土木工程外文翻译

本科毕业设计（论文）外文翻译译文学生姓名：院（系）：专业班级：指导教师：完成日期：钢筋混凝土填充框架结构对拆除两个相邻的柱的响应作者：Mehrdad Sasani 美国波士顿东北大学，斯奈尔400设计中心MA02115收稿日期：2007年7月27日，修整后收稿日期2007年12月26日，录用日期2008年1月24日，网上上传日期2008年3月19日。

摘要：本文是评价圣地亚哥旅馆对同时拆除两根相邻的外柱的响应问题，圣地亚哥旅馆是个6层钢筋混凝土填充框架结构。

结构的分析模型应用了有限元法和以此为基础的分析模型来计算结构的整体和局部变形。

分析结果跟实验结果非常吻合。

当测量的竖向位移增加到为四分之一英寸（即6.4mm）的时候，结构就发生连续倒塌。

通过实验分析方法评价和讨论随着柱的移除而产生的变形沿着结构高度上的发展和荷载动态重分配。

讨论了轴向和弯曲的变形传播的不同。

结构横向和纵向的三维桁架在填充墙的参与下被认为是荷载重分配的主要构件。

讨论了两种潜在的脆性破坏模型（没有拉力加强的梁的脆断和有加筋肋的梁的挤出）。

分析评价了结构对额外的重力和无填充墙时的响应。

Elsevier有限责任公司对此文保留所有权利。

关键词：连续倒塌；荷载重分配；对荷载抵抗能力；动态响应；非线性分析；脆性破坏。

1. 介绍：作为减小由于结构的局部损坏而造成大量伤亡的可能性措施的一部分，美国总务管理局【1】和国防部【2】出台了一系列制度来评价结构对连续倒塌的抵抗力。

【3】定义连续倒塌为，由原始单元的局部破坏在单元间的扩展最终造成结构的整体或不成比例的大部破坏。

通过Ellingwood 和Leyendecker【4】建议的方法，ASCE/SEI 7定义了两种一般模型来减小结构设计时连续倒塌效应产生的损害，它们分为直接和间接的设计方法。

一般建筑规范和标准用增加结构的整体性的间接设计方法。

间接设计法也应用于美国国防部的降低连续倒塌设计和未归档设备标准中。

尽管间接设计法可以降低连续破坏的风险【6，7】，对基于此法设计的结构破坏后的表现的判断是不容易实现的。

有一种基于直接设计的方法通过研究瞬间消除受载构件，比如柱子，对结构的影响来评价结构的连续倒塌。

美国防部和国家事务管理局的规章是要求去除一个受荷构件，考虑其影响。

这样的规范目的是评价结构的整体性和结构的一个单元出现严重的毁坏时的分荷能力。

这种方法是研究结构受连续倒塌的影响的程度，但是事实上初始结构损伤的影响不止局限于某一根柱子。

在本论文中，应用通过实验证实的分析结果，评价圣地亚哥旅馆抵抗连续破坏的能力，实验中瞬间移除两个相邻的柱子，其中一个柱是拐角柱。

为了爆除这两个柱子，将炸药放在预先在柱子上钻的孔里面。

柱子然后再用几层保护材料包裹好，以避免爆炸时的冲击波和碎片影响结构的其他部分。

2. 建筑的特性圣地亚哥旅馆建造于1914年，在1924年又向南扩展了一部分，此部分包括两个分离的结构。

图.1是从南边看旅馆的样子。

注意这张照片，旅馆的第一和第三层被用黑色的布蒙了起来。

这个六层的旅馆是无延性的钢筋混凝土框架结构，其中还有由空心砖构成的填充外墙。

扩展部分的填充墙有两层共203mm厚。

第一层的楼高为6.0m，其他楼盖高为3.2m，顶楼高度为5.13m。

图.2为其中一个扩展部分的第二层。

图.3为对本建筑的实施计划，即瞬间爆除一层相邻的柱A2和A3，以评价其影响。

左图：图.1 圣地亚哥旅馆的南端视角，本论文研究其中心结构右图：图.2 扩展结构的第二层（南端视角）下图：图.3 拟对旅馆南扩展部分实施的柱的移除计划，第一层要被移除的柱用叉号标出如图.3所示楼盖系统纵向（南北向）有一个托梁。

