外文翻译弹塑性分析方钢管混凝土框架结构的抗震性能.doc

弹塑性分析方钢管混凝土框架结构的抗震性能聂建国、秦 凯、肖 岩土木工程系,清华大学,北京100084,中国;土木工程系、南加州大学、洛杉矶 证90089美国摘要：为了调查方钢管混凝土结构的抗震性能，对10 层由方钢管混凝土柱和钢粱组成的片刻抵抗框架进行弹塑性分析。结果表明弹塑性分析对横向载荷模式是敏感的，因此，为了使惯性约束力量分布均匀，至少使用两个负荷模式。对未来的方钢管混凝土结构的弹塑性分析，用汉司公式或USC-RC计算方钢管混凝土柱的M-曲线和N-M表面相互作用都是适用的。P-因素严重影响了MRF的抗震性能，所以，在研究MRF的抗震性能时应把它拿出来进行研究。同时，对三类钢筋混凝土结构进行分析比较,让钢筋混凝土结构和方钢管混凝土结构进行抗震性能的比较。结果表明,方钢管混凝土结构的延性和抗震性能高于钢筋混凝土结构。因此，在地震地区优先推荐选用方钢管混凝土结构。关键词: 方钢管混凝土、弹塑性分析、容量曲线、钢筋混凝土引言在过去的二十多年里，多位学者提出并发展了弹塑性分析这一方法，包括Saiidi ,Sozen, Fajfar , Gaspersic, Bracci 等等。这种方法也被用来作为设计和评估现有建筑物的抗震性能的一种工具. 弹塑性分析的目的在于通过静态的无弹力分析来预计特定地震中强度和变形要求，并将这些要求与有效容量进行比较，从而推测出预期表现结构系统。弹塑性分析基于非线性的静态分析，即假设在一个有一定高度的建筑上施加一个横向荷载，并从0到最高限逐渐增加横向荷载直至建筑崩溃。在此过程中，重力荷载是保持不变的。弹塑性分析在建筑物以下几个特征的预测方面很有用：1）基本剪顶位移图代表的建筑物能力；2）评估物的最高旋转和延展性；3）极限荷载中塑性铰的分布；4）以极限负荷中局部损害指数的形式表示的建筑物中损害的分布。目前，尽管弹塑性分析已被许多研究者和设计人员运用于钢筋混凝土建筑物，但是我们却很少看到有其运用于地铁的报道。钢管混凝土在建筑中的运用越来越广泛。这部分归功于它们极好的抗震能力，例如高强度、高柔韧性以及高能量吸收能力等。目前，对这些建筑的理论性研究主要集中在管道的静态研究，而对其抗震性的研究则很少。对钢管混凝土中弹性塑性历史纪录的分析已由Li等论述了。他们研究的结果显示，在强烈地震荷载下， 建筑物会受到一些可修复的损伤，这也就证明了钢管混凝土在抗震方面表现要好一些。研究了用作抗震实验的四栋五层建筑物，它们由钢管混凝土和钢筋混凝土组成的。SAP2000也用来计算建筑物的抗震反应，已分析历史记录。钢管混凝土和钢筋混凝土的动态行为和抗震反应也被研究了。以此作者得出结论，与钢筋混凝土相比，钢管混凝土的抗震性能是相当好的。Li等在一个两间三层的钢管混凝土框架上作了实验，通过对其施加垂直荷载和横向荷载。在钢管混凝土框架模型试验基础上，研究者们完成了非线性有限元分析。计算出的结果与实验结果相符，从而为钢管混凝土抗震提供了一种适用方法。尽管最近几年已有多位研究者研究了钢管混凝土的抗震性，但弹塑性分析法仍然受到其合理性、适应性以及功效性的限制。这些方法中关于力学模型的样子，副作用以及计算效率都需要进一步改进，而且我们还需要做更多的实验来检验这些分析方法的精确性。方钢管混凝土虽然约束效果不如圆钢管混凝土显著，但是由于具有节点形式简单、截面惯性矩大、稳定性能好、便于采取防火措施等诸多优点，因此，近年来方钢管混凝土结构已经受到人们的广泛关注，实际工程应用不断增加。但是，到目前为止，有关方钢管混凝土结构体系方面的研究还很少，因此，本文对一幢10 层方钢管混凝土框架结构进行了弹塑性分析。1 弹塑性分析根据对由方钢管混凝土柱和钢粱组成的10 层片刻抵抗的框架结构的研究。方钢管混凝土结构的结构成员的计划、标高, 和典型的横断面条件如图1所示。使用SAP2000对方钢管混凝土结构进行弹塑性分析 。在SAP2000中，把100 毫米深的大厦的地板当作壳元素，方钢管混凝土柱和钢粱当作框架元素。梁、柱结构的尺寸和材料如表1所示 。1.1 铰性能地震时在框架结构中塑性铰通常形成在梁、柱的两端。对于梁单元,塑性铰大多是由单向弯矩造成, 但是对于柱结构, 塑性铰主要由轴向荷载和双向弯矩造成。所以, 在弹塑性分析中由梁和柱在不同受力情况下产生的不同类型的塑性铰应该分别的应用弹塑性分析。在SAP2000中, 使用M3 铰模仿在单向弯矩作用下造成的塑性铰, 因此用户定义的M3铰这个模型被应用在钢粱上。计算钢粱的片刻自转曲线, 当满足以下假定才适用: 1) 以古典双线性硬化模型应用为代表的应力-应变行为的钢梁; 2) 平面部分无穷大。钢粱为典型的M- 曲线如图2所示。同样, PMM铰是由SAP2000使用模拟塑性铰在轴向荷载和双向弯曲的作用下造成的。因此,用户定义的PMM 铰适用于方钢管混凝土柱模型。使用汉司公式和南加州大学提出的钢筋混凝土模型计算方钢管混凝土的M-曲线和N-M互作用表面, 并做比较。方钢管混凝土的典型的N-M相互作用表面和M-曲线如图3所示。1.2 横向载荷模式在设计地震中横向载荷模式旨在代表惯性力分布。显然,对于不同程度（即弹性变形的程度）和不同时候的地震应配置不同的惯性力。在预计当地设计地震中，由于没有一个单一的模式能捕捉负荷变化的要求,因此，在预计惯性力分布时，使用两个方向的横向荷载模式进行弹塑性分析。其一是倒三角型的横向载荷剪力法计算基准；另一种是使用SAP2000设计荷载计算模式包括高级模式效果。横向荷载应用在X方向和Y方向调查整体结构的抗震性能。因为东等提出了参考P-效应严重影响刚性框架的稳定性。因此,为了调查P-效应对方钢管混凝土结构的抗震性能，推出了弹塑性分析和没有占P-效应。1.3 结果弹塑性分析的结果可以用来估计潜在的延性结构, 评价其抗荷载能力,并找出故障机制。因而分析弹塑性结果对获得方钢管混凝土结构的抗震性能非常有帮助。1.3.1 荷载变形关系在用弹塑性分析估计结构的抗震性能方面，结构的容量为代表的基础架构与剪切位移图是非常有用的。用弹塑性分析获得的结构容量曲线如图4所示, 从中我们看到顶部位移过（1.6m）会造成AccelX(Y)-Han-P,AccelX(Y)-USC-RC-P,EQX(Y)-Han-P,EQX(Y)-USC-RC-P,和EQX(Y)-Han-P+终止,当整个结构都形成塑性铰就会导致AccelX(Y)-Han-P+、 AccelX(Y)-USC-RC-P+、and EQX(Y)-USC、RC-P+的终止。使用AccelX(Y)的侧向荷载模式比使用EQX(Y)的侧向荷载模式下的底部抗剪强度要大的多。因此,我们可以得出结论：侧向荷载作用下的弹塑性分析结果很精确。