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弯钢框架结点在变化轴向 荷载和侧向位移的作用下的周期性行为
摘要:这篇论文讨论的是在变化的轴向荷载和侧向位移的作用下，接受测试的四种
受弯钢结点的周期性行为.梁的试样由变截面梁,翼缘以及纵向的加劲肋组成。受测试样加载轴向荷载和侧向位移用以模拟侧向荷载对组合梁抗弯系统的影响。实验结果表明试样在旋转角度超过0。03弧度后经历了从塑性到延性的变化。纵向加劲肋的存在帮助传递轴向荷载以及延缓腹板的局部弯曲. 1、 引言
为了评价变截面梁（RBS）结点在轴向荷载和侧向位移下的结构性能,对四个全尺寸的样品进行了测试.这些测试打算评价为旧金山展览中心扩建设计的受弯结点在满足设计基本地震等级（DBE）和最大可能地震等级（MCE)下的性能。基于上述而做的对RBS受弯结点的研究指出RBS形式的结点能够获得超过0.03弧度的旋转角度.然而，有人对于这些结点在轴向和侧向荷载作用下的抗震性能质量提出了怀疑。 旧金山展览中心扩建工程是一个3层构造，并以钢受弯框架作为基本的侧向力抵抗系统。Fig.1是一幅三维透视图.建筑的总标高为展览厅屋顶的最高点,大致是35。36m（116ft）。展览厅天花板的高度是8.23m（27ft）,层高为11。43m（37。5ft）。建筑物按照1997统一建筑规范设计。
框架系统由以下几部分组成：四个东西走向的受弯框架，每个电梯塔边各一个；四个南北走向的受弯框架，在每个楼梯和电梯井各一个的；整体分布在建筑物的东西两侧.考虑到层高的影响,提出了双梁抗弯框架系统的观念。
通过连接大梁， 受弯框架系统的抵抗荷载的行为转化为结构倾覆力矩部分地被梁系统的轴向压缩—拉伸分担，而不是仅仅通过梁的弯曲。结果，达到了一个刚性侧向荷载抵抗系统.竖向部分与梁以联结杆的形式连接.联结杆在结构中模拟偏心刚
性构架并起到与其相同的作用。通常地联结杆都很短，并有很大的剪弯比。 在地震类荷载的作用下，CGMRFS梁的最终弯矩将考虑到可变轴向力的影响.梁中的轴向力是切向力连续积累的结果. 2．CGMRF的解析模型
非线性静力推出器模型是以典型的单间CGMRF模板为指导。图2展示了模型的尺寸规格和多个部分。翼缘板尺寸为28。5mm 254mm(1 1/8in 10in），腹板尺寸为9.5mm 476mm（3/8in 18 3/4in）.推进器模型中运用了SAP 2000计算机程序。框架的特色是全约束(FR).FR受弯框架是一种由结点应变引起的挠度不超过侧向挠度的5％的框架。这个5％仅与梁—柱应变有关，而与柱底板区应变引起的框架应变无关。
模型通过屈服应力和匹配强度的期望值来运行。这些值各自为372Mpa（54ksi）和518Mpa(75ksi)。Fig。3显示了塑性铰的荷载-应变行为是通过建筑物地震恢复的NEHRP指标以广义曲线的形式逼近的. y以Eps5.1和5。2为基底运算，如下： P-M铰合线荷载-应变模型上的点C，D和E的取值如表5。4
y以0.01rad为幅度取值见表5.8。切变铰合线荷载-应变模型点C，D和E取值见表5.8.对于连续梁,假定两个模型点B和C之间的形变硬化比有3%的弹性比. Fig。4定性的给出了侧向荷载下的CGMRF中的弯矩，切应力和正应力的分布。其中切应力和正应力对梁的影响要小于弯矩的作用，尽管他们必须在设计中加以考虑.内力分布图解见Fig。5，可见，弹性范围和非弹性范围的内力行为基本相同。内力的比值将随框架的屈服和内力的重分布的变化而变化。基本内力图见Fig。5，然而，仍然是一样的。
非静力推进器模型的运行通过柱子顶部的侧向位移的单调增加来实现，如Fig。5所示.在四个RBS同时屈服后，发生在腹板与翼缘端部的竖向的统一屈服将开始形成。这是框架的屈服中心，在柱子被固定后将在柱底部形成塑性铰。Fig.7给出了基本切应力偏移角。图中还给出了框架中非弹性活动的次序。对于一个弹性组成,推进器将有一个特有的很长的过渡(同时形成塑性铰）和一个很短的屈服平稳阶段。 塑性旋转能力, 被定义为：结点强度从开始递减到低于80%的总的塑性旋转角.这个定义不同于第9段（附录）AISC地震条款的描述。使用Eq源于RBS塑性旋转能力被定在0.037弧度.被 替代, 用来计算理论屈服强度与实际屈服强度的区别（标号
是50钢)。 3．实践规划
如图6所示，实验布置是为了研究基于典型的CGMRF结构下的结点在动力学中的能量耗散.用图中所给的塑性位移，塑性转角,塑性偏移角，由几何结构，有如下:这里的δ和γ包括了弹性组合.上述近似值用于大型的非弹性梁的变形破坏.图6a表明用图6b所示的位移控制下的替代组合能够表示CGMRF结构中的典型梁的非弹性行为。
图8所示，建立这个实验装置来发展图6a和图6b所示的机构学。轴心装置附以3个2438mm×1219mm×1219mm（8ft×4ft×4ft）RC块。并用24个32mm径的杆与实验室的地板固定。这种装置允许在每次测验后换实验样品。
根据实验布置的动力学要求,随着侧面的元件放置，轴向的元件，元件1和元件2，将钉到B和C中去， 如图8所示。因此，轴向元件提供的轴向力P可以被分解为相互正交的力的组合， 和 ，由于轴向力的倾斜角度不超过 ，因此 近似等于P。然而，侧向力分量， ，引起了一个在梁柱交接处的附加弯矩。如果轴向元件压试样的话，那么将会加到侧向力中,若轴向是拉力，对于侧向元件来说则是个反向力。当轴向元件有个侧向位移 ,他们将在梁柱交接处引起一个附加弯矩,因此，梁柱交接处的弯矩等于: M=HL+P
