多高层钢_混凝土组合框架结构体系弹塑性分析模型_聂建国

结构动力弹塑性与倒塌分析(Ⅰ)——滞回曲线改进、ABAQUS子程序开发与验证柳国环;练继建;国巍【摘要】详述并明确了钢材静态损伤滞回模型中3种类型加卸载路径,重点改进了混凝土滞回规则中再加载路径拐点前的二次曲线与拐点后的直线规则,定义了再加载至骨架曲线的刚度退化指数型表达式.进而,开发了直接能够与ABAQUS主程序保持数据相互调用的UMAT隐式和VUMAT显式算法子程序,并给出子程序与ABAQUS主程序链接的框架示意图.最后,通过5种具有试验结果的构件对所开发程序加以检验.结果表明:(1)改进的混凝土再加载滞回规则可较好描述混凝土加载曲线,克服了二次型规则的再加载曲线与卸载曲线在拐点前相交的可能性,体现了拐点后再加载至骨架曲线的刚度退化;(2)开发实现的隐式算法UMAT与显式算法双精度VUMAT子程序不仅可行,而且具有足够的计算精度.【期刊名称】《地震研究》【年(卷),期】2014(037)001【总页数】9页(P123-131)【关键词】滞回模型;弹塑性;ABAQUS;UMAT;VUMAT【作者】柳国环;练继建;国巍【作者单位】天津大学建筑工程学院,天津300072;天津大学水利工程仿真与安全国家重点实验室,天津300072;天津大学建筑工程学院,天津300072;天津大学水利工程仿真与安全国家重点实验室,天津300072;中南大学土木工程学院,湖南长沙410075【正文语种】中文【中图分类】TV3180 前言当今，随着经济的快速发展和社会的不断进步，大跨和超高层等超限结构日益增多。

根据当前的规范要求，超限结构的地震反应分析需要作为一项专门的工作来进行，如结构在大震作用下的动力弹塑性表现行为(叶献国等，2003;宣钢等，2003;杜修力等，2007)，然后对计算结果是否符合相关规范和(或)规程的相关具体要求进一步审查。