而且, 容量曲线的趋向在X 方向和在Y 方向是相似的，如图4所示。因此, 在这种情况下可以用一个方向计算整体结构的抗震性能.参考图4可知,尽管M-曲线和N-M的方钢管混凝土柱的表面相互作用不同，但在有弹性区域它们的容量曲线几乎重合。使用汉司公式计算的M-和N-M曲线比那些用USC-RC计算的屈服强度值要大, 但与其它参量比较区别要小。图4显示，在弹塑性分析中，由于P-的影响最后基本剪力迅速地减少。屈服强度值的减小也是由于同样的原因。故我们能得出结论,由于P-的影响严重而影响框架的抗震性能, 因此我们应考虑到所有在未来MRF 地震分析中可能发生的因素。1.3.2 最后层间偏移在弹塑性分析中最后层间偏移值如图5所示。在预测方钢管混凝土结构的微弱变形方面，这些数据是有用的。从图5,我们看到一至三层的层间侧移明显高于其它层。所以, 从这个例子可以看出，方钢管混凝土结构的微弱的部分应该是第一到三层, 并且他们在工程学应用必须加强。1.3.3 分配塑性铰 在方钢管混凝土柱及横向载荷方向的P-影响、M- 和 N-M曲线的各弹塑性分析中，尽管横向载荷的模式不同，但我们都可以发现有类似塑性铰分布。图6表示在不同水平的EQX-USC-RC-P-的弹塑性分析案中，混泥土框架塑性的产生和发展的程度。塑性铰首先在柱基础的持力层产生，如图6.a所示。随着侧向荷载的增加, 塑性铰出现于该地基各柱的第一层底部和第二层和第三层的部分柱。而且, 在二到六层的部分梁的两端也出现塑性铰如图6b所示。最后，在梁和柱的两端塑性铰的数量不断增加如图6c 。随着水平的荷载的增加塑性绞的数量也跟着增加。最后，由于整体结构顶部位移超出目标或出现塑性绞而超出了弹塑性分析条件,在此阶段（图6d），柱的基础部分的塑性铰得到了充分的发挥，其余的方钢管混凝土柱和塑性铰钢梁在第二至第三层也有一定的发展。由上我们可以得出这样的结论:一到三层应该是弱段方钢管混凝土结构，而在工程应用中他们必须要加强。这样的结论与1.3.2的结论相一致。2 对比为了比较方钢管混凝土结构与钢筋混凝土结构的地震表现,我们研究了四种10层框架结构的方钢管混凝土柱与钢筋混凝土柱。使用SAP2000对这些结构进行弹塑性分析 。为比较的便利，除了垂直的柱之外结构是几乎完全相同,它们都是用不同的材料和层面组成如表2示。尺寸相当于钢筋混凝土柱强度计算基础上,与方钢管混凝土柱等价的弹性模量. 尺寸相当于钢筋混凝土柱强度计算基础上,使EA与方钢管混凝土柱相等，其中E为柱的弹性模量、 A是面积。同样, 根据EI 相等计算等效钢筋混凝土柱, 并且边长等效钢筋混凝土柱，其中I 是转动惯量, 并且B 为方钢管混凝土的边长。为对这些不同结构进行弹塑性分析 , 使用由SAP2000计算的AccelX(Y)横向荷载模式；P-影响未被考虑。从混凝土钢管和钢筋混凝土结构的X方向容量曲线（图7a），我们也许会发现：由于方钢管混凝土结构顶部的位移超过了1.6m，而超出了弹塑性分析的使用范围被迫停止。此时的结构已转变成了塑性绞结构。但钢筋混凝土结构顶位移达不到此目标, 我们可以得出这样的结论:方钢管混凝土结构的延性和变形能力比钢筋混凝土结构的延性和变形能力优越.而且，方钢管混凝土的屈服强度和底部抗剪强度比钢筋混凝土结构高，故方钢管混凝土结构的抗震能力优于钢筋混凝土结构的抗震能力。此结论也可由图7b看出。方钢管混凝土结构和圆钢管混凝土结构的弹塑性分析结果比较如图7所示。根据了s A、 c A与方钢管混凝土柱的sA、cA相等计算圆钢管混凝土柱的尺寸, s A 是钢管部分, 而c A 是被填装的混凝土部分。虽然方钢管混凝土柱比圆钢管混凝土柱的轴向承载力低, 他们是优越在抗弯能力。在这个模型中规定轴向压缩比要小于0.2, 因此柱的抗弯能力比轴向承载能力重要。结果，在这个模型中方钢管混凝土结构的抗震能力比圆钢管混凝土结构优越。3 结论在本文里，比较了由方钢管混凝土柱, 圆钢管混凝土柱, 和钢筋混凝土柱组成的10层框架结构的抗震性能，用弹塑性分析比较方钢管混凝土, 圆钢管混凝土, 和钢筋混凝土结构在地震下的反应得出如下结论：1）弹塑性分析结果表示, 方钢管混凝土结构的延展性和抗震能力比钢筋混凝土结构优越。故，在地震地区优先推荐选用方钢管混凝土结构。2）因为弹塑性分析结果对侧向荷载模式是敏感的, 所以在弹塑性分析中推荐至少使用两个负荷模式使惯性力均匀分布。3）方钢管混凝土柱的M-曲线和N-M表面相互作用弹塑性分析结果存在轻微地影响。所以, 对未来的方钢管混凝土结构的弹塑性分析，曲线计算、汉司公式计算或USC-RC计算都是适用的。4）因为P-因素严重影响到MRF的抗震能力, 因此，在未来研究中这个影响应该被考虑到在MRF地震分析中。聂建国、秦 凯、肖 岩；弹塑性分析方钢管混凝土框架结构的抗震性能；清华大学学报（英文版）；2006年版；第一期，P124-130。TSINGHUA SCIENCE AND TECHNOLOGY ISSN1007-021420/21pp124-130 Volume11,Number1,February2006Push-Over Analysis of the Seismic Behavior of a Concrete-FilledRectangular Tubular Frame Structure*NIE Jianguo (聂建国) *, QIN Kai (秦凯), XIAO Yan (肖岩)Department of Civil Engineering, Tsinghua University, Beijing 100084, China; Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089, USA Abstract: To investigate the seismic behavior of concrete-filled rectangular steel tube (CFRT) structures, apush-over analysis of a 10-story moment resisting frame (MRF) composed of CFRT columns and steelbeams was conducted. The results show that push-over analysis is sensitive to the lateral load patterns, so the use of at least two load patterns that are expected to bound the inertia force