其中H是侧向力,L是力臂，P是轴向力， 是侧向位移。
四个梁柱结点全尺寸实验做完了。拉伸试样检测的结果和构件尺寸见表2.所有柱和梁的钢筋为A572标号50钢( =344。5Mpa）.经测定的梁翼缘屈服应力值等于372Mpa（54ksi），整体的强度范围是从502Mpa（72。8ksi）到543Mpa(78.7ksi）。 表3列出了各个试样的全截面和RBS中间变截面处的塑性弯矩值（受拉应力下的数据）。
本文所指的试样专指试样1到4。被检试样细部图见图9到图12。在设计梁柱结点时用到了以下数据:
梁翼缘部分采用RBS结构.配备环形掏槽，如图11和图12所示.对于所有的试样，切除30％翼缘宽度.切除工作做的十分精细，并打磨光滑且与梁翼缘保持平行以尽量见效切口。
应用全焊接腹板结点.梁腹板与柱翼缘之间的结点采用全焊缝焊接(CJP）。所有CJP
焊接严格依照AWS D1.1结构焊接规范.
采用双侧板加CJP形式连接梁翼缘的顶部和底部和柱表面到变截面开始处，如图11和图12。侧板尾部打磨光滑以便同RBS连接.侧板采用CJP形式与柱边缘相连接。侧板的作用是增加受弯单元的承受能力，平稳过渡是为了减少应力集中而导致的破裂.
两根纵向的加劲肋,95mm×35mm（3 3/4in ×1 3/8 in)，以12。7mm的角焊缝焊接到腹板的中间高度，如图9和10。加劲肋采用CJP的形式焊接到柱的边缘。切除梁翼缘顶部和低部的坡口焊缝处的多余焊接部分。以便消除坡口焊接断口处可能产生的断裂.除去翼缘低部的衬垫板条.以便消除衬垫板条带来的断口效应并增加安全性。使用与梁翼缘厚度近似相同的连续板。所有试样板厚均为一英寸。由于RBS是受检试样最容易区分的特征，纵向的加劲肋在延缓局部弯曲和提高结点可靠性方面扮演着重要的角色。 4．荷载历史
试样被加以周期性交替的荷载，其末端的位移△y的增加如图4所示。梁的末端位移受伺服控制装置3和4的影响。当作用轴向力时，制动器1和2是活动的，以此用它的受力来模拟从连接处传到梁上的剪力。可变的轴向荷载在+0。5△y处增加到2800KN.在那以后,通过最大的侧向位移，这个荷载保持恒定。在试样被推回时,轴向力维持恒定直至0.5△y，然后减小到零，此时的试样通过中和轴。根据本文第2部分有关轴向力受以上约束的论述，可以推断出以P=2800KN来研究RBS负载是合理的。测试将会继续，直至试样损坏,或者到实验预期的限制。 5.实验结果
每个试样的滞后反应见图13和图16。这些图表显示了梁弯矩相对的的塑性旋度。梁的弯矩在RBS试样的中间测量,并通过取一个等价的梁端力乘以制动器侧向中心线到RBS中间的距离来计算。（试样1和2为1792mm，试样3和4为23972mm）。用来计算附加弯矩的等价侧向力由于P-△。旋转角是这样定义的，用制动器的侧向位移除以制动器侧向中心线到RBS中间的距离。塑性旋度计算如下：
其中V是剪力，K是弹性在范围内 的比。在测试期间的测量和观察表明，试样1和4的所有塑性旋度均在梁的内部发展。板的连接区域和柱子保持弹性，如设计预期的
一样。
表5列出了每个试样在测试最后的塑性旋度。塑性旋度合格性能的目标级被定在±0.03rad，依AISC钢结构建筑抗震条例而定。所有试样均达到了合格的性能标准。所有试样均有良好的塑性变形和能量耗散。当负载周期为±1△y时,底部首先屈服，然后随着负载周期逐渐扩散增加。 5。1 试样1和2
试样1和2的变化见图13.在第7和第8个周期以及1△y，最初屈服发生在底缘处。对于所有的受测试的试样，最初的屈服均发生在这个部位，这是由试样底部的弯矩引起的.随着荷载作用的继续，屈服开始沿着RBS底缘传递.从3.5△y开始,发生腹板弯曲并且相邻的底缘开始屈服。屈服开始沿RBS上边缘传递，一些次要的屈服传递到中间的加劲肋。在5△y开始，轴向压力增大到3115KN，一个剧烈的腹板的翘曲产生并伴随着局部弯曲。腹板和翼缘的局部弯曲随着荷载的累次 加载而逐渐明显。这里要说明的是，在滞后回线中,腹板和翼缘的局部弯曲并没附有重要的损坏。当作用到5.75△y时,在RBS的尾部和衬板连接处，试样1的底缘产生一个裂缝。随着荷载周期的增加到7△y时,裂缝迅速扩大并穿过了整个底缘。一旦底缘完全断裂,腹板将开始断裂.这个断裂首先在RBS的末端出现，然后沿剪切槽的净截面传播，通过加劲肋的中间并通过另一边的加劲肋的净截面.在实验中,试样1的最大作用弯矩是梁的塑性承载力的1。56倍。在作用到6。5△y时,试样2也在底缘处出现一个裂缝，是在RBS末端与翼板的交接处.随着荷载周期的增加,第15△y时，裂缝缓慢的发展穿过了底缘.试样2的测试到此结束,因为已经到了实验装置加载的极限。 加给试样1和试样2的最大荷载是890KN。从正的象限中看到的弯折是由于施加的变化的轴向拉力导致。力—位移曲线的正斜率证明了这个区域的负载容量并没有减弱。然而，由于腹板和翼缘的局部弯曲的影响，负的区域的负载容量有轻微的削弱。试样1的照片如图14和图15.由图14可以看到，底缘处发生严重的局部弯曲,并可以看到与底缘相连的腹板部分。弯曲沿展到整个RBS的长度方向.RBS中形成塑性胶，并伴随着梁的腹板和翼缘的大规模的屈服。由图15可见，裂缝由RBS的连接传递到了侧面的翼板。在底缘的一个断裂导致了试样1的最终断裂.这个断裂导致梁几乎失去承载能力。图15还说明了试样1产成了0。05rad的塑性旋度,并且在柱子表面没有疲劳损伤。