根据两个混凝土构件受压的实验结果，对一个标准的混凝土柱，受压承载力为31MPa。

混凝土的弹性模量大概为26300MPa左右。

同样，通过横截面12.7mm的钢筋受拉实验，其屈服和极限抗拉强度分别为427和600MPa。

钢筋的极限变形为0.17。

钢筋的弹性模量近似为200000MPa。

这个建筑按计划将被爆破摧毁。

作为摧毁的一个步骤，第一层和第三层的填充墙被移除。

移除时上面没有活荷载。

所有的非结构部件包括隔墙、管道设备、家具都被事先搬走了，只有梁、柱、楼板梁和在边梁上的填充墙被留下。

3. 传感器布置混凝土和钢筋的应变传感器是用来测量梁和柱的应变变化的。

线性电位计用来测量整体和局部变形。

混凝土应变测量仪常900mm，最大应变为±0.02.钢筋应变测量仪应变极限为±0.2。

应变测量仪可以带到几百千赫兹。

电位计用来测量建筑中梁沿一端的转动和整体位移，这些以后将讲到。

电位计的分辨率为0.01mm，最大速度为1.0m/s，实验中最大记录速度为0.35m/s。

4. 有限元模型通过有限单元法，在软件SAP2000【8】中生成一个建筑模型。

梁和柱都被抽象成Bernoulli单元。

T和L型梁的翼缘计算宽度为四倍的较厚板的厚度【5】。

塑性铰可以发生在任何钢筋可能发生屈服的地方，包括单元的端点、加筋肋分离点和弯矩的屈服点。

在分析中，塑性铰的范围是构件高度的一半。

现行版本的SAP2000不能计算出单元斜裂缝的构成。

为了得出正确的构件挠曲刚度，反复做以下步骤：首先假设建筑的所有单元都是没有裂缝的；然后，需要弯矩同构件的出现裂缝的弯矩相比较。

分别降低板厚和梁的惯性矩35%，使需求弯矩大于裂缝出现弯矩。

梁外部出现裂缝的正负弯矩分别为58.2knM和37.9knM。

需要注意的是柱子没有裂缝出现。

再后，再按以上方法重新分析建筑和弯矩简图。

重复这些步骤直到所有的裂缝区域被鉴定和用模型表示出来。

除了两端区域建筑结构里的梁上部不配筋（图.4）。

例如，梁A1-A2在距A1点305mm以后，其上部不配筋（如图.4和5）。

为了确定出可能丧失挠曲强度的截面位置，将裂纹铰布置在上部没有配筋的可能的弯曲破坏点上。

塑性铰的挠曲强度设为于Mcr相等，当所受的弯矩达到Mcr时，该截面即发生破坏。

图.4 二层的梁A3-B3和梁A1-A2详细配筋情况楼盖系统有沿纵向（南北向）的次梁。

图.6所示为一典型的楼盖的横截面。

为了计算出次梁和板的可能的非线性响应，用梁单元为楼盖建立模型。

次梁按T型梁计算，翼缘的计算宽度为各自板厚的四倍【5】。

选取轴2和轴3的纵梁和其之间的一个宽20英寸的梁间的格栅为板的计算模型。

为了给出板沿横向的计算模型，同样用一个宽20英寸于横梁平行的梁。

在方形的板中其剪力流和梁单元的中的不一样。

所以其扭转刚度取为整个截面刚度的一半【9】。

图.5 梁的上部配筋弯曲位置（于梁A1-A2相似，在邻近建筑靠近柱A1的地方）图.6 典型的楼盖的次梁系统图.7 实验和分析的第二层柱A3的竖向位移建筑的2、4、5、6层有填充墙，并在门窗等开口位置有过梁，如前面提到的第1、三层的填充墙，在爆除前已经拆掉。