一般情况下，对于这种特殊结构的计算通常需要用到非线性计算能力相对较高级的大型分析软件，例如:ABAQUS、MSC.MARC和LSDyna。

TSINGHUA SCIENCE AND TECHNOLOGYISSN1007-021420/21pp124-130Volume11,Number1,February2006Push-Over Analysis of the Seismic Behavior of a Concrete-Filled Rectangular 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, USAAbstract: To investigate the seismic behavior of concrete-filled rectangular steel tube (CFRT) structures, a push-over analysis of a 10-story moment resisting frame (MRF) composed of CFRT columns and steel beams 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 -Mφ curves and -N M interaction surfaces of the CFRT columns calculated either by Han’s formulae 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 MRF seismic 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 concreteIntroductionOver the past twenty years the static push-over proce-dure has been presented and developed by several au-thors, including Saiidi and Sozen[1], Fajfar and Gasper-sic[2], Bracci et al.[3], amongst others. This method is also described and recommended as a tool for design and assessment purposes for the seismic rehabilitation of existing buildings[4]. The purpose of push-over analysis 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 static inelastic analysis, and by comparing these de-mands 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) the maximum 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﹡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: niejg@; Tel: 86-10-62772457NIE Jianguo (聂建国) et al Push-Over Analysis of the Seismic Behavior of …125 concrete (RC) structures and steel structures have beencarried out by many researchers and designers, at present push-over analyses for the concrete-filled steel tube (CFT) structures are rarely reported in the literature.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 capacity [5]. At present, theoretical analysis of these structures focuses mostly on the static behavior of the CFT 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 that no 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 the structures. 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 to that 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 wascompleted [9]. The calculated results coincided with the test results, providing a practical method for the seismic design of CFT frames. Although the seismic behavior 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 tubular columns are inferior to concrete-filled steel circular tubular columns in terms of bearing capacity, they are superior in many other aspects, such as beam-column connection 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 rectangular steel 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, andtypical cross-sections of structural members of the CFRTFig. 1 Plan, elevation, and typical cross-sections of structural members of the CFRT structure (mm)Tsinghua Science and Technology, February 2006, 11(1): 124-130 126structure are shown in Fig. 1. The SAP2000 programis used for the push-over analysis of the CFRT struc-ture. The floors of the building are 100 mm deep, andare modeled as shell elements in SAP2000. The di-mensions and material properties of the structuralmembers are shown in Table 1. In SAP2000 theCFRT columns and steel beams are modeled as frameelements.Table 1 Dimensions and material properties of thestrutural members of the CFRT structureStory No. Steel beams(mm)CFRT columns(mm)1,2 7003001324 700203 7003001324 700184-6 6923001320 700187-10 6923001320 70016 Material property Q345 Q345C401.1 Hinge propertiesIn frame structures plastic hinges usually form at the ends of beams and columns under earthquake action. For beam elements, plastic hinges are mostly caused by uniaxial bending moments, whereas for column elements, plastic hinges are mostly caused by axial loads and biaxial bending moments. Therefore, in push-over analysis different types of plastic hinges should 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 are adopted: 1) a classical bilinear isotropic hardening model is applied to represent the stress-strain behav-ior of the steel beam; and 2) plane sections remain plane. The typical M-φ curve for the steel beams is shown in Fig. 2.Fig. 2 M-φcurve of steel beams in the 1st-3rd storiesSimilarly, the PMM hinge is used by SAP2000 to simulate the plastic hinge caused by axial load and biaxial bending moments. User-defined PMM hinges are therefore applied to the CFRT columns in this model. The M-φ curves and N-M interaction surfaces of the CFRT columns are calculated using both Han’s formulae[10] and the USC-RC program(RC program put forward by University of Southern California), for the purpose of comparison. The typical N−M interac-tion surface and M-φ curve of the CFRT columns areshown in Fig. 3.Fig. 3 -N M interaction surface and -Mφ curve of CFRT 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 earthquake[11]. It is clear that the distribution of inertia forces will vary 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. TheNIE Jianguo (聂建国) et al Push-Over Analysis of the Seismic Behavior of (127)horizontal loads are applied in the X-direction and Y-direction in turn for the purpose of investigating the seismic behavior 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 the -P∆ 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 the failure mechanism. It is thus important to analyze the push-over results to obtain the seismic behavior of the CFRT structure.1.3.1 Load-deformation relationshipThe capacity of the structure as represented by the base 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 Accel X(Y)-Han-P−, Accel X(Y)-USC-RC-P−, EQ X(Y)-Han-P−, EQ X(Y)-USC-RC-P−, and EQ X(Y)-Han-P+ the termination is caused by exceeding the target top displacement (1.6 m), while for the cases Accel X(Y)-Han-P+, Ac-cel X(Y)-USC-RC-P+, and EQ X(Y)-USC, RC-P+ the termination is caused by the formation of a plastic mechanism for the whole structure. The initial stiff-ness values and yield base shears of the cases using Accel X(Y) lateral load patterns are higher than the cases using EQ X(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 the X-direction and in the Y-direction are similar, as shown in Fig. 4. Consequently, the seismic behavior of the whole 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 -Mφ curves and -N M interaction surfaces of the CFRT columns. The post-yield stiffness values for cases using -Mφ and -N M curves calculated by Han’s formulae are higher than those calculated by USC-RC program, but the differences are small compared to other parameters.Figure 4 also shows that the ultimate base shears de-crease remarkably in the push-over analyses as a result of the -P∆effect. Similarly, the post-yield stiffness de-creases for the same reason. Therefore, we can draw a con-clusion that the -P∆ effect affects the seismic behavior of the moment resisting frame seriously and consequently, the effect should be taken into account in any future MRFseismic analyses.Fig. 4 Capacity curves of different push-over cases of the CFRT structureNotes: EQ X(Y) represents cases using the inverted trian-gular lateral load pattern calculated by the base shear method, Accel X(Y) represents cases using the design lat-eral load pattern calculated using SAP2000 including higher mode effects; Han represents cases using the -Mφ and -N M curves calculated by Han’s formulae, USC-RC represents cases using the -Mφ and -N M curves calculated using the USC-RC program; P− repre-sents cases without considering the -P∆ effect, P+ represents cases including the -P∆ effect.1.3.2 Final interstory driftsThe interstory drifts at the moment of termination in the push-over analyses are shown in Fig. 5. These data are useful in predicting the weak stories of the CFRT structure. From Fig. 5, we observe that the interstory drifts of the 1st-3rd stories are remarkably higher thanTsinghua Science and Technology, February 2006, 11(1): 124-130 128those of the other stories. Therefore, the weak section of the CFRT structure should be the first 3 stories for this ex-ample, and it is necessary to strengthen them in engineering application.1.3.3 Plastic hinge distributionsIt can be found that the plastic hinge distributions are similar in all the push-over analysis cases despite variations in the lateral load patterns, the -P∆ ef-fect, the -Mφ and -N M curves of the CFRT col-umns and the lateral load directions. Figure 6 illus-trates the progressive occurrence and extent of theplastic behavior of the CFRT frame atvarious Fig. 5Final interstory drifts of different push-over cases of the CFRT structureFig. 6 Progressive occurrence of plastic hinges in EQ X-USC-RC-P− push-over analysisNIE Jianguo (聂建国) et al Push-Over Analysis of the Seismic Behavior of (129)performance levels for the EQ X-USC-RC-P− push-over analysis case. Plastic yielding first occurs at base-support sections of the first-story column members as seen in Fig. 6a. With increasing the lateral load, plastic hinges occur at all of the base-support sections of the first-story columns and some of the bottom sections of the second-story and third-story columns. More-over, both end-sections of some beams in the 2nd-6th stories also reach plastic yielding at this stage as shown in Fig. 6b. Subsequently, the number of plastic hinges at the sections of the CFRT columns and steel beams inreases continually as shown in Fig. 6c. The extent of plastic behavior of the hinges develops with increas-ing horizontal load. Finally, the push-over analysis terminates due to either exceeding the target top dis-placement or the formation of a plastic mechanism for the whole structure. At this stage, shown in Fig. 6d, the extent of the plastic hinges at base-support sections of the first-story columns develops sufficiently, while the other plastic hinges of the CFRT columns and steel beams in the 2nd-3rd stories also develop to a certain extent. Therefore, we can draw the conclusion that the weak section of the CFRT structure should be the 1st-3rd stories for this example, and it is necessary to strengthen them in engineering application, in agree-ment with the conclusion drawn in Section 1.3.2.2 ComparisonFor the purpose of comparing the seismic performance of CFRT structures with RC structures, four kinds of 10-story frames, composed of CFRT and RC columns, have been studied. SAP2000 was used for push-over analyses of these structures. For convenience of comparison, the structures are almost identical except for the vertical columns, which are formed from different materials and dimensions, as shown in Table 2. The dimensions of the strength-equivalent RC columns are calculated based on the EA equivalence with the CFRT columns where E is the modulus of elasticity, A is the area of the section. Similarly, the stiffness-equivalent RC columns are calculated on the basis of EI equivalence, and the side-length-equivalent RC columns are calculated on the basis of B equivalence with the CFRT columns, where I is the moment of inertia of the section, and B is the side-length of the columns. For the push-over analyses of these different structures, the Accel X(Y) lateral load patterns calculated using SAP2000 were used; -P∆ effects were not taken into account.Table 2 Dimensions of the vertical columns indifferent structures (mm) Story No. 1,2 3-6 7-10 CFRT columns 70020 70018 70016 CFT columns 79022.6 79020.3 79018.1 Strength-equivalentRC columns855 842 828 Stiffness-equivalentRC columns822 813 805 Side-length-equivalentRC columns700 700 700From the X-direction capacity curves of the CFRT and RC structures, shown in Fig. 7a, we may find that the termination of the push-over analysis for the CFRT structure is caused by exceeding the target top displacement of 1.6 m, while the termination of the push-over analyses for RC structures is caused by the formation of a plastic mechanism over the whole structure. As the RC structures cannot reach the target top displacement, we can draw the conclusion that the CFRT structure is superior to the RC structures inFig. 7 Capacity curves of different structuresTsinghua Science and Technology , February 2006, 11(1): 124-130130 terms of ductility and deformation capacity. Moreover, the yield and ultimate base shears of the CFRT struc-ture are higher than those of the RC structures, so the conclusion that the CFRT structure has better earth-quake resistance capacity than the RC structures can be drawn. Similar conclusions can be obtained from inspection of Fig. 7b, so the seismic behavior of the CFRT structure is superior to the RC structures.The push-over results of CFRT structure and CFT structure are also compared in Fig. 7. The dimensions of the CFT columns are calculated based on s A and c A equivalence with the CFRT columns, where s Ais the section area of steel tube, and c A is the section area of filled concrete. Although the CFRT columns are inferior to the CFT columns in terms of axial bearing capacity, they are superior in flexural capacity. In this model, the axial compression ratio is less than 0.2, so the influence of the moment resistant capacity of the columns is more important than the axial bearing ca-pacity. As a result, the seismic behavior of the CFRT structure is superior to the CFT structure in this model.3 ConclusionsIn this paper the seismic behaviors of five kinds of 10-story frame structures, composed of CFRT columns, CFT columns, and RC columns, have been studied. The seismic responses of the CFRT, CFT, and RC structures in push-over analyses have been compared and some concluding remarks can be obtained as follows:1) The push-over analysis results show that the duc-tility and seismic behavior of the CFRT structure are superior to those of the RC structures. Consequently, CFRT structures are recommended in seismic regions. 2) Since the push-over analysis results are sensitive to the lateral load patterns, the use of at least two load patterns that are expected to bound the inertia force distributions is recommended in push-over analysis. 3) The push-over analysis results are slightly influenced by the M-φ curves and N-M interaction surfaces of the CFRT columns. Therefore, curves calculated either by Han’s formulae or by the USC-RC program are suitable for future push-over analyses of CFRT structures.4) Since the P-∆ effect seriously affects the seismic behavior of MRF, this effect should be taken into account in MRF seismic analyses in future research. References[1] Saiidi M, Sozen M A. Simple nonlinear seismic analysis ofRC structures. Journal of the Structural Division , 1981, 107(5): 937-952.[2] Fajfar P, Gaspersic P. The N2 method for the seismic damageanalysis of RC buildings. Earthquake Engineering and Struc-tural Dynamics , 1996, 25(1): 31-46.[3] Bracci J M, Kunnath S K, Reinhorn A M. Seismic perform-ance and retrofit evaluation of reinforced concrete structures. Journal of Structural Engineering , 1997, 123(1): 3-10. [4] FEMA. NEHRP guidelines for the seismic rehabilitation ofbuildings. Federal Emergency Management Agency, Report No. FEMA-273. Washington D.C., 1997.[5] Shams Mohammad, Saadeghvaziri M A. State of the art ofconcrete-filled steel tubular column. ACI Structural Journal , 1997, 94(5): 558-571.[6] Li Xiangzhen, Cheng Guoliang, Yu Dejie, Zhou Fulin. Elasto-plastic time-history analysis of concrete filled steel tubular structure. World Earthquake Engineering , 2002, 18(1): 73-76. (in Chinese)[7] Huang Xiangyun, Zhou Fulin, Xu Zhonggen. Comparativestudy on the earthquake behavior of concrete filled steel tubu-lar structures. World Earthquake Engineering , 2001, 17(2): 86-89. (in Chinese)[8] Li Zhongxian, Xu Chengxiang, Wang Dong, Wang Chengbo.Experimental research on the seismic behavior of concrete filled steel tubular frame structure. Building Structure , 2004, 34(1): 3-6. (in Chinese)[9] Ding Yang, Xu Chengxiang, Dai Xuexin, Li Xianzhong.Nonlinear finite element analysis of concrete filled steel tubu-lar frame structure. Building Structure , 2004, 34(1): 7-10. (in Chinese)[10] Han Linhai. Concrete-filled Steel Tubular Structure. Beijing:Science Press, 2000: 169-200. (in Chinese)[11] Krawinkler H, Seneviratna G D P K. Pros and cons of a push-over analysis of seismic performance evaluation. Engineering Structures , 1998, 20(4-6): 452-464.[12] Kim Hee Dong, Lee Myung Jae. The -P ∆ effects of non-symmetric frames. In: Proceedings of Sixth Pacific Structural Steel Conference. Beijing, China, 2001: 394-399.。