5。2 试样3和试样4
试样3和试样4的变化曲线如图16。最初的屈服发生在荷载周期第7到第8周之间，底缘的重要屈服发生在1△y处。随着荷载周期的发展，屈服开始沿RBS的底缘传播.在1.5△y时，腹板弯曲发生并明显伴随着底缘的屈服.屈服开始沿着RBS的顶部传播，一些次要的屈服沿着加劲肋中部传播。在荷载周期到3.5△y时，一个剧烈的腹板翘曲产生并伴随着翼缘的局部弯曲。腹板和翼缘的局部弯曲随着累次加载变得逐渐明显。当加载到4.5△y时，轴向荷载增大到3115KN，并导致屈服传播到中间横向加强构件。随着荷载周期的增加，腹板和翼缘的局部弯曲变得更加剧烈。对于2个试样,受实验装置的约束测试到此结束。在试样3和试样4中没有破坏产生。然而，在将试样3移动到实验室之外时，却发现在底缘与柱子的焊接处有一个微小的裂缝。加给试样3和试样4的最大荷载分别是890KN和912KN。试样的负载容量在实验后削弱了20%，这是由腹板和翼缘的局部弯曲引起的.这个慢性的恢复在大概塑性旋度产生0。015到0.02后开始。如图17所示,试样3在正的象限中的负载容量没有减弱（轴向的拉伸作用在梁上），由力-位移的包络图可见。图18是试样3的测试前的照片。图19是试样4在0。014的位移作用周期后的照片,显示了铰合区域的屈服和局部弯曲。梁的腹板的屈服沿着其整个深度方向。最强的屈服发生在腹板的底部，底缘和中间加劲肋之间。腹板的顶部也发生了屈服,虽然其剧烈程度不如底部。纵向的加劲肋也发生了屈服。柱子的连接板部分没有发生屈服。在接近柱子表面的梁的未经削弱的部分也没有显示发生屈服。最大位移是174mm,最大弯矩发生在RBS中部，为梁的塑性弯矩值的1.51倍。塑性铰的旋度达到了0.032rad（铰接点设置在距离柱子表面0.54d处,其中d是梁的长度）。 5.2.1 结点处的应变分布
试样3的外表面边缘的应变分布见图20和21。试样1、2、4的应变记录和分布状态呈现了相似的趋势。同样的，这些试样的屈服次序也同试样3的相似.在负周期时,离柱子51mm的顶部外表面处的应变低于0.2％。位于顶部同一位置的翼缘，仅在受压时屈服.图22和图23显示了沿着底缘外表面中心线的纵向应变，其中取22是正向周期下的,图23是负向周期下的。从图23我们可以看出，在周期在—1。5△y以后，RBS上的应变比附近的柱子上的应变要大好几倍；这是由翼缘的局部弯曲造
成的。底缘局部弯曲发生在整个板的平均应变达到形变硬化值时，板的变截面部分在纵向力下完全屈服，从而导致一个十分弯曲的波纹。 5。2。2 累计能量的消散
试样的累计能量消散见图24。累计能量消散是以封入区域的横向荷载的滞后回线之和表示的。能量消散在加载到12周以后在2。5△y处开始增加。对于飘移电平，点平的很小变化会带来很大的能量耗散。试样2比试样1消耗更多的能量，它是在RBS过度部分断裂的。然而，对于2个试样来说，在θ=0。04rad时,其周期是相似的.总的来说，在试样1和试样2中，负的周期下的能量消散比正的周期下能量消散大1。55倍。对于试样3和试样4来说，负的能量消散是正负平均水平的120％。在底缘RBS屈服后，屈服的组合现象,应变硬化,面内形变和面外形变，局部弯曲均很快发生。 6．结论
基于由实验而得的数据,以及应用于仪器的解析法，得出如下结论： 1、 对于所有的试样,塑性旋度均超出0。3％。 2、 RBS的塑性过程是平稳发展的。
3、 试样超出抗弯强度的比率，试样1等于1。56，试样4等于1。51。抗弯 强度承载能力取决于标定的屈服强度和FEMA—273梁-柱等式。 4、 底缘和腹板的塑性局部弯曲对其荷载承受能力没有重大的削弱.
5、 尽管翼缘的局部弯曲不使强度立即产生削弱，但是它确实导致腹板的局部弯曲。
6、 设置在梁的腹板中部的纵向加劲肋,能够帮助传递轴向力，还能延缓腹板的局部弯曲。然而，它却产生如此大的一个超过强度的比率，从而使焊接结点、板条区域以及柱子的承载能力在设计时大打折扣.
7、 在负载周期时，塑性旋度为0.015到0。02rad时将会产生一个逐渐的强度的减弱。在正向周期时也没有.
8、 轴想压缩荷载在小于0。0325Py时，对结点应变能力影响不大.
9、 CGMRFS技术与适当的设计以及详细的RBS连接,是一个可靠的抗震系统。
附件2:外文原文(电子或复印件）
Cyclic behavior of steel moment frame
connections under varying axial load and lateral displacements