填充墙是用良好的空隙砖砌成的，空心砖的净空是其总大小的一半。

填充墙的平面效应增强了建筑的刚度和强度，并且影响建筑的对荷载反应即变形。

如果忽略墙的影响将得不到准确的建筑的刚度和强度。

在SAP2000中考虑了两种填充墙的形式：一种是用平面框架模型（模型A），另一种是FEMA365【10】中建议的受压杆件模型（模型B）。

4.1模型A是平面框架模型，但是，现行版本的SAP2000只能计算线性框架模型，不能计算裂缝的发展情况。

填充墙的抗拉强度大概为26psi，弹性模量为644ksi【10】。

由于裂缝的发展对填充墙的刚度影响很大，重复以下步骤来计算裂缝的形成：（1）假设填充墙是线性的而且没有开裂，运行非线性历史分析。

由于梁中的塑性铰的存在，梁中弯矩大于裂缝出现弯矩时候，对截面惯性矩有一个折减。

（2）判定填充墙出现的依据是看其应力于墙的抗拉强度大小关系。

（3）节点在拉应力大于抗拉强度的地方分离。

重复上面的步骤直到裂缝区域被确定。

4.2.模型B（受压杆件模型）如FEMA356【10】所述用受压杆件来代替填充墙，杆件的方向根据移除柱后的结构变形形式和开口位置确定。

4.3.柱的移除按以下步骤模拟柱的移除。

结构是在只受永久荷载下分析的，内力在柱端测定，将随着柱的移除而卸荷。

模型的建立是在移除第一层的柱A2、A3的情况下进行的。

结构同样是在永久荷载下进行静态分析的。

在此情况下，测得的柱端内力被当成永久外部荷载施加在结构上。

注意此分析结果跟第一步的分析是等价的。

第二步中大小相等方向相反的柱端力，被瞬间施加在原柱的位置上，然后进行动态分析。

4.4.实验和分析结果的比较结构计算最大竖向位移在第二层的柱A3上，图7所示为按模型A的实验和分析的梁A3竖向位移的比较。

实验数据是用三个粘在A3两端的传感器记录的。

实验和分析得到的最大位移分别是6.1mm和6.4mm，相差尽为4%。

实验和分析的位移产生所用时间分别为0.069S和0.066S。

分析结果显示永久位移为5.3mm，比实验结果小14%，实验结果为6.1mm。

图.8.第二层的柱A3在模型A和B下分别沿时间的竖向位移图.8.比较了第二层的柱A3分别在模型A和B下分析的沿时间的竖向位移。

由图中可以看出，按受压杆件模型（模型B）得出的最大竖向位移为11.4mm,比用模型A得出的结果高出约80%。

在图.7.可以看出按模型A得出的结果与实验结果是想接近的，B模型得出的结构变形过高。

如果最大竖向位移偏大的话，填充墙开裂情况会更加严重，更偏向于受压杆件形成，模型A和模型B得出结果差异将减小。

图.9.比较了用模型A时第二层的柱A2的分析和实验的位移值。

同样，第一次达到最大位移值的实验和分析值非常接近，分析的永久位移值比实验的位移值略微低些。

图.10.所示为根据模型A得出的最大竖向位移的结构变形放大200倍后的情况。

图.9.第二层的柱A2竖向位移实验和分析结果比较图.10.按模型A，FEM分析的结构变形形式（第二层的实验得出变形形式也给出）通过实测得的变形形式在图中也用实线标出了。