distributions is recom-mended. The M - curves and - interaction surfaces of the CFRT columns calculated either by Hansformulae or by the USC-RC program (reinforced concrete program put forward by University of Southern Califonia) are suitable for future push-over analyses of CFRT structures. The P- effect affects the MRFseismic behavior seriously, and so should be taken into account in MRF seismic analysis. In addition, three kinds of RC structures were analyzed to allow a comparison of the earthquake resistance behavior of CFRT structures and RC structures. The results show that the ductility and seismic performance of CFRT struc-tures are superior to those of RC structures. Consequently, CFRT structures are recommended in seismic regions.Key words: concrete-filled rectangular steel tube; push-over analysis; capacity curve; reinforced concretestatic inelastic analysis, and by comparing these de-IntroductionOver the past twenty years the static push-over proce-dure has been presented and developed by several au-thors, including Saiidi and Sozen1, Fajfar and Gasper-sic2, Bracci et al.3, amongst others. This method is also described and recommended as a tool for designand assessment purposes for the seismic rehabilitationof existing buildings4. The purpose of push-overanalysis is to evaluate the expected performance of a structural system by estimating its strength and defor-mation demands in design earthquakes by means of a Received: 2004-06-30; revised: 2004-11-07Supported by the Overseas Youth Cooperative Foundation of the National Natural Science Foundation of China (No. 50128807) To whom correspondence should be addressed. E-mail: ; Tel: 86-10-62772457mands to available capacities at the performance levels. Push-over analysis is basically a nonlinear static analysis that is performed by imposing an assumed dis-tribution of lateral loads over the height of a structure and increasing the lateral loads monotonically from zero to the ultimate level corresponding to the incipient collapse of the structure. The gravity load remains con-stant during the analysis. Push-over analysis is very useful in estimating the following characteristics of a structure: 1) the capacity of the structure as represented by the base shear versus top displacement graph; 2) themaximum rotation and ductility of critical members; 3)the distribution of plastic hinges at the ultimate load;and 4) the distribution of damage in the structure, as expressed in the form of local damage indices at the ul-timate load. Although push-over analyses of reinforced NIE Jianguo (聂建国) et alPush-Over Analysis of the Seismic Behavior of 125concrete (RC) structures and steel structures have been carried out by many researchers and designers, at present push-over analyses for the concrete-filled steeltube (CFT) structures