Abstract: This paper discusses the cyclic behavior of four steel moment connections tested under variable axial load and lateral displacements. The beam specim- ens consisted of a reducedbeam section, wing plates and longitudinal stiffeners。 The test specimens were subjected to varying axial forces and lateral displace— ments to simulate the effects on beams in a Coupled-Girder Moment—Resisting Framing system under lateral loading。 The test results showed that the specim- ens responded in a ductile manner since the plastic rotations exceeded 0。03 rad without significant drop in the lateral capacity. The presence of the longitudin— al stiffener assisted in transferring the axial forces and delayed the formation of web local buckling。 1. Introduction
Aimed at evaluating the structural performance of reduced-beam section (RBS） connections under alternated axial loading and lateral displacement, four full-scale specimens were tested. These tests were intended to assess the performance of the moment connection design for the Moscone Center Exp- ansion under the Design Basis Earthquake (DBE） and the Maximum Considered Earthquake （MCE). Previous research conducted on RBS moment connections [1,2] showed that connections with RBS profiles can achieve rotations in excess of 0。03 rad。 However, doubts have been cast on
the quality of the seismic performance of these connections under combined axial and lateral loading。
The Moscone Center Expansion is a three-story， 71，814 m2 (773，000 ft2) structure with steel moment frames as its primary lateral force—resisting system。 A three dimensional perspective illustration is shown in Fig. 1。 The overall height of the building， at the highest point of the exhibition roof, is approxima— tely 35。36 m (116ft） above ground level. The ceiling height at the exhibition hall is 8。23 m (27 ft） , and the typical floor-to—floor height in the building is 11.43 m （37.5 ft). The building was designed as type I according to the requi- rements of the 1997 Uniform Building Code. The framing system consists of four moment frames in the East–West direct— ion, one on either side of the stair towers, and four frames in the North–South direction， one on either side of the stair and elevator cores in the east end and two at the west end of the structure [4］。 Because of the story height， the con— cept of the Coupled—Girder Moment-Resisting Framing System (CGMRFS) was utilized.
