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2004年8月16号基于性能的抗震设计方法和复合屈曲约束支撑框架的性能摘要屈曲约束支撑框架的概念相对较为新颖，近年来它的应用在美国、日本和台湾得到增强。然而，对于一般实践的详细设计规则当前还处于发展阶段。从2002年夏开始，密歇根大学的研究者已经开始和台湾地震工程研究中心的队伍展开合作，在设计、分析和应用模拟动力测试方法对这种框架进行全方位测试等方面进行联合研究。选定的结构是由混凝土灌注的钢管圆柱、钢梁和复合屈曲约束支撑组成的三层三跨的框架。这种框架是应用密歇根大学最近发展的基于能量的塑性设计程序设计而成的。这种方法利用了选定的目标作业份额（对这个框架在50年中2.0%到10%荷载50年设计范围中的2.5%到2%）和总体的屈曲原理。由于在端部连接和支撑的钢壳之间设计空隙的更多精确控制的需要，屈曲约束支撑框架是对这种最新成熟设计方法的最好候选者。这篇文章简要介绍了由密歇根大学研究的基于能力原理的设计方法和由台湾地震工程研究中心的科研小组为计算框架底部剪力的设计计算结果而采用的基于位移的设计程序模式，并对两种方法对于一次台湾地震而设计的框架无弹性响应结果进行了对比。同样的框架也在美国进行了设计，并依据美国的标准在地面运动下进行了分析。由密歇根大学设计的框架对台湾和美国的地面运动都基本符合动力响应。介绍屈曲约束支撑极好的地震反应激励了台湾地震工程研究中心的实验计划，也鼓励了密歇根大学的研究者们对分析和设计之间结合的进一步研究。在这个计划中，屈曲约束支撑为2003年10月在台湾地震工程研究中心进行模拟动力荷载实验的三层三跨框架提供了最基本的抗力结构。原型建筑的结构布置如图一a所示，实验框架的立面如图一b所示。针对实验目的，假定这些跨中的两个能够抵抗作用在一个三层建筑原型的全部地震力。地震力作用的框架在图一a中用粗线表示。图一:（a）圆形建筑的平面布置图 （b）测试框架图测试框架描述本框架通过两个互相分离的机构来抵抗地震荷载。最基本的抵抗力由框架中主要跨（图一b）的屈曲约束支撑来提供。这一跨被设计为一个完全的支撑框架，而所有的梁柱连接和支撑与柱间的连接作为最简单的连接。在每一个地震作用的框架中，支撑被设计为抵抗地震作用力的80%，剩余的20%有外侧的两跨来抵抗。外侧两跨作为瞬间框架，同时外侧梁柱接头作为瞬间连接。所有柱子都由混凝土灌注钢管组成。内外侧柱子采用不同的型材，随着建筑物高度的增加尺寸保持不变。梁上采用大法兰。各层采用不同尺寸的梁，而在同一层上的所有跨都采用相同尺寸的梁。屈曲约束支撑的特性屈曲约束支撑的特色是在混凝土灌注钢管中插入一个钢芯（图二a）钢芯和混凝土灌注钢管由于钢芯表面的脱胶材料而保持相互分离。灌注的混凝土和钢管的作用是防止钢芯屈曲，以至于在大位移撤消后支撑有一个很好的荷载位移响应。脱胶材料能够保证作用在屈曲支撑上的力仅仅由钢芯承载，而不会作用在周围材料上。在台湾的地震工程研究中心，各种不同配置的屈曲约束支撑在大周期轴力作用下进行试验，从而挑选出最适宜实验框架的配置（图二a）一个挑选出的屈曲约束支撑的配置对应的典型荷载位移响应如图二b所示。正如看到的，得到了整个的滞后线圈和完美的能量扩散。然而，要注意的是压缩的屈服荷载要比拉伸的高出10%左右。这一点要在框架设计中进行说明。图二：（a）采用的屈曲约束支撑结构 （b）屈曲约束支撑的典型荷载位移响应设计要素为满足一般的性能要求，依据不同的设计程序设计了三个原型框架来进行对比。第一个框架由台湾的地震工程研究中心的科研小组设计，这个框架的底部剪力计算依据基于位移的多模式抗震设计程序，这个指导方针还在2002年规定了台湾的抗震设计规则。这个框架是根据弹性方法设计的。第二个框架（密歇根大学设计的第一个框架）由密歇根大学的团队设计。他们的底部剪力假定了台湾地震工程研究中心的结果，但他们采用了最近形成的塑性设计方法。第三个框架（密歇根大学的第二个框架）在计算底部剪力时采用了由密歇根大学研究的基于能量的简单程序。框架的设计采用了同密歇根大学第一个框架一样的塑性设计方法。基本设计参数由台湾地震工程研究中心的科研小组依据2002年起草的台湾抗震设计规则选定。每一层的地震作用平均的分配到到两个抗震框架上。作用在每层上的地震作用如下，一层和二层：714千磅 三层564千磅。为了计算原型建筑的设计底部剪力采用了两种不同的性能标准，并把其中较大的结果作为实验框架的设计依据。根据第一个性能标准（保护准则），当建筑遭受在未来50年超过10%的地震烈度（10/50）时，最大顶部位移设定为0.02弧度。根据第二个性能标准（预防准则），在建筑物遭受2/50的地震作用时，最大顶部位移设定为0.025弧度。10/50和2/50这些地震事件会通过适当的因素进行测量来表示为真实的地面运动。这种测量是通过在周期为一秒的SDOF系统中考虑5%的衰减模拟加速度谱线进行的。这些测量因素同样由相同的加速度谱线决定，并与台湾地震规则中规定的在坚硬的岩石场地10/50和2/50的地震事件相关规则相对应。这两个测试结果分别有0.461g和0.622g的地震加速度。根据框架的设计原则和简单性能分析，整个底部剪力将被分配到三个楼层上。每层上的力将按下面公式进行计算。 (1)mi和i分别表示各层的质量和位移，Vd表示总的设计底部剪力。各层的地震力的相对值如下：一层：0.11 二层：0.365 三层：0.525设计底部剪力台湾设计方案这一部分将简单介绍台湾地震工程研究中心对底部剪力的设计，更加详细的介绍会在其他地方看到（文献1）。第一步，将框架理想化为有三个自由度的MDOF体系。三种模式的模型影响因素以及模型的质量和模型各层的位移都将进行计算。对于这个特殊的框架，由于第二和第三中模式的贡献率（MCF分别为0.008和0.002）相对于第一模式（MCF=0.99）来说无关紧要，所以只把第一模式作为实验目标。因此，在第一模式下的第三楼层位移将被作为与模型目标顶部位移相关的有效系统位移eff。第二步，计算框架第一模式的延展性。因为支撑框架承受了80%的地震作用，所以有效系统的屈曲位移根据支撑点的屈曲位移计算，再增加25%作为瞬间框架的影响。根据各层的最大位移，计算各层的延展性，然后取平均值作为系统的有效延展性。采用这种延展性和有效目标位移eff，系统的有效周期将通过非弹性地面运动谱线得出。根据这个时间周期，计算出系统相应的有效坚硬度Keff。最后，目标位移点的底部剪力通过eff和Keff的简单相乘计算出。根据假设在5%拉力下的线性荷载位移曲线和计算出的延展度，最终的底部剪力可以简化为屈服底部剪力。屈服底部剪力作为框架的设计底部剪力（Vd）。两个性能标准中，第二个标准的底部剪力起支配作用，等于415千磅。密歇根大学设计方案采用密歇根大学研究的程序对底部剪力进行重新计算（文献2,3）。其中地震对结构顶点弹性输入能量的一小部分等于结构达到最大目标位移所需的能量。这个程序的简单介绍如下。图三：倒塌预防准则的理性框架响应首先，用理性的三线性曲线来模拟最大底部剪力和位移的关系，如图三所示。这个三线性曲线是分别根据支撑框架的最大底部剪力剖面图和瞬间框架得到的。这些剖面图是理性的弹塑性响应曲线。支撑框架的屈服点最大位移可以根据框架的几何构造计算出。正如前面提到的假定支撑框架在这一点承受未知设计底部剪力Vd的80%。根据过去的分析结果，瞬间框架的最大屈服位移假定为2%，承受剩余设计底部剪力的20%。将这两个双线性曲线叠加得到整个框架位移荷载的三线性曲线（如图三所示）。根据这个曲线计算出框架的延展度。第二部，根据弹性SDOF系统，利用Housner给出的公式计算出最大输入能量，公式如下所示： （2）M和Sv分别表示总质量和模拟线谱速率。然而，对于非弹性系统，这个公式就需要进行改良（如图四a所示）。因此，在公式（2）中添加修正因子将理性弹塑性系统添加到选定的目标位移中，如图四a中所示。通过采用这个修正因子，并将Sv转化为线谱加速度Ceg，模型所需能量Em可表示为下式所示， （3）W和T分别表示系统的质量和基本周期，Ce表示最大的联合底部剪力。根据IBC2000（文献5）的抗震规定，三层框架的T 可以估计为0.37秒。