需求反应谱（TC和TD根据EC8）。为了进行说明，表示填充墙的框架，根据确定特定理想化系统RT关系呈现于图2。两个情节，一个用于给定的延展性，另一个为提供给定的折减系数（强度）。作为比较，也会显示无强度退化弹塑性系统关系。The effect of masonry infills on the seismic response of a four-storey reinforced concrete framea deterministic assessmentMatjaz Dolsek_, Peter FajfarUniversity of Ljubljana, Faculty o
9、f Civil and Geodetic Engineering, Jamova 2, SI-1000 Ljubljana, SloveniaReceived 11 May 2007; received in revised form 28 December 2007; accepted 7 January 2008Available online 14 February 2008AbstractThe effect of masonry infills on the seismic response of a four-storey reinforced concrete frame has
10、 been studied using the N2 method. The method is based on pushover analysis and the inelastic spectrum approach. It was recently extended in order to make it applicable to infilled reinforced concrete frames. In the paper the method is summarized and applied to the deterministic seismic assessment o
11、f a four-storey reinforced concrete frame with masonry infills, with openings and without them. A comparison has been made with the behaviour of the bare frame. The most common analytical modelling technique, which employs compressive diagonal struts for modelling of the masonry infill, and one-comp
12、onent lumped plasticity elements for modelling the flexural behaviour of the beams and columns, was applied. The results of the analyses indicate that the infills can completely change the distribution of damage throughout the structure. The infills can have a beneficial effect on the structural res
13、ponse, provided that they are placed regularly throughout the structure, and that they do not cause shear failures of columns.c 2008 Elsevier Ltd. All rights reserved.Keywords: Seismic assessment; Reinforced concrete frame; Masonry infill; Infilled RC frame; Simplified nonlinear analysis1. Introduct
14、ionReinforced concrete (RC) frames with masonry infill are a popular structural system in many parts of the world 1. If the infills are properly distributed throughout the structure and properly considered in the design, then they usually have a beneficial effect on the seismic response of the struc
15、ture.On the other hand, negative effects can be caused by irregular positioning of the infills in plan, and especially in elevation 1, 2. A soft-storey collapse is typical for infilled structures in which the infills are missing in one, e.g. the bottom storey. However, a first-storey mechanism and s
16、ubsequent collapse can also occur in the case of RC frame buildings with a regular distribution of masonry infills if the global ductility of the bare frame and the local ductilities of the structural elements are low, if the masonry infills are weak and brittle, and if the ground motion is strong c
17、ompared to the design strength 3. Any method for the analysis or design of infilled frames should properly take into account the highly nonlinear behaviour of this system during strong earthquakes. A good review of design provisions related to infilled frames has been presented by Kaushik et al. 4.
18、A comprehensive overview of the analytical modelling techniques of infilled frame structures was prepared, for example, by Moghaddam and Dowling 5 and, more recently, by Crisafulli, Carr and Park 6. The mostcommonly used technique to model infill panels is that of single or multiple compressive equi
19、valent diagonal struts. In this paper the effects of masonry infill on the seismic response of a four-storey reinforced concrete frame are discussed. A simplified seismic performance assessment method, recently proposed by the authors 7, has been used. In one variant, the infill is without openings
20、(the “fully infilledframe”, Section 3.1), whereas in the other variant there are openings for windows and doors in infills (the “partially infilled frame”, Section 3.1). A comparison has been made with the behaviour of the bare frame. The partially infilled frame and the bare frame were pseudo-dynam
21、ically tested at full-scale in the ELSA laboratory in ISPRA 8. In the analyses, the masonry infill panels were modelled by means of two diagonal struts, which can only carry compression. The flexural behaviour of the beams and columns was modeled by one-component lumped plasticity elements, consisti
22、ng of an elastic beam and two inelastic rotational hinges (defined by a momentrotation relationship). The mathematical model was validated by comparing the results of nonlinear dynamic analyses with the experimental results. The OpenSees program was used for all the analyses 9. The seismic assessmen