are rarely reported in theliterature. CFT columns have become increasingly popular in structural applications. This is partly due to their ex-cellent earthquake resistant properties such as high strength, high ductility, and large energy absorption capacity5. At present, theoretical analysis of thesestructures focuses mostly on the static behavior of theCFT members, such that the seismic responses of the CFT structures have been rarely studied. Some re-search on the seismic behavior of CFT structures is,however, documented in the literature. The elasto-plastic time-history analysis of CFT structures has been discussed by Li et al.6 Their results show thatno irreparable damage occurs in structures under in-tense earthquake loading, which demonstrates that CFT structures excel in seismic performance. The seismic behaviors of four kinds of 5-story frame structures that are composed of CFT and of RC col-umns have been studied by Huang et al.7 The SAP2000 program was used in the time-history analyses for calculating the seismic responses of thestructures. The dynamic behavior and earthquake re-sponse of the CFT and RC structures were analyzed.The authors conclude that the earthquake resistance behavior of CFT structures is excellent compared tothat of RC structures. Experimental investigation of a 2-span, 3-story model of a CFT frame has been car-ried out under vertical stable loads and lateral cyclic loads by Li et al.8 Based on the CFT frame model experiment, a nonlinear finite element analysis wascompleted9. The calculated results coincided with the test results, providing a practical method for theseismic design of CFT frames. Although the seismicbehavior of CFT frame structures has been investi-gated by many researchers in recent years, the differ-ent elasto-plastic analysis methods are confined by their rationality, applicability, and efficiency. These methods need to be modified regarding aspects of their mechanical models, hysteretic characteristics,and calculation efficiency, and more experimental re-search still needs to be carried out to check the accu-racy of these analysis methods.Although concrete-filled steel rectangular tubularcolumns are inferior to concrete-filled steel circulartubular columns in terms of bearing capacity, they aresuperior in many other aspects, such as beam-columnconnection constructability, stability, and fire resis-tance. Therefore, they are increasingly used for high-rise buildings in many countries all around the world. However, application of concrete-filled rectangularsteel tube (CFRT) structures is still restricted because of the lack of engineering information on the overall seismic behavior of CFRT structures. For the purpose of investigating the seismic responses under severe earthquake conditions, a push-over analysis of a 10-story CFRT structure has been carried out and is re-ported in this paper.1 Push-Over AnalysisA 10-story moment resisting frame structure that is com-posed of concrete-filled rectangular steel tube columns and steel beams was studied. The plan, elevation, and typical cross-sections of structural members of the CFRTFig. 