用这个周期，可以从台湾抗震规则草图（2002）给定的设计响应谱线得到Ce。可以根据Leelataviwat提出的-T关系（如图四b所示）得到。图四：（a）弹性、非弹性能量的输入 （b）周期能量修正因素改良的输入能量Em等于作用在框架上的地震作用,如图四a所示的位移。为这个目的，假定了双线性荷载位移关系图（如图四a所示）和随框架高度线性分配的楼层位移。如上所述，可以得到各层的地震力分配。根据这个能量平衡方程，得到设计底部剪力Vd.依据台湾所采用的方法，由第二准则（在2/50地震作用下有2.5%的位移）计算得到的等于340千磅，需要注意它比台湾采用的方法得到的计算结果小。13th World Conference on Earthquake EngineeringVancouver, B.C., CanadaAugust 1-6, 2004Paper No. 497PERFORMANCE-BASED SEISMIC DESIGN AND BEHAVIOR OF ACOMPOSITE BUCKLING RESTRAINED BRACED FRAMEPrabuddha DASGUPTA1, Subhash C. GOEL2, Gustavo PARRA-MONTESINOS3, and K. C. TSAI4SUMMARYThe concept of Buckling Restrained Braced Frames is relatively new and recently their use has increasedin the U.S., Japan and Taiwan. However, detailed design provisions for common practice are currentlyunder development. Since the summer of 2002, researchers at the University of Michigan (UM) havebeen working cooperatively in a joint study with research team at the National Center for Research onEarthquake Engineering (NCREE), Taiwan, involving design, analysis and full scale testing of such aframe by pseudo-dynamic method.The selected structure is a three story, three bay frame consisting of concrete-filled-tube (CFT) columns,steel beams, and composite buckling restrained braces. The frame was designed using an Energy-BasedPlastic Design procedure recently developed by co-author Goel at UM. The method utilized selectedtarget drifts (2.0% for 10% in 50 year and 2.5% for 2% in 50 year design spectra for this frame) andglobal yield mechanism. Because of the need for more precise control of design clearances between theend connections and steel casing of the braces, buckling restrained braced frames are excellent candidatesfor application of this newly developed design methodology.The paper briefly presents the energy-based approach developed at UM as well as a modal displacementbaseddesign procedure adopted by the research team at NCREE for calculation of design base shear forthe frame. Results from inelastic response analyses of frames deigned by the two methods for a Taiwanearthquake are compared. The same frame was also designed for a U.S. location and analyzed underground motions scaled for U.S. standards. The frames designed by the UM approach exhibitedsatisfactory dynamic responses for both Taiwan and U.S. ground motions.INTRODUCTIONExcellent seismic behavior of buckling restrained braces (BRBs) (Tsai 1) encouraged an experimentalprogram at the National Center for Research on Earthquake Engineering (NCREE), Taiwan, inconjunction with analysis and design studies by researchers in the U.S. at the University of Michigan. In1 Ph.D. Candidate, University of Michigan, Ann Arbor, MI2 Professor, University of Michigan, Ann Arbor, MI3 Assistant Professor, University of Michigan, Ann Arbor, MI4 Professor, National Taiwan University, Taiwanthis program, the BRBs provide the primary seismic resistance mechanism to a 3-story 3-bay frame,tested under pseudo-dynamic loading at NCREE in October 2003. General layout of the prototypebuilding is shown in Figure 1a, while a view of the test frame is shown in Figure 1b. For design purpose,two of such frames were assumed to resist the total seismic force for a 3-story prototype building. Theseismic frames are indicated by thick lines in Figure 1a.DESCRIPTION OF TEST FRAMEThe frame was designed to resist the seismic loading through two separate mechanisms. The primaryresistance is