振动与冲击第31卷第14期JOURNAL OF VIBRATION AND SHOCKVol．31No．142012基金项目：国家自然科学基金委－青年科学基金资助项目（51008171）收稿日期：2011－06－27修改稿收到日期：2011－08－03第一作者尧国皇男，博士后，高级工程师，1980年生通讯作者王卫华男，博士后，讲师，1980年生超高层钢框架－钢筋混凝土核心筒结构弹塑性时程分析尧国皇1，2，王卫华1，3，郭明2（1．清华大学土木工程系，北京100084；2．深圳市市政设计研究院有限公司，深圳518029；3．华侨大学土木工程学院，厦门361021）摘要：基于合理的材料弹塑性（损伤）本构关系模型，利用通用有限元软件ABAQUS 建立了超高层钢框架－钢筋混凝土核心筒结构的精细有限元模型，考虑了结构的几何非线性和材料非线性性能，包括了钢材和混凝土材料的塑性损伤演化。

进行罕遇地震作用下的弹塑性时程分析，获得了核心筒和楼板的损伤演化过程、顶点位移时程曲线、基底剪力时程曲线、楼层位移角包络曲线以及地震作用下整体结构的能量反应规律。

结果表明，罕遇地震作用下混凝土最大损失出现在这类结构体系中核心筒底部，为保证其在罕遇地震作用下更好的工作性能，建议在核心筒底部加强区域增设型钢和提高剪力墙配筋率等措施。