1 Plan, elevation, and typical cross-sections of structural members of the CFRT structure (mm) 126 Tsinghua Science and Technology, February 2006, 11(1): 124-130structure are shown in Fig. 1. The SAP2000 program is used for the push-over analysis of the CFRT struc-ture. The floors of the building are 100 mm deep, and are modeled as shell elements in SAP2000. The di-mensions and material properties of the structural members are shown in Table 1. In SAP2000 the CFRT columns and steel beams are modeled as frame elements.Table 1 Dimensions and material properties of the strutural members of the CFRT structureSimilarly, the PMM hinge is used by SAP2000 to simulate the plastic hinge caused by axial load andbiaxial bending moments. User-defined PMM hinges are therefore applied to the CFRT columns in this model. The M- curves and N-M interaction surfaces of the CFRT columns are calculated using both Hans formulae10 and the USC-RC program(RC program put forward by University of Southern California), for the purpose of comparison. The typical NM interac-tion surface and M- curve of the CFRT columns are Story No.1,234-67-10Material property Steel beams(mm) 700 300 13 24700 300 13 24692 300 13 20692 300 13 20Q345CFRT columns(mm) 700 20700 18700 18700 16Q345 C40shown in Fig. 3.1.1 Hinge propertiesIn frame structures plastic hinges usually form at theends of beams and columns under earthquake action. For beam elements, plastic hinges are mostly causedby uniaxial bending moments, whereas for column elements, plastic hinges are mostly caused by axialloads and biaxial bending moments. Therefore, in push-over analysis different types of plastic hingesshould be applied for the beam elements and the col-umn elements separately.In SAP2000, the M3 hinge is used to simulate the plastic hinge caused by uniaxial moment, so user-defined M3 hinges are applied to the steel beams in this model. To calculate moment-rotation curves of the steel beams, the following assumptions areadopted: 1) a classical bilinear isotropic hardening model is applied to represent the stress-strain behav-ior of the steel beam; and 2) plane sections remainplane. The typical M- curve for the steel beams is shown in Fig. 2. Fig. 2M- curve of steel beams in the 1st-3rd storiesFig. 