provided by buckling restrained braces in the central bay of the frame (Figure 1b). This bayis designed to act as a purely braced frame with all beam-to-column and brace-to-column connectionsmade as simple (pinned) connections. The braces are designed to resist 80% of the total seismic force foreach seismic frame, while 20% of the load is resisted by the two external bays, designed as momentframes with moment connections at the joints of exterior beams and columns. All columns are made ofconcrete filled tubes. Different sections are chosen for interior and exterior columns, while keeping thesame size along the building height. Wide flange sections are used for beams. Different beam sizes areused at different floors, while keeping the same size in all the bays at each floor.423 ft6ft323 ft(a) (b)Figure 1: (a) Layout of the prototype building, (b) View of the test frameBUCKLING RESTRAINED BRACE PROPERTIESBuckling restrained braces are typically made by encasing a steel core member in a concrete filled steeltube (Figure 2a). The steel core is kept separated from the concrete filled tube by a layer of unbondingmaterial applied on the surface of the steel core. The role of concrete encasing and steel tube is to preventbuckling of the steel core, so that a well formed load-displacement response of the brace is achievedunder large displacement reversals. The unbonding material ensures that the force coming into the BRB iscarried by the core only, without engaging the encasing material. Different configurations of BRBs weretested at NCREE under large reversed cyclic axial loading and an optimum configuration was selected foruse in the test frame (Tsai 1) (Figure 2a). A typical load-displacement response obtained from theselected BRB configuration is shown in Figure 2b. As can be seen, full hysteretic loops and excellentenergy dissipation were achieved. However, it is to be noted that the yield load reached in compressionwas about 10% higher than that reached in tension. This needs to be accounted for while designing theframe.Seismic frame313 ftBRBs423 ft623 ft 323 ft(a) (b)Figure 2: (a) Configuration of the BRB adopted, and (b) Typical load-displacement behavior of a BRB(From Tsai 1)DESIGN CONSIDERATIONSA comparative study is presented on the behavior of three prototype frames designed to meet commonperformance criteria through different design procedures. The first frame was designed by the researchteam at NCREE. For this frame, calculation of base shear was done following a multi-modaldisplacement-based seismic design (DSD) procedure and the guidelines stipulated in the 2002 DraftTaiwan Seismic Design Code. Design of that frame was done by elastic method. The second frame wasdesigned by the team at University of Michigan. In this case, same base shear as calculated by theNCREE team was assumed. However, a plastic design procedure, recently developed by Goel, wasadopted to design the frame (UM Frame 1). The third frame (UM Frame 2) was designed for a base shearcalculated by following a simple energy-based procedure developed at UM (Leelataviwat 2, Lee 3).Frame design was done by the plastic design method as used for UM Frame 1.The basic design parameters were selected by the research team at NCREE following the 2002 DraftTaiwan Seismic Design code. Total seismic weight of each floor was divided equally between the twoseismic frames. The seismic weights applied on each frame were as follows,1st