在二层的梁A1-A2、A3-B3的上下端部应力重分配复杂的地方共用了14个电位计。

梁上部和对应的下部电位计接在一起用来测量梁的扭转变形。

用上下端部电位计的差值除以电位计的距离（沿梁高）。

分析推算的二层梁端部变形曲线如图中的曲线所示。

由图可以看出，分析的变形梁的变形曲线跟实验所得结果非常吻合。

根据模型A分析结果表明预示钢筋屈服的塑性铰只有两个，四个没有上部配筋的截面，到达屈服极限而开裂。

图.10.给出了所有的塑性铰及开裂位置。

Response of a reinforced concrete infilled-frame structure to removal of two adjacent columnsMehrdad Sasani_Northeastern University, 400 Snell Engineering Center, Boston, MA 02115,United StatesReceived 27 June 2007; received in revised form 26 December 2007; accepted24 January 2008Available online 19 March 2008AbstractThe response of Hotel San Diego, a six-story reinforced concrete infilled-frame structure, is evaluated following the simultaneous removal of two adjacent exterior columns. Analytical models of the structure using the Finite Element Method as well as the Applied Element Method are used to calculate global and local deformations. The analytical results show good agreement with experimental data. The structure resisted progressive collapse with a measured maximum vertical displacement of only one quarter of an inch (6.4 mm). Deformation propagation over the height of the structure and the dynamic load redistribution following the column removal are experimentally and analytically evaluated and described. The difference between axial and flexural wave propagations is discussed. Three-dimensional Vierendeel (frame) action of the transverse and longitudinal frames with the participation of infill walls is identified as the major mechanism for redistribution of loads in the structure. The effects of two potential brittle modes of failure (fracture of beam sections without tensile reinforcement and reinforcing bar pull out) are described. The response of the structure due to additional gravity loads and in the absence of infill walls is analytically evaluated.c 2008 Elsevier Ltd. All rights reserved.Keywords: Progressive collapse; Load redistribution; Load resistance; Dynamic response; Nonlinear analysis; Brittle failure1. IntroductionAs part of mitigation programs to reduce the likelihood of mass casualties following local damage in structures, the General Services Administration [1] and the Department of Defense [2] developed regulations to evaluate progressive collapse resistance of structures. ASCE/SEI 7 [3] defines progressive collapse as the spread of an initial local failure from element to element eventually resulting in collapse of an entire structure or a disproportionately large part of it. Following the approaches proposed by Ellingwood and Leyendecker [4], ASCE/SEI 7 [3] defines two general methods for structural design of buildings to mitigate damage due to progressive collapse: indirect and direct design methods. General building codes and standards [3,5] use indirect design by increasing overall integrity of structures. Indirect design is also used in DOD [2]. Although the indirect design method can reduce the risk of progressive collapse [6,7] estimation ofpost-failure performance of structures designed based on such a method is not readily possible. Oneapproach based on direct design methods to evaluate progressive collapse of structures is to study the effects of instantaneous removal of load-bearing elements, such as columns. GSA [1] and DOD [2] regulations require removal of one load bearing element. These regulations are meant to evaluate general integrity of structures and their capacity of redistributing the loads following severe damage to only one element. While such an approach provides insight as to the extent to which the structures are susceptible to progressive collapse, in reality, the initial damage can affect more than just one column. In this study, using analytical results that are verified against experimental data, the progressive collapse resistance of the Hotel San Diego is evaluated, following the simultaneous explosion (sudden removal) of two adjacent columns, one of which was a corner column. In order to explode the columns, explosives were inserted into predrilled holes in the columns. The columns were then well wrapped with a few layers of protective materials. Therefore, neither air blast nor flying fragments affected the structure.2. Building characteristicsHotel San Diego was constructed in 1914 with a south annex added in 1924. The annex included two separate buildings. Fig. 1 shows a south view of the hotel. Note that in the picture, the first and third stories of the hotel are covered with black fabric. The six story hotel had a non-ductile reinforced concrete (RC) frame structure with hollow clay tile exterior infill walls. The infills in the annex consistedof two wythes (layers) of clay tiles with a total thickness of about 8 in (203 mm). The height of the first floor was about 190–800 (6.00 m). The height of other floors and that of the top floor were 100–600 (3.20 m) and 160–1000 (5.13 m), respectively. Fig. 2 shows the second floor of one of the annex buildings. Fig. 3 shows a typical plan of this building, whose response following the simultaneous removal (explosion) of columns A2 and A3 in the first (ground) floor is evaluated in this paper. The floor system consisted of one-way joists running in the longitudinal direction (North–South), as shown in Fig. 3. Based on compression tests of two concrete samples, the average concrete compressive strength was estimated at about 4500 psi (31 MPa) for a standard concrete cylinder. The modulus of elasticity of concrete was estimated at 3820 ksi (26 300 MPa) [5]. Also, based on tension tests of two steel samples having 1/2 in (12.7 mm) square sections, the yield and ultimate tensile strengths were found to be 62 ksi (427 MPa) and 87 ksi (600 MPa), respectively. The steel ultimate tensile strain was measured at 0.17. The modulus of elasticity of steel was set equal to 29 000 ksi (200 000 MPa). The building was scheduled to be demolished by implosion. As part of the demolition process, the infill walls were removed from the first and third floors. There was no live load in the building. All nonstructural elements including partitions, plumbing, and furniture were removed prior to implosion. Only beams, columns, joist floor and infill walls on the peripheral beams were present.3. SensorsConcrete and steel strain gages were used to measure changes in strains of beams and columns. Linear potentiometers were used to measure global and local deformations. The concrete strain gages were 3.5 in (90 mm) long having a maximum strain limit of ±0.02. The steel strain gages could measure up to a strain of ±0.20. The strain gages could operate up to a several hundred kHz sampling rate. The sampling rate used in the experiment was 1000 Hz. Potentiometers were used to capture rotation (integral of curvature over a length) of the beam end regions and global displacement