3 - interaction surface and M - curve ofCFRT columns in the 1st and 2nd stories1.2 Lateral load patternsThe lateral load patterns are intended to represent the distribution of inertia forces in a design earthquake11.It is clear that the distribution of inertia forces willvary with the severity of the earthquake (i.e., the extent of inelastic deformations) and with time during an earthquake. Since no single load pattern can capture the variations in the local demands expected in a de-sign earthquake, two lateral load patterns that are ex-pected to bound the inertia force distributions are used in this push-over analysis. One is an inverted triangular lateral load pattern calculated by the base shear method; the other is the design lateral load pattern calculated using SAP2000 including higher mode effects. The NIE Jianguo (聂建国) et alPush-Over Analysis of the Seismic Behavior of horizontal loads are applied in the X-direction and Y-compared to other parameters.127direction in turn for the purpose of investigating the seismicbehavior of the whole structure.As Dong et al. mentioned in Ref. 12, the P- effect seriously affects the stability of an unbraced frame. There-fore, push-over analyses with and without accounting for theP- effect are carried out in order to investigate the P- effect on the seismic behavior of the CFRT structure.1.3 ResultsThe results of the push-over analysis can be used to es-timate the potential ductility of the structure, to evalu-ate its lateral load resistant capacity, and to identify thefailure mechanism. It is thus important to analyze thepush-over results to obtain the seismic behavior of theCFRT structure.1.3.1 Load-deformation relationshipThe capacity of the structure as represented by thebase shear versus top displacement graph is very use-ful in estimating the seismic behavior of a structure in a push-over analysis. The capacity curves obtained in the push-over analyses are shown in Fig. 4, from which we find that for the cases AccelX(Y)-Han-P,AccelX(Y)-USC-RC-P, EQX(Y)-Han-P, EQX(Y)-USC-RC-P, and EQX(Y)-Han-P+ the termination iscaused by exceeding the target top displacement(1.6 m), while for the cases AccelX(Y)-Han-P+, Ac-celX(Y)-USC-RC-P+, and EQX(Y)-USC, RC-P+ the termination is caused by the formation of a plasticmechanism for the whole structure. The initial stiff-ness values and yield base shears of the cases using AccelX(Y) lateral load patterns are higher than the cases using EQX(Y) lateral load patterns. Therefore, the conclusion can be drawn that the push-over analy-sis results are sensitive to lateral load patterns. More-over, the trends of the capacity curves in theX-direction and in the Y-direction are similar, as shownin Fig. 4. Consequently, the seismic behavior of thewhole structure can be evaluated by one of the direc-tions for this case. As shown in Fig. 4, the capacity curves are almost the same in the elastic region despite the different M - curves and -interaction surfaces of the CFRT columns. The post-yield stiffness values forcases using