and 2nd Floor: 714 kips, and 3rd Floor: 564 kipsIn order to calculate the design base shear for the prototype building, two performance criteria wereconsidered and the one that resulted in higher design base shear was chosen for the design of the testframe. In the first performance criterion (Life Safety), maximum roof drift was set at 0.02 radian when thebuilding is subjected to an earthquake that has a 10% probability of exceedance in 50 years (10/50). In thesecond performance criterion (Collapse Prevention), maximum roof drift was set at 0.025 radian for a2/50 seismic event. A real ground motion time history was scaled by appropriate factors to represent the10/50 and 2/50 events. Scaling was done by considering the 5% damped Pseudo Spectral Acceleration(PSA) of a SDOF system with period T=1 sec. The scaling factors were determined by equating thisspectral acceleration to the corresponding values prescribed in the draft Taiwan seismic code for 10/50and 2/50 events at a hard rock site. The two resulting time histories have PGA values of 0.461g and0.622g, respectively.For the purpose of frame design and for performing the push-over analysis, the total base shear needs tobe distributed over the three floor levels. The force at i-th floor was calculated by using the followingequation:N dii ii ii VmmF=1, (1)where i i m and are the mass and target displacement, respectively, of the i-th floor, and d V is the totaldesign base shear. The relative floor forces obtained are as follows:1st Floor: 0.11, 2nd Floor: 0.365, and 3rd Floor: 0.525DESIGN BASE SHEARTaiwan DesignA brief description of the NCREE procedure to arrive at the design base shear is presented in this section.A detailed description of this procedure can be found elsewhere (Tsai 1).In the first step, the frame was idealized as a MDOF system with three degrees of freedom. ModalContribution Factors (MCF) for the three modes, as well as their modal masses and modal story drifts,were then computed. Since, for this particular frame, the contributions from the 2nd and 3rd modes (MCF =0.008 and 0.002, respectively) were insignificant compared to the contribution from the 1st mode (MCF =0.99) (Tsai 1), only the 1st mode was considered for design purposes. Thus, the three floordisplacements of the 1st mode were used to obtain an effective system displacement eff associated withthe modal target roof drift.In the next step, the ductility demand for the 1st mode of the frame was computed. Because 80% of theseismic force was to be carried by the braced frame, yield drift of the effective system was computedbased on the drift at the point of brace yielding and increased by 25% to account for the contribution fromthe moment frame. From the target maximum story drifts, ductility demand for each story was calculatedand a simple average was taken as the effective ductility demand for the system. Using this ductilitydemand, and from the effective target displacement eff , the effective time period of the system wasobtained from the inelastic displacement spectrum of the ground motion considered. Correspondingeffective stiffness eff K value of the system was computed from this time period.Finally, the base shear required at the point of target drift was computed by simply multiplying eff Kby eff . This ultimate base shear was reduced to the yield base shear by assuming a bi-linear loaddisplacementcurve with a strain hardening of 5% and the