23、t discussed and applied in this paper is deterministic. In the companion paper 10 a probabilistic assessment is presented.2. Summary of the N2 methodThe N2 method 11, which was developed at the University of Ljubljana and has been implemented in Eurocode 8 (EC8) 12, has been recently extended to inf
24、illed frames 13,7. In this paper, the basic approach for planar building structures and its extension to infilled frames are briefly summarized. The N2 method combines pushover analysis of a multidegree- of-freedom (MDOF) model with the response spectrum analysis of an equivalent single-degree-of-fr
25、eedom (SDOF) model. The lateral load distribution vector , employed in pushover analysis, is related to the assumed displacement shape vector _ (_n = 1, n denotes the roof level) bywhere M is the diagonal mass matrix. There are no fixed rules for the choice of the displacement shape. Some guidelines
26、 may be given in the regulatory documents. The base sheartop displacement relationship obtained by pushover analysis has to be idealized, usually by a bilinear (elasto-plastic) idealization. In this way the yield force Fy , and the yield displacement Dy , are determined. The transformation to an equ
27、ivalent SDOF model is made by dividing the base shear and top displacementof the MDOF model with a transformation factor which is defined as where 1 is the unity vector and m_ is the effective mass. The elastic period of the idealized system is defined as The capacity curve, which can be
28、plotted in the acceleration displacement (AD) format and visually compared with demand spectra plotted in the same format, is determined from the idealized forcedeformation curve of the equivalent SDOF system by dividing the force by m_. The relation between the (spectral) acceleration and the yield
29、 force Fy of the MDOF system is thus defined as The reduction factor R due to energy dissipation capacity is defined as the ratio of the acceleration demand Sae in terms of the elastic spectral acceleration for the period T , to the acceleration capacity Say (i.e. spectral acceleration corresponding
30、 to the yield force, Eq. (3) Note that the reduction factors used in seismic codes (e.g. the behaviour factor q used in Eurocode 8) take into account also the reduction due to overstrength, and are thus not equivalent to the reduction factor R defined in Eq. (5). The relationships between the reduct
31、ion factor R, the ductility , and the period T (the RT relations) depend on the type of structural system, and are provided in the literature. The simplest relation is the “equal displacement rule”, which is often used for ordinarystructures with periods in the medium- and long-period range.In order
32、 to apply the N2 method to infilled RC frames, two modifications need to be made to the basic (simple) versionof the method implemented in EC 8. Firstly, the pushover curve has to be idealized as a multi-linear forcedisplacement relation rather than a simple elasto-plastic one. A typicalidealized fo
33、rcedisplacement envelope corresponding to an infilled RC frame is shown in Fig. 1. It can be divided into four parts. The first, equivalent elastic part represents both the initial elastic behaviour and the behaviour after cracking has occurred in both the frame and the infill. The second part, betw
34、een points P1 and P2, represents yielding. This part is typically short, due to the low ductility of infilledframes. In the third part, which is an important characteristic of infilled structures, strength degradation of the infill governs the structural response until the point P3 is reached, where
35、 the infill fails completely. After this point, only the frame resists the horizontal loads. Secondly, inelastic spectra have to be determined by using specific reduction factors (i.e. the RT relation) appropriate for infilled frames, e.g. those proposed in 13. The structural parameters determining
36、the reductionfactor, which are employed in addition to the parameters used in a usual, e.g. elasto-plastic system (i.e. the initial period and global ductility), are ductility at the beginning of strength degradation s = D2/D1 (Fig. 1), and the reduction of strength after the failure of the infills
37、ru = F3/F1 (Fig. 1). The reduction factor also depends on the corner periods of the elastic demand spectrum (TC and TD according to EC8). For illustration, the RT relations for a specific idealized system representing an infilled frame, determined according to 13, are presented in Fig. 2. Two plots are provided, one for a given ductility, and the other for a given reduction factor (strength). For comparison, the relations for an elasto-plastic system without strength degradation are also shown.