采用非线性有限元分析方法，可较为清晰的揭示这类结构体系在罕遇地震作用下的工作特性，有关方法可为同类研究提供参考。

关键词：超高层；钢框架－核心筒结构；弹塑性分析；时程分析；有限元分析中图分类号：TU973．14文献标识码：AElastic-plastic time history analysis on super rise steel frame-core wall structureYAO Guo-huang 1，2，WANG Wei-hua 1，3，GUO Ming 2（1．Department of Civil Engineering ，Tsinghua University ，Beijing 100084，China ；2．Shenzhen Municipal Design ＆Research Institute Co．，Ltd ，Shenzhen 518029，China ；3．College of Civil Engineering Huaqiao University ，Xiamen 361021，China ）Abstract ：Based on rational plasticity constitutive model of steel and concrete ，the FEM package ABAQUS wasadopted to establish the fine FEM model of super rise steel frame-R．C．core wall structure ，including the geometric nonlinearity and the material nonlinearity ，such as the plastic damage development of concrete material properties．The elastic-plastic time history analysis of the structure under rarely met earthquake was carried out．The calculating results ，including the damage evolution process of core-wall and floor slab ，vertex displacement time-history curves ，basal shear time-history curves ，and floor displacement angle envelope curves as well as the energy response law of the whole structure were attained．The results show that the maximum damage of concrete exists in the bottom of the super rise steel frame-R．C．core wall structure ，and additional profile steels and reinforcing bars were suggested to be set to improve the workable ability under rarely met earthquake．It can also be seen that the elastic-plastic time history analysis can reveal the behaviours of the structural system under rare earthquake ，and the method mentioned may give a reference to correlative researches．Key words ：super rise ；steel frame-core wall structure ；elastic-plastic analysis ；time history analysis ；FEM analysis 长期以来我国超高层建筑传统地采用钢筋混凝土结构体系，而钢－混凝土混合结构在我国超高层建筑中应用只是近十年才兴起的［1］。

钢筋混凝土框架柱的弹塑性分析[摘要] 国内建筑结构针对中震、大震作用下基于性能抗震设计的弹塑性分析，规范虽然对有关高层建筑提出了要求，但分析标准还很不明确，国内工程师只得参考国际标准或规范。

该文通过对钢筋混凝土框架柱的仿真分析与我国及美国规范计算结果进行比较，以论证国内建筑结构参考国际标准或规范，进行针对中震、大震作用下基于性能抗震设计的弹塑性分析的可靠性及应注意的事项。

一、引言我国规范针对中震、大震作用下结构基于性能的抗震设计，是以规定大量的抗震措施，来保证建筑结构达到中震可修，大震不倒的目标，但对中震、大震作用下的结构分析涉及甚少。

针对大震作用下结构整体破坏，虽有结构整体弹塑性层间位移角的控制，但对内部结构构件的检验水准，只能参照有关构件承载力计算的相关规定，即可按规范计算出构件的屈服承载力，这大致等同国际标准或报告中的对安全使用、立即入住水准LS的规定。

本文是针对我国建筑结构大震不倒水准的结构弹塑性分析而进行的研究，故在采用ANSYS进行仿真分析时，材料的强度取值均相应采用我国规范标准。

但约束混凝土的本构模型及构件性能目标限值，我国规范现暂无确切的规定，则只好参照有关构件承载力计算的相关规定及国际标准或报告。

本次研究，结合《混凝土结构设计规范》（GB50010-2002）[以下均简称我国规范]、《美国房屋建筑混凝土结构规范》(ACI318-05) [以下均简称美国规范]并参考国际通用的美国标准FEMA356，通过对塑性铰的屈服承载力的两国规范计算结果与ANSYS仿真分析结果进行比较，进而论证采用SAP2000对我国建筑结构进行结构弹塑性分析时，其结果的准确性及有关注意事项。