By coupling the girders, the lateral load—resisting behavior of the moment framing system changes to one where structural overturning moments are resisted partially by an axial compression–tension couple across the girder system， rather than only by the individual flexural action of the girders. As a result， a stiffer lateral load resisting system is achieved. The vertical element that connects the girders is referred to as a coupling link.
Coupling links are analogous to and serve the same structural role as link beams in eccentrically braced frames. Coupling links are generally quite short, having a large shear— to-moment ratio.
Under earthquake—type loading, the CGMRFS subjects its girders to wariab- ble axial forces in addition to their end moments. The axial forces in the Fig. 1。 Moscone Center Expansion Project in San Francisco， CA girders result from the accumulated shear in the link. Fig 2。 Analytical model of CGMRF
Nonlinear static pushover analysis was conducted on a typical one—bay model of the CGMRF. Fig. 2 shows the dimensions and the various sections of the model. The link flange plates were 28.5 mm 254 mm （1 1/8 in 10 in) and the web plate was 9.5 mm 476 mm (3 /8 in 18 3/4 in). The SAP 2000 computer program was utilized in the pushover analysis [5]. The frame was characterized as fully restrained（FR). FR moment frames are those frames for 1170which no more than 5％ of the lateral deflections arise from connection deformation ［6］。 The 5％ value refers only to deflection due to beam–column deformation and not to frame deflections that result from column panel zone deformation ［6, 9］。
The analysis was performed using an expected value of the yield stress and ultimate strength. These values were equal to 372 MPa (54 ksi) and 518 MPa （75 ksi）， respectively。 The plastic hinges' load–deformation behavior was approximated by the generalized curve suggested by NEHRP
Guidelines for the Seismic Rehabilitation of Buildings ［6] as shown in. Fig. 3。 △y was calcu— lated based on Eqs. (5.1) and （5.2） from [6］， as follows：
P–M hinge load–deformation model points C, D and E are based on Table 5.4 from [6] for
△y was taken as 0。01 rad per Note 3 in ［6］, Table 5.8。 Shear hinge load- load–deformation model points C, D and E are based on Table 5。8 [6]， Link Beam, Item a. A strain hardening slope between points B and C of 3% of the elastic slope was assumed for both models。
The following relationship was used to account for moment–axial load interaction ［6]:
where MCE is the expected moment strength， ZRBS is the RBS plastic section modulus （in3)， is the expected yield strength of the material （ksi), P is the axial force in the girder (kips） and is the expected axial yield force of the RBS, equal to （kips）。 The ultimate flexural capacities of the beam and the link of the model are shown in Table 1。
Fig. 4 shows qualitatively the distribution of the bending moment, shear force， and axial force in the CGMRF under lateral load。 The shear and axial force in the beams are less significant to the response of the beams as compared with the bending moment， although they must be considered in design. The qualita- tive distribution of internal forces illustrated in Fig. 5 is fundamentally the same for both elastic and inelastic ranges of behavior。
The specific values of the internal forces will change as elements of the frame yield and internal for- ces are redistributed. The basic patterns illustrated in Fig。 5, however， remain the same.
Inelastic static pushover analysis was carried out by applying monotonically increasing lateral displacements, at the top of both columns, as shown in Fig. 6. After the four RBS have yielded simultaneously， a uniform yielding in the web and at the ends of the flanges of the vertical link will form. This is the yield mechanism for the frame ， with plastic hinges also forming at the base of the columns if they are fixed。 The base shear versus drift angle of the model is shown in Fig. 7 . The sequence of inelastic activity in the frame is shown on the figure. An elastic component， a long transition （consequence of the beam plastic hinges being formed simultaneously) and a narrow yield plateau characterize the pushover curve。
The plastic rotation capacity, qp， is defined as the total plastic rotation beyond which the connection strength starts to degrade below 80％ [7]. This definition is different from that outlined in Section 9 （Appendix S） of the AISC Seismic Provisions ［8, 10］。 Using Eq。 （2） derived by Uang and Fan ［7］， an estimate of the RBS plastic rotation capacity was found to be 0。037 rad:
Fyf was substituted for Ry•Fy [8]， where Ry is used to account for the differ— ence between the nominal and the expected yield strengths (Grade
50 steel, Fy=345 MPa and Ry =1。1 are used). 3。 Experimental program
The experimental set-up for studying the behavior of a connection was based on Fig. 6(a）. Using the plastic displacement dp， plastic rotation gp， and plastic story drift angle qp shown in the figure, from geometry, it follows that:And: in which d and g include the elastic components。 Approximations as above are used for large inelastic beam deformations. The diagram in Fig。 6(a) suggest that a sub assemblage with displacements controlled in the manner shown in Fig. 6（b） can represent the inelastic behavior of a typical beam in a CGMRF。
The test set-up shown in Fig。 8 was constructed to develop the mechanism shown in Fig. 6（a) and （b). The axial actuators were attached to three 2438 mm × 1219 mm × 1219 mm （8 ft × 4 ft × 4 ft） RC blocks。 These blocks were tensioned to the laboratory floor by means of twenty-four 32 mm diameter dywidag rods. This arrangement permitted replacement of the specimen after each test.