ductility demand as computed earlier. Thisyield base shear served as the design base shear (Vd) of the frame. Of the two performance criteria, thebase shear computed from the second criterion governed and was equal to 415 kips.UM DesignThe base shear was re-calculated by using a procedure developed at UM (Leelataviwat 2, Lee 3),where a fraction of the peak elastic input energy of an earthquake to a structure is equated to the energyneeded by the structure in getting pushed up to the maximum target displacement. The procedure isbriefly described below.In the first step, the base shear-roof displacement profile of the frame was modeled by an idealized trilinearcurve, as shown in Figure 3. This tri-linear curve was obtained by considering the base shear-roofdisplacement profiles of the braced frame and the moment frame separately. Both of these profiles wereidealized by elastic-perfectly plastic responses. Roof drift of the braced frame at yield point can be easilycalculated from the geometry of the frame. As mentioned earlier, the base shear carried by the bracedframe at this point was assumed as 80% of the total design base shear Vd, which is an unknown at thisstage. Based on past analysis results, roof drift of the moment frame at yield was assumed as 2%, carryingthe remaining 20% of the total base shear. These two bi-linear curves were superimposed to obtain the trilinearload-displacement curve of the whole frame (Figure 3). This tri-linear curve was further simplifiedto a bi-linear curve (Figure 3) by equating the areas under the two curves. The design ductilitydemand for the frame was calculated from this curve.00.811.20 0.5 1 1.5 2 2.5 3Roof Drift (%)Base Shear/VdFigure 3: Idealized frame responses for Collapse Prevention criterionIn the next step, the peak input energy was calculated by considering an elastic SDOF system and byusing the equation given by Housner 4, as shown below,221E = MSv , (2)where M and Sv are the total mass and the pseudo spectral velocity of the system, respectively. However,for an inelastic system, this equation needs to be modified (Figure 4a). Thus, a modification factor wasapplied to Eqn. (2) to estimate the energy needed to push the idealized elastic-perfectly plastic system tothe selected target displacement, as shown in Figure 4a. Applying this modification factor and convertingSv to spectral acceleration C g e , the modified required energy, m E , can be re-written as,22 21 = m e CTE Wg , (3)where W and T are the total weight and the fundamental period of the system, respectively. e C is themaximum base shear coefficient. Following the seismic provisions of IBC 2000 5, the value of T for the3-story frame was estimated as 0.37 sec. Using this period, e C was obtained from the design responsespectra given in the Draft Taiwan Seismic Code (2002) for the two considered hazard levels. The value of was obtained from the T relationship (Figure 4b) proposed by Leelataviwat 2.The modified input energy, m E is then equated to the total work done by the seismic forces applied to theframe as it is pushed to the target drift as shown in Figure 4a. For this purpose, a bi-linear loaddisplacementbehavior (Figure 4a) and a linear distribution of the floor displacements along the height ofthe frame were assumed. A distribution of floor forces, as mentioned earlier, was also assumed. From thisIdealized tri-linear curveSimplified bi-linear curveBrace yieldingMoment fr