假定轴压比大于0.4，箍筋抗剪承载力大于或等于设计剪力的3/4，构件性能目标限值取值如下。

安全使用水准IO(即B点），大致与我国的小震不坏目标相当：我国规范：弹塑性总应变限值，偏心受压时为0.0033，轴心受压时为0.002。

㊃综㊀述㊃钢结构(中英文),38(12),1-26(2023)DOI :10.13206/j.gjgS 23062902ISSN 2096-6865CN 10-1609/TF㊀㊀编者按:当前我国第五代GB 18306 2015‘中国地震动参数区划图“明确了基本㊁多遇㊁罕遇和极罕遇等四级作用的地震动参数确定方法并提高了工程结构抗震设防标准㊂组合结构适应国家新型城镇化建设重大需要,在城市人口密集区域和抗震设防高烈度区域具有广泛应用价值㊂由于钢管混凝土柱存在间接约束以及界面滑移等特性,其抗震能力可进一步挖掘,以提升强震下重要工程结构的安全性,或者在维持相同性能时节约材料用量㊂学者们通过模型试验㊁理论研究以及关键技术研发,所形成的系列成果在工程结构中得到了成功应用㊂为此,‘钢结构(中英文)“杂志特邀丁发兴教授为主编,系统组织了两期(本期及2024年第1期) 组合结构抗震性能与韧性提升 专栏,向读者介绍国内针对钢管混凝土柱㊁钢管混凝土柱-组合梁节点㊁组合框架以及组合框架-筒体结构等方面的最新研究成果,探讨各有效措施对抗震性能的影响规律,以期推动组合结构技术的完善与升级㊂钢-混凝土组合结构抗震性能研究进展∗丁发兴1,2㊀许云龙1㊀王莉萍1,2㊀吕㊀飞1,2㊀段林利1,2㊀余志武1,2(1.中南大学土木工程学院,长沙㊀410075;2.湖南省装配式建筑工程技术研究中心,长沙㊀410075)摘㊀要:钢-混凝土组合结构因具有抗弯刚度大㊁承载力高㊁延性好和施工便捷等优点,适应国家新型城镇化建设重大需要,在城市人口密集区域和抗震设防高烈度区域应用广泛㊂在提高工程结构抗震设防标准的背景下,研究钢-混凝土组合结构的抗震性能,进一步提升其抗震韧性,建立具有更高韧性的钢-混凝土组合结构抗震设计方法对促进建筑结构实现 双碳 战略目标具有重要意义㊂为此,归纳总结了钢-混凝土组合结构抗震性能的研究进展,包括钢-混凝土组合梁㊁钢管混凝土柱及钢管混凝土柱-组合梁节点的滞回性能试验研究,以及钢-混凝土组合结构体系的拟静力㊁拟动力及振动台试验研究,讨论并比较了各种抗震分析模型及其方法,提出了当前研究存在的一些问题和尚需深入研究的方向㊂基于现有研究成果总结得到:1)组合梁主要依靠钢梁耗能,可采取增大钢梁截面尺寸的措施提高耗能能力㊂钢管混凝土柱主要依靠钢管和混凝土耗能,可采取拉筋增强约束措施直接约束混凝土,使其由脆性向塑性转变从而提高框架柱的耗能能力㊂与其他类型组合节点相比,刚性连接组合节点具有更好的耗能能力㊂2)罕遇地震下框架结构以梁耗能为主,而在超罕遇地震下仍以梁作为主要耗能部件将使工程成本大幅增加㊂由于超罕遇地震发生概率极低,若采取适当的增强约束措施使柱也具备耗能能力并参与耗能,则可在适当增加工程建设成本的同时使结构具有抵抗超罕遇地震的能力,此时组合结构抗震设计理念可由罕遇地震时的 强柱弱梁,梁耗能为主 向超罕遇地震时的 梁柱共同耗能 推进㊂3)基于平截面假定的杆系纤维模型计算软件通常适用于弹性和弹塑性小变形阶段分析,而当组合结构处于塑性大变形阶段时,结构杆件便不再符合平截面假设㊂对强震下组合结构体系的动力响应仿真模拟需要克服弹塑性小变形阶段的假定条件,采用适用于塑性大变形阶段结构分析的混凝土三轴弹塑性本构模型及相应的体-壳元模型是一种有效的途径㊂4)剪力墙结构具有整体性好㊁侧向刚度大等优点,但传统构造下其抗震能力较弱,可通过提升连梁和墙肢等耗能构件的耗能能力以增强结构整体耗能能力,如采用钢-混凝土组合连梁㊁型钢混凝土连梁或合理构造钢板连梁,以及型钢-约束混凝土或钢管混凝土墙肢等㊂5)工程结构在使用阶段面临着诸多灾害考验,传统方法根据不同外荷载进行独立抵抗设计,忽视了多灾害耦合作用机制,使结构综合抗灾性能难以满足使用需求,故建立安全可靠的抗多灾害设计方法和结构体系是结构工程师在防灾减灾领域的一项重大课题㊂关键词:钢-混凝土组合梁;钢管混凝土柱;钢-混凝土组合结构;抗震性能;试验研究∗国家自然科学基金项目(51978664)㊂第一作者:丁发兴,男,1979年出生,博士,教授㊂通信作者:王莉萍,女,1987年出生,博士,副教授,wlp2016@㊂收稿日期:2023-06-290㊀引㊀言中国是世界上地震灾害最严重的国家之一,地震灾害给人类社会活动造成了不可估量的损失㊂大量建筑结构因抗震能力不足而倒塌,造成的人员伤1丁发兴,等/钢结构(中英文),38(12),1-26,2023亡和经济损失使得抗震减灾技术成为结构工程师们面临的主要考验㊂为提高建筑结构的抗震性能,研究者们在结构布置和局部构造等方面展开了大量的研究工作㊂钢-混凝土组合结构因充分发挥了两种材料的力学性能优势,提升了结构的刚度㊁承载力和耗能能力而在高层及超高层建筑结构中得到了广泛应用[1]㊂随着经济社会的发展,工程结构抗震设防标准也在不断提升,研究钢-混凝土组合结构的抗震性能,进一步提升其抗震韧性,建立具有更高韧性的钢-混凝土组合结构抗震设计方法,对促进建筑结构实现 双碳 战略目标具有重要意义㊂组合结构中,钢-混凝土组合梁和钢管混凝土柱的材料利用效率最高,其抗震性能提升明显㊂为此,笔者对国内外相关钢-混凝土组合结构的主要研究成果进行归纳总结,对组合结构抗震性能方面需要进一步深入研究的工作进行展望,以期为后续研究工作提供一些参考和建议㊂1㊀钢-混凝土组合构件及节点抗震性能1.1㊀钢-混凝土组合梁钢-混凝土组合梁由钢梁和混凝土板通过栓钉连接而成,发挥了混凝土的抗压性能和钢材的抗拉性能优势㊂Daniels等[2]对组合框架中的组合梁进行了抗震性能研究,并给出了组合梁的弹塑性分析方法㊂文献[3-5]先后对组合梁进行了低周往复试验研究,结果表明组合梁具有良好的耗能能力和延性,增设腹板加劲肋或增加腹板厚度能明显提高组合梁的极限承载力,改善构件延性㊂Gattesco 