Therefore, the force applied by the axial actuator, P, can be resolved into two or thogonal components， Paxial and Plateral。 Since the inclination angle of the axial actuator does not exceed 3.0, therefore Paxial is approximately equal to P [4］。 However, the lateral component， Plateral, causes an additional moment at the beam-to column joint. If the axial actuators compress the specimen， then the lateral components will be adding to the
lateral actuator forces, while if the axial actuators pull the specimen, the Plateral will be an opposing force to the lateral actuators. When the axial actuators undergo
axial actuators undergo a lateral displacement _， they cause an additional moment at the beam—to—column joint (P—△ effect)。 Therefore, the moment at the beam-to column joint is equal to:
where H is the lateral forces， L is the arm, P is the axial force and _ is the lateral displacement.
Four full—scale experiments of beam column connections were conducted。 The member sizes and the results of tensile coupon tests are listed in Table 2 All of the columns and beams were of A572 Grade 50 steel （Fy 344.5 MPa). The actual measured beam flange yield stress value was equal to 372 MPa （54 ksi）， while the ultimate strength ranged from 502 MPa （72.8 ksi) to 543 MPa (78.7 ksi)。
Table 3 shows the values of the plastic moment for each specimen （based on measured tensile coupon data） at the full cross-section and at the reduced section at mid—length of the RBS cutout。
The specimens were designated as specimen 1 through specimen 4。 Test specimens details are shown in Fig. 9 through Fig。 12. The following features were utilized in the design of the beam–column connection： The use of RBS in beam flanges. A circular cutout was provided， as illustr— ated in Figs. 11 and 12. For all specimens， 30％ of the beam flange
width was removed. The cuts were made carefully, and then ground smooth in a direct- tion parallel to the beam flange to minimize notches.
Use of a fully welded web connection。 The connection between the beam web and the column flange was made with a complete joint penetration groove weld （CJP）. All CJP welds were performed according to AWS D1.1 Structural Welding Code
Use of two side plates welded with CJP to exterior sides of top and bottom beam flan— ges， from the face of the column flange to the beginning of the RBS， as shown in Figs. 11 and 12. The end of the side plate was smoothed to meet the beginning of the RBS。 The side plates were welded with CJP with the column flanges. The side plate was added to increase the flexural capacity at the joint location， while the smooth transition was to reduce the stress raisers， which may initiate fracture
Two longitudinal stiffeners， 95 mm × 35 mm （3 3/4 in × 1 3/8 in), were welded with 12。7 mm （1/2 in） fillet weld at the middle height of the web as shown in Figs. 9 and 10。 The stiffeners were welded with CJP to column flanges。
Removal of weld tabs at both the top and bottom beam flange groove welds。 The weld tabs were removed to eliminate any potential notches introduced by the tabs or by weld discontinuities in the groove weld run out regions. Use of continuity plates with a thickness approximately equal to the beam flange thickness。 One-inch thick continuity plates were used for all
specimens。
While the RBS is the most distinguishing feature of these test specimens， the longitudinal stiffener played an important role in delaying the formation of web local buckling and developing reliable connection performance4. Loading history
Specimens were tested by applying cycles of alternated load with tip displacement increments of _y as shown in Table 4. The tip displacement of the beam was imposed by servo—controlled actuators 3 and 4。 When the axial force was to be applied, actuators 1 and 2 were activated such that its force simulates the shear force in the link to be transferred to the beam。 The variable axial force was increased up to 2800 kN (630 kip） at 0。5_y. After that， this lo— ad was maintained constant through the maximum lateral displacement.