in the building, as described later. The potentiometers had a resolution of about 0.0004 in (0.01 mm) and a maximum operational speed of about 40 in/s (1.0 m/s), while the maximum recorded speed in the experiment was about 14 in/s (0.35 m/s).4. Finite element modelUsing the finite element method (FEM), a model of the building was developed in the SAP2000 [8] computer program. The beams and columns are modeled with Bernoulli beam elements. Beams have T or L sections with effective flange width on each side of the web equal to four times the slab thickness [5]. Plastic hinges are assigned to all possible locations where steel bar yielding can occur, including the ends of elements as well as the reinforcing bar cut-off and bend locations. The characteristics of the plastic hinges are obtained using section analyses of the beams and columns and assuming a plastic hinge length equal to half of the section depth. The current version of SAP2000 [8] is not able to track formation of cracks in the elements. In order to find the proper flexural stiffness of sections, an iterative procedure is used as follows. First, the building is analyzed assuming all elements are uncracked. Then, moment demands in the elements are compared with their cracking bending moments, Mcr . The moment of inertia of beam and slab segments are reduced by a coefficient of 0.35 [5], where the demand exceeds the Mcr. The exterior beam cracking bending moments under negative and positive moments, are 516 k in (58.2 kN m) and 336 k in (37.9 kN m), respectively. Note that no cracks were formed in the columns. Then the building is reanalyzed and moment diagrams are re-evaluated. This procedure is repeated until all of the cracked regions are properly identified and modeled.The beams in the building did not have top reinforcing bars except at the end regions (see Fig. 4). For instance, no top reinforcement was provided beyond the bend in beam A1–A2, 12 inches away from the face of column A1 (see Figs. 4 and 5). To model the potential loss of flexural strength in those sections, localized crack hinges were assigned at the critical locations where no top rebar was present. Flexural strengths of the hinges were set equal to Mcr. Such sections were assumed to lose their flexural strength when the imposed bending moments reached Mcr.The floor system consisted of joists in the longitudinal direction (North–South). Fig. 6 shows the cross section of a typical floor. In order to account for potential nonlinear response of slabs and joists, floors are molded by beam elements. Joists are modeled with T-sections, having effective flange width on each side of the web equal to four times the slab thickness [5]. Given the large joist spacing between axes 2 and 3, two rectangular beam elements with 20-inch wide sections are used between the joist and the longitudinal beams of axes 2 and 3 to model the slab in the longitudinal direction. To model the behavior of the slab in the transverse direction, equally spaced parallel beams with 20-inch wide rectangular sections are used. There is a difference between the shear flow in the slab and that in the beam elements with rectangular sections modeling the slab. Because of this, the torsional stiffness is setequal to one-half of that of the gross sections [9].The building had infill walls on 2nd, 4th, 5th and 6th floors on the spandrel beams with some openings (i.e. windows and doors). As mentioned before and as part of the demolition procedure, the infill walls in the 1st and 3rd floors were removed before the test. The infill walls were made of hollow clay tiles, which were in good condition. The net area of the clay tiles was about 1/2 of the gross area. The in-plane action of the infill walls contributes to the building stiffness and strength and affects the building response. Ignoring the effects of the infill walls and excluding them in the model would result in underestimating the building stiffness and strength.Using the SAP2000 computer program [8], two types of modeling for the infills are considered in this study: one uses two dimensional shell elements (Model A) and the other uses compressive struts (Model B) as suggested in FEMA356 [10]guidelines.4.1. Model A (infills modeled by shell elements)Infill walls are modeled with shell elements. However, the current version of the SAP2000 computer program includes only linear shell elements and cannot account for cracking. The tensile strength of the infill walls is set equal to 26 psi, with a modulus of elasticity of 644 ksi [10]. Because the formation ofcracks has a significant effect on the stiffness of the infill walls, the following iterative procedure is used to account for crack formation:(1) Assuming the infill walls are linear and uncracked, a nonlinear time history analysis is run. Note that plastic hinges exist in the beam elements and the segments of the beam elements where moment demand exceeds the cracking moment have a reduced moment of inertia.(2) The cracking pattern in the infill wall is determined by comparing stresses in the shells developed during the analysis with the tensile strength of infills.(3) Nodes are separated at the locations where tensile stress exceeds tensile strength. These steps are continued until the crack regions are properly modeled.4.2. Model B (infills modeled by struts)Infill walls are replaced with compressive struts as described in FEMA 356 [10] guidelines. Orientations of the struts are determined from the deformed shape of the structure after column removal and the location of openings.4.3. Column removalRemoval of the columns is simulated with the following procedure.(1) The structure is analyzed under the permanent loads and the internal forces are determined at the ends of the columns, which will be removed.(2) The model is modified by removing columns A2 and A3 on the first floor. Again the structure is statically analyzed under permanent loads. In this case, the internal forces at the ends of removed columns found in the first step are applied externally to the structure along with permanent loads. Note that the results of this analysis are identical to those of step 1.(3) The equal and opposite column end forces that were applied in the second step are dynamically imposed on the ends of the removed column within one millisecond [11] to simulate the removal of the columns, and dynamic analysis is conducted.4.4. Comparison of analytical and experimental resultsThe maximum calculated vertical displacement of the building occurs at joint A3 in the second floor. Fig. 7 shows the experimental and analytical (Model A) vertical displacements of this joint (the AEM results will be discussed in the next section). Experimental data is obtained using the recordings of three potentiometers