等[6-7]㊁Taplin等[8]和Bursi等[9-10]着重研究了剪力连接件对组合梁抗震性能的影响,指出剪力连接件的布置方式直接影响界面滑移量,进而影响组合梁极限承载力㊂国内聂建国等[11]首先进行了6组钢-混凝土叠合板组合梁低周往复荷载试验研究,结果表明钢-混凝土叠合板组合梁的滞回曲线饱满,且存在界面滑移,其剪力连接度直接影响构件正向极限抗弯承载力,而反向极限抗弯承载力则可依据简化塑性方法计算得出㊂此后,蒋丽忠等[12-16]和Ding等[17]先后对低周往复荷载下钢-混凝土组合梁的抗震性能进行了系列试验研究,分别探讨了剪力连接度㊁力比㊁栓钉直径㊁腹板厚度㊁纵向和横向配箍率对组合梁抗震性能的影响规律,并建立了恢复力模型[13]㊂Liu等[18]建立了三维实体-壳元模型,其中钢梁采用壳单元,混凝土采用实体单元,栓钉采用梁单元或弹簧单元,分析结果表明组合梁的抗震能力主要依靠钢梁翼缘,增大钢梁尺寸有利于提高抗震能力,而增大栓钉剪力连接度也有利于提高钢梁的耗能㊂1.2㊀钢管混凝土柱钢管混凝土柱由外钢管内部填充混凝土而成㊂自1965年日本九州大学学者Sasaksi和Wakaba-yashi对方钢管配筋混凝土柱进行拟静力试验后[19],Tomii等[20]也开展了圆钢管混凝土柱拟静力试验研究,表明钢管混凝土柱比钢筋混凝土柱具有更大的极限承载力,更好的延性和耗能能力,以及更小的刚度退化等特点㊂Elremaily等[21]最早根据试验结果和理论分析指出钢管约束作用提升了柱承载力和抗震性能㊂随后有关钢管混凝土柱抗震性能研究越来越丰富,研究者们分别从材料强度㊁轴压比㊁宽(径)厚比和长细比等方面探讨了钢管混凝土柱抗震性能规律㊂在材料强度方面,吕西林等[22]㊁韩林海等[23]和Liu等[24]先后研究了混凝土强度对钢管混凝土柱抗震性能的影响规律,结果显示随着混凝土强度的提升,试件初始刚度略有增大,极限承载力也有所提高,但其延性和耗能能力均下降,且刚度退化加快㊂游经团等[25]和Yadav等[26]的试验结果表明:增大钢管屈服强度能够明显提升极限承载力,但对初始抗弯刚度几乎无影响㊂Varma等[27-28]探讨了钢材强度对柱抗震性能的影响规律,低轴压比下柱的延性系数随钢材强度的增大而降低,而当轴压比较大时,该规律并不明显㊂在轴压比方面,吕西林等[22]㊁Liu等[24]㊁游经团等[25]㊁Varma等[27-28]㊁张春梅等[29]㊁李学平等[30]㊁李斌等[31]㊁聂瑞锋等[32]和Cai等[33]通过试验研究发现,轴压比是影响柱抗震能力的直接因素,增大轴压比导致水平承载力㊁延性和耗能能力下降,刚度退化明显㊂在宽(径)厚比方面,吕西林等[22]㊁Liu等[24]㊁Yadav等[26]和李学平等[30]的试验表明,试件水平极限承载力随着宽(径)厚比增大而降低㊂Varma 等[27-28]㊁李斌等[31]和余志武等[34]指出,提高宽(径)厚比可使其延性系数下降㊂聂瑞锋等[32]和Matsui等[35]指出,宽(径)厚比越大,耗能能力越弱㊂在长细比方面,李斌等[31]㊁聂瑞锋等[32]和邱增美等[36]通过试验研究表明,随着长细比的增加,钢管混凝土柱初始刚度明显降低,刚度退化加快,水平2钢-混凝土组合结构抗震性能研究进展承载力和耗能能力变弱,延性系数也明显下降,当长细比达到一定值时延性系数下降更快㊂为加强大宽(径)厚比钢管对混凝土的约束作用而提升其抗震性能,学者们陆续提出了诸多约束措施,如在柱端部焊接钢板或角钢[37],包裹纤维复合材料[38],设置约束拉杆[39]㊁栓钉[40]㊁加劲肋[41]或斜拉肋[42]等局部加强措施,如图1a ~1g 所示,这些局部加强构造一定程度上延缓了柱端塑性铰的形成与发展㊂a 钢板约束;b 角钢约束;c 纤维复合材料约束;d 拉杆约束;e 栓钉约束;f 加劲肋约束;g 斜拉肋约束;h 内拉筋约束㊂图1㊀各种约束方式下的钢管混凝土柱由于钢管对混凝土的约束作用为间接被动约束,丁发兴[43]在比较各种约束方式后提出了内拉筋约束钢管混凝土柱技术,如图1h 所示,并揭示了内拉筋直接约束混凝土的工作原理㊂此后,丁发兴课题组开展了端部拉筋钢管混凝土柱抗震性能试验研究,截面形式包括矩形[44]㊁圆形[45]㊁椭圆形[46]㊁圆端形[47]等,探讨了拉筋与钢管内表面接触方式的影响[48],试验结果表明,实际轴压比高达0.8的超高轴压比钢管混凝土柱仍呈现延性破坏,且钢管混凝土柱塑性铰展现出小偏压和大偏压两个阶段,其韧性得到进一步提升㊂同时,课题组基于体-壳元模型进行了有限元模拟,其中混凝土采用实体单元,钢管采用壳单元,拉筋采用杆单元,分析结果表明,压弯荷载下拉筋具有降低界面滑移㊁直接约束混凝土以及促进钢管抗弯等效果,从而提高抗弯刚度㊁承载力和耗能能力,其中拉筋大幅度提高了混凝土的耗能能力[49]㊂1.3㊀钢管混凝土柱-组合梁节点作为钢-混凝土组合结构的关键传力部位,组合节点的剪力主要通过钢梁腹板传递,其次通过节点区混凝土和钢管壁间的黏结力和摩擦力传递,而弯矩则主要由加强环板㊁内隔板等构件传递[50]㊂现有节点试验不少是以钢管混凝土柱和纯钢梁的连接为研究对象,而相关组合框架及组合节点的试验研究结果表明,钢梁与楼板在进入弹塑性阶段之后仍能发挥明显的组合效应[51],这种组合效应能显著提高结构的刚度㊁强度及耗能能力,抑制钢梁上翼缘屈曲,增强钢梁的稳定性[52]㊂另外,当节点区域受正向弯矩作用时,楼板与钢梁的组合效应更为显著[53-54],楼板的存在将使中性轴上移,导致钢梁下翼缘应变明显增大,从而促使下翼缘更易发生屈服及破坏,降低组合梁的转动能力[55]㊂鉴于钢筋混凝土楼板对节点区域及结构体系具有重要影响,笔者仅对考虑楼板的组合节点抗震性能试验进行梳理㊂组合梁节点及框架试验表明负弯矩区钢梁下翼缘由于受压易过早出现局部屈曲和失稳的问题,李杨等[56]在普通组合梁负弯矩区下翼缘增设一块混凝土板,开展了钢-混凝土双面组合梁节点的抗震性能试验,与普通组合梁节点相比,双面组合梁节点具有更高的刚度和承载力,但在刚度退化㊁延性系数和耗能能力等方面无明显优势㊂在削弱式节点方面,Xiao 