maximum lateral displacement。 As the specimen was pushed back the axial force remained constant until 0.5 y and then started to decrease to zero as the specimen passed through the neutral position ［4]. According to the upper bound for beam axial force as discussed in Section 2 of this paper, it was concluded that P =2800 kN （630 kip） is appropriate to investigate this case in RBS loading. The tests were continued until failure of the specimen, or until limitations of the test set—up were reached. 5。 Test results
The hysteretic response of each specimen is shown in Fig. 13 and Fig. 16。
These plots show beam moment versus plastic rotation。 The beam moment is measured at the middle of the RBS， and was computed by taking an equiva— lent beam-tip force multiplied by the distance between the centerline of the lateral actuator to the middle of the RBS (1792 mm for specimens 1 and 2, 3972 mm for specimens 3 and 4)。 The equivalent lateral force accounts for the additional moment due to P– △ effect。 The rotation angle was defined as the lateral displacement of the actuator divided by the length between the centerline of the lateral actuator to the mid length of the RBS。 The plastic rotation was computed as follows ［4］:
where V is the shear force, Ke is the ratio of V/q in the elastic range。 Measurements and observations made during the tests indicated that all of the plastic rotation in specimen 1 to specimen 4 was developed within the beam. The connection panel zone and the column remained elastic as intended by design.
5。1. Specimens 1 and 2
The responses of specimens 1 and 2 are shown in Fig。 13。 Initial yielding occurred during cycles 7 and 8 at 1_y with yielding observed in the bottom flange. For all test specimens， initial yielding was observed at this location and attributed to the moment at the base of the specimen [4]。 Progressing through the loading history， yielding started to propagate along the RBS bottom flange. During cycle 3。5_y initiation of web buckling was noted
adjacent to the yielded bottom flange。 Yielding started to propagate along the top flange of the RBS and some minor yielding along the middle stiffener。 During the cycle of 5_y with the increased axial compression load to 3115 KN （700 kips） a severe web buckle developed along with flange local buckling。 The flange and the web local buckling became more pronounced with each successive loading cycle. It should be noted here that the bottom flange and web local buckling was not accompanied by a significant deterioration in the hysteresis loops。 A crack developed in specimen 1 bottom flange at the end of the RBS where it meets the side plate during the cycle 5.75_y。 Upon progressing through the loading history, 7_y, the crack spread rapidly across the entire width of the bottom flange。 Once the bottom flange was completely fractured, the web began to fracture。 This fracture appeared to initiate at the end of the RBS，then propagated through the web net section of the shear tab, through the middle stiffener and the through the web net section on the other side of the stiffener。 The maximum bending moment achieved on specimen 1 during theDuring the cycle 6。5 y, specimen 2 also showed a crack in the bottom flange at the end of the RBS where it meets the wing plate。 Upon progressing thou- gh the loading history， 15 y, the crack spread slowly across the bottom flan— ge。 Specimen 2 test was stopped at this point because the limitation of the test set-up was reached。
The maximum force applied to specimens 1 and 2 was 890 kN （200 kip)。
The kink that is seen in the positive quadrant is due to the application of the varying axial tension force。 The load-carrying capacity in this zone did not deteriorate as evidenced with the positive slope of the force–displacement curve. However, the load-carrying capacity deteriorated slightly in the neg— ative zone due to the web and the flange local buckling。
Photographs of specimen 1 during the test are shown in Figs. 14 and 15. Severe local buckling occurred in the bottom flange and portion of the web next to the bottom flange as shown in Fig. 14。 The length of this buckle extended over the entire length of the RBS。 Plastic hinges developed in the RBS with extensive yielding occurring in the beam flanges as well as the web. Fig。 15 shows the crack that initiated along the transition of the RBS to the side wing plate. Ultimate fracture of specimen 1 was caused by a fracture in the bottom flange. This fracture resulted in almost total loss of the beam— carrying capacity。 Specimen 1 developed 0.05 rad of plastic rotation and showed no sign of distress at the face of the column as shown in Fig。 15。 5.2。 Specimens 3 and 4
The response of specimens 3 and 4 is shown in Fig。 16. Initial yielding occured during cycles 7 and 8 at 1_y with significant yielding observed in the bottom flange。 Progressing through the loading history， yielding started to propagate along the bottom flange on the RBS。 During cycle 1。5_y initiation of web buckling was noted adjacent to the yielded bottom flange. Yielding started to propagate along the top flange of the RBS and some
minor yielding along the middle stiffener. During the cycle of 3.5_y a severe web buckle developed along with flange local buckling。 The flange and the web local buckling bec— ame more pronounced with each successive loading cycle.