等[57]和Li 等[58]对带楼板的狗骨式节点进行了拟静力试验,结果表明,减小梁截面可促进削弱区域塑性铰的形成,有效避免节点核心区焊缝撕裂㊂在传统刚性节点方面,聂建国课题组先后完成了内隔板式节点[59]㊁栓钉内锚固式节点㊁外隔板式节点[60]和内隔板贯通式节点[61]的拟静力试验研究㊂研究发现:内隔板式节点表现出较强的极限承载能力,但其位移延性系数低;而栓钉内锚固式节点具有较强的变形能力,但极限承载力较低;相比之下,外隔板式节点和内隔板贯通式节点在极限承载能力㊁位移延性系数和耗能能力等方面均具有良好的性能[60-61]㊂此外,聂建国等[62]建立了组合节点剪力-剪切变形曲线的恢复力模型,提出了组合节点屈服抗剪承载力和极限抗剪承载力计算公式㊂韩林海课题组[63-64]采用外环板式节点对圆钢管混凝土柱-组合梁节点进行拟静力试验研究,提出了节点的抗剪承载力公式和核心区剪力-剪切变形恢复力模型㊂周期石等[65]提出了楼板钢筋和钢梁翼缘削弱穿入钢管混凝土柱的刚接节点,发现楼板钢筋的穿入增强了节点区域钢梁抗弯刚度和楼板的组合效应,而钢梁翼缘削弱的穿入降低了穿入钢梁对浇筑柱中混凝土的影响㊂研究表明,对于钢梁翼缘削弱穿入钢管混凝土柱的刚接节点,当削弱程度不大时,节点具有良好的抗震性能,但仍将降低节点的刚3丁发兴,等/钢结构(中英文),38(12),1-26,2023度㊁承载力和耗能能力㊂在半刚性节点方面,Mirza等[66]分别对半刚性单边螺栓节点进行了静力和拟静力试验,并根据有限元分析结果给出了构造设计方法㊂王静峰等[67-69]进行了半刚性单边螺栓节点试验,包含圆㊁方钢管和带纵向加劲肋钢管的拟静力试验以及带纵向加劲肋钢管混凝土柱的拟动力试验㊂试验结果表明,圆钢管混凝土柱-组合梁节点的承载力和弹性刚度要大于方截面[67];外伸端板连接节点的承载力和弹性刚度要大于平齐端板连接,而其转动能力和延性性能要低于平齐端板连接[68-69]㊂Yu等[70]提出了上焊下栓式的节点连接方式,即钢梁上翼缘与柱隔板焊接,下翼缘与柱隔板通过螺栓连接,螺栓连接处板件的滑移有利于降低钢梁下翼缘应力,避免出现过早断裂的现象㊂欧洲规范[71]中,根据初始转动刚度大小,将节点分为铰接㊁半刚性连接和刚性连接;根据抗弯承载力大小,将节点分为铰接㊁部分强度和全强度㊂Ding 等[72]认为该分类标准对于半刚性连接节点的定义较为宽泛,难以准确判定试件的类型,应根据节点的初始转动刚度㊁抗弯承载力和耗能能力等性能指标综合定义,并将其细化为半刚接㊁准刚接㊁Ⅰ类刚接和Ⅱ类刚接四类㊂据此,丁发兴等[73]完成了端板螺栓连接和加强环连接组合梁节点的拟静力试验,利用柱内拉筋 强柱 构造和加劲肋 强梁 构造技术实现了节点核心区强连接,显著提升了螺栓连接节点的初始转动刚度㊁抗弯承载力和耗能能力,使栓连节点达到了刚性节点的性能要求㊂同时,内拉筋 强柱 构造技术实现了轴压比高达0.8时,组合节点梁端发生弯曲破坏的失效模式㊂除了以上相关平面框架组合节点抗震性能试验研究外,樊健生等[74-75]从加载路径㊁混凝土楼板㊁柱类型及节点位置等方面对空间组合内隔板贯通式节点进行了拟静力试验,结果表明空间受力的节点在承载力和延性性能等方面均有明显下降,因此平面荷载作用不能完全反映其抗震性能,在节点设计中应考虑空间荷载的耦合作用㊂2㊀钢-混凝土组合结构体系抗震性能组合梁㊁柱及其组合节点等构件的研究最终以在结构体系中的应用为落脚点,因而各类组合构件集成后的体系响应是工程实践重要的关注点之一㊂笔者以钢-混凝土组合框架结构为主要对象,根据不同试验方法分别梳理了研究者在有关结构体系抗震方面的研究成果㊂2.1㊀试验研究2.1.1㊀拟静力试验Matsui[76]㊁Kawaguchi等[77-78]㊁马万福[79]㊁钟善桐等[80]㊁李斌等[81]㊁王来等[82]㊁李忠献等[83]和王先铁等[84]对钢-混凝土组合框架模型进行了系列抗震性能试验研究,指出钢-混凝土组合框架结构的抗震性能要优于钢筋混凝土框架和钢框架结构㊂为研究混凝土楼板在框架结构中的组合效应,聂建国等[85]完成了4层单跨纯钢框架和组合框架结构的拟静力试验㊂结果表明:与整体性较差的纯钢框架相比,组合框架的抗侧刚度因混凝土楼板空间作用而大幅提升㊂Tagawa等[86]㊁Nakashima 等[87]和聂建国等[52,88]分别进行了足尺框架子结构拟静力试验,探讨了混凝土楼板对结构刚度㊁强度㊁耗能及变形能力的影响规律,确定了在结构设计中楼板组合效应的有效计算宽度㊂王文达等[89]㊁王先铁等[90]和余志武等[91]以柱截面形状㊁材料强度㊁含钢率㊁轴压比和梁柱线刚度比等为研究对象,对组合框架结构开展了往复荷载作用下的试验研究,探讨了各参数对组合框架结构抗震性能的影响规律,提出了钢管混凝土框架荷载-侧移实用恢复力模型及位移延性系数简化计算方法㊂王静峰等[92-94]和王冬花等[95]研究了往复荷载作用下半刚性单边高强螺栓连接组合框架的抗震性能和破坏机理,分析了滞回及骨架曲线㊁强度和刚度退化规律㊁延性及耗能能力等力学性能指标,并建立了半刚性钢管混凝土框架的弹塑性地震反应分析模型,提出了一种适用于半刚性钢管混凝土框架的P-Δ关系曲线的简化二阶方程和弹塑性层间位移的简化计算方法㊂此外,赵均海等[96]提出了装配式复式钢管混凝土框架结构及其极限承载力简化计算方法,阐述了柱-柱拼接节点和加强块梁柱节点在此类结构中的应用效果㊂Ren等[97]和王波等[98]在钢管混凝土框架中增设屈曲约束支撑装置,研究水平反复荷载作用下耗能减震部件对结构抗震性能的影响㊂结果表明:增设屈曲支撑不仅对结构的刚度和承载力有提升作用,还能延缓塑性铰的形成,增强结构延性和耗能能力㊂丁发兴等[99]完成了2层2跨组合框架对比试验研究,结果表明:内拉筋强柱构造措施提升了框架结构的刚度和承载力,延缓了柱端塑性铰的形成,增强了结构延性和耗能能力㊂由此可见,内拉筋提升框架柱的刚度㊁承载力和耗能能力,其效果相当于增4钢-混凝土组合结构抗震性能研究进展设屈曲支撑㊂2.1.2㊀拟动力试验宗周红等[100]通过对缩尺比例为1/3的半刚性两层空间组合框架的拟动力试验,从层间刚度㊁自振频率㊁加速度反应㊁位移反应和滞回曲线等方面评估了该结构的动力响应和耗能性能,研究了峰值加速度㊁频谱特性和强震持续时间对结构动力响应和力学性能的影响,建立了组合框架结构动力分析模型㊂Herrera等[101]按照3/5的比例对一幢节点采用T型连接方式的4层组合框架进行了拟动力试验,结果表明此类节点的组合框架满足美国相关设计标准㊂在半刚性节点组合框架方面,He等[102]对缩尺比例为4/7的端板螺栓连接组合框架子结构模型先后进行了拟动力㊁拟静力和静力推覆试验,从层间位移及剪力㊁应变㊁转角和耗能等方面分析结构在多遇地震㊁设防地震㊁罕遇地震和超罕遇地震水准下的动力响应㊂完海鹰等[103]对节点采用长螺栓式双腹板顶底角钢半刚性连接的钢管混凝土框架进行拟动力试验研究,探讨不同峰值加速度下结构的受力特征㊁刚度退化㊁动力响应及耗能能力㊂王静峰等[104-105]通过两组拟动力试验分别研究了钢管混凝土柱-组合梁框架和钢管混凝土柱-钢梁框架的动力性能和破坏特征,探讨了柱截面形式和端板类型对结构性能的影响㊂试验结果表明,圆形柱组合框架的最大位移响应和累积耗能均大于方形柱组合框架,但其初始刚度和承载力则弱于方形柱组合框架㊂此外,王静峰等[106]还采用混合试验方法对装配式中空夹层钢管混凝土组合框架开展了拟动力试验研究,分析了该组合框架结构在峰值加速度为0.62g和1.24g时的动力响应和破坏机理㊂在屈曲约束支撑组合框架方面,Tsai等[107-108]完成了多级地震作用下3层3跨足尺钢管混凝土柱屈曲约束支撑框架拟动力试验研究,探讨了屈曲约束支撑对结构整体抗震性能的影响,并从有效刚度㊁耗能和位移延性系数等方面评估了支撑构件连接方式的有效性㊂郭玉荣等[109]完成了防屈曲支撑组合框架子结构拟动力试验,提出了防屈曲支撑可增强结构的抗侧刚度和变形恢复能力㊂2.1.3㊀振动台试验黄襄云等[110-111]利用振动台试验对5层2跨2开间钢管混凝土空间框架结构的动力特性㊁加速度反应和位移反应进行了分析,并分别按等强度㊁刚度㊁截面积的原则将钢管混凝土柱换算成钢筋混凝土柱进行试算,综合评定了该结构的抗震性能㊂杜国锋等[112]采用单输入㊁单输出方式对8层单跨2开间钢管混凝土柱-钢梁框架进行动力特性试验,并通过3种不同地震波作用分析了结构的最大地震作用力㊁层间剪力㊁位移和应变反应㊂邹万山等[113]通过振动台试验得出,不同频谱特性的地震波对模型结构的加速度和位移反应分布曲线形状影响较小,且模型各层绝对加速度主要由前两阶振型决定,其他高阶振型的影响可以忽略㊂罗美芳[114]研究了不同工况下4层钢-混凝土组合框架结构的动力响应及破坏模式,评价了该结构的抗震性能㊂童菊仙等[115-116]设计并制作了有㊁无侧向耗能支撑的5层单跨2开间的方钢管混凝土柱框架模型,利用振动台试验对两种框架的动力特性和地震响应进行分析,得到了结构的振型㊁周期和阻尼比等基本属性,以及地震波作用下的位移㊁加速度和应力响应㊂结果表明:即使没有楼板的组合作用,结构仍具有较好的抗震性能;侧向支撑可承担部分水平地震作用,减小了结构的动力反应㊂陈建斌[117]和吕西林等[118]完成了国内首个方钢管混凝土高层组合框架-支撑结构振动台试验㊂试验中发现结构支撑体系的破坏较为严重,试验结果表明:该结构的动力性能介于钢筋混凝土结构和钢结构之间且更倾向于钢结构,其塑性㊁韧性和抗震性能表现良好,并通过计算结果显示阻尼器对加快结构峰值反应后的振动衰减具有较大作用㊂为研究地震作用下半刚性连接组合梁框架的动力特性以及破坏模式,李国强等[119]进行了1个足尺半刚性连接组合梁框架结构模型振动台试验研究㊂结果显示:当峰值加速度高达1.2g时,结构整体仍未发生明显损坏,表明该结构形式可满足高烈度区域的抗震设防要求㊂Han等[120]对两个由组合框架结构和钢筋混凝土剪力墙混合形成的高层建筑模型进行了振动台试验,对比分析了圆钢管混凝土柱和方钢管混凝土柱对该混合结构体系整体性能的影响,验证了组合框架结构与核心剪力墙结构在地震作用下优良的复合效应和抗震性能㊂2.2㊀理论分析静力弹塑性分析法是以反应谱为基础,首先依据抗震需求谱和结构能力谱得到地震作用下建筑结构所产生的目标位移,随后在建筑结构上施加稳定的竖向荷载,同时施加单调递增的水平荷载直至达到目标位移,最后评估结构最终状态下的抗震性能㊂通过该方法可以评估地震作用下结构的内力和变形5。