During the cycle 4。5 y， the axial load was increased to 3115 KN (700 kips) causing yielding to propagate to middle transverse stiffener. Progressing through the loading history， the flange and the web local buckling became more severe。 For both specimens, testing was stopped at this point due to limitations in the test set—up. No failures occurred in specimens 3 and 4. However， upon removing specimen 3 to outside the laboratory a hairline crack was observed at the CJP weld of the bottom flange to the column. The maximum forces applied to specimens 3 and 4 were 890 kN （200 kip) and 912 kN (205 kip）. The load—carrying capacity deteriorated by 20% at the end of the tests for negative cycles due to the web and the flange local buckling。 This gradual reduction started after about 0.015 to 0。02 rad of plastic rotation. The load-carrying capacity during positive cycles (axial tension applied in the girder） did not deteriorate as evidenced with the slope of the force–displacement envelope for specimen 3 shown in Fig。 17。
A photograph of specimen 3 before testing is shown in Fig。 18. Fig. 19 is a Fig。 16. Hysteretic behavior of specimens 3 and 4 in terms of moment at middle RBS versus beam plastic rotation。
photograph of specimen 4 taken after the application of 0。014 rad displacem— ent cycles， showing yielding and local buckling at the hinge region. The beam web yielded over its full depth。 The most intense yielding was observed in the web bottom portion， between the bottom flange and the middle stiffener。 The web top portion also showed yielding， although less severe than within the bottom portion。 Yielding was observed in the longitudinal stiffener。 No yiel— ding was observed in the web of the column in the joint panel zone。 The un- reduced portion of the beam flanges near the face of the column did not show yielding either。 The maximum displacement applied was 174 mm, and the maximum moment at the middle of the RBS was 1。51 times the plastic mom ent capacity of the beam. The plastic hinge rotation reached was about 0。032 rad (the hinge is located at a distance 0。54d from the column surface,where d is the depth of the beam)。 5。2。1. Strain distribution around connection
The strain distribution across the flanges–outer surface of specimen 3 is shown in Figs. 20 and 21. The readings and the distributions of the strains in specimens 1, 2 and 4 （not presented) showed a similar trend. Also the seque— nce of yielding in these specimens is similar to specimen 3. The strain at 51 mm from the column in the top flange–outer surface remained below 0。2% during negative cycles. The top flange， at the same location, yielded in compression only.
The longitudinal strains along the centerline of the bottom–flange outer face
are shown in Figs. 22 and 23 for positive and negative cycles, respectively。 From Fig.23， it is found that the strain on the RBS becomes several times larg- er than that near the column after cycles at –1.5_y; this is responsible for the
flange local buckling。 Bottom flange local buckling occurred when the average strain in the plate reached the strain—hardening value (esh _ 0。018） and the reduced—beam portion of the plate was fully yielded under longitudinal stresses and permitted the development of a full buckled wave. 5。2。2. Cumulative energy dissipated
The cumulative energy dissipated by the specimens is shown in Fig. 24. The cumulative energy dissipated was calculated as the sum of the areas enclosed the lateral load–lateral displacement hysteresis loops。 Energy dissipation sta— rted to increase after cycle 12 at 2。5 y (Fig。 19）。 At large drift levels, energy dissipation augments significantly with small changes in drift. Specimen 2 dissipated more energy than specimen 1， which fractured at RBS transition. However, for both specimens the trend is similar up to cycles at q =0。04 rad
In general, the dissipated energy during negative cycles was 1.55 times bigger than that for positive cycles in specimens 1 and 2。 For specimens 3 and 4 the dissipated energy during negative cycles was 120％， on the average, that of the positive cycles。
The combined phenomena of yielding, strain hardening， in—plane and out-
of-plane deformations, and local distortion all occurred soon after the bottom flange RBS yielded. 6。 Conclusions
Based on the observations made during the tests, and on the analysis of the instrumentation， the following conclusions were developed： 1. The plastic rotation exceeded the 3% radians in all test specimens. 2. Plastification of RBS developed in a stable manner。
3。 The overstrength ratios for the flexural strength of the test specimens were equal to 1.56 for specimen 1 and 1.51 for specimen 4。 The flexural strength capacity was based on the nominal yield strength and on the FEMA-273 beam–column equation.
4。 The plastic local buckling of the bottom flange and the web was not accompanied by a significant deterioration in the load—carrying capacity. 5。 Although flange local buckling did not cause an immediate degradation of
strength， it did induce web local buckling.
6。 The longitudinal stiffener added in the middle of the beam web assisted in transferring the axial forces and in delaying the formation of web local buckling. How ever， this has caused a much higher overstrength ratio, which had a significant impact on the capacity design of the welded joints， panel zone and the column.
7。 A gradual strength reduction occurred after 0。015 to 0。02 rad of plastic
rotation during negative cycles. No strength degradation was observed during positive cycles.
8. Compression axial load under 0。0325Py does not affect substantially the connection deformation capacity.
9. CGMRFS with properly designed and detailed RBS connections is a reliable system to resist earthquakes.
出自《工程索引》，The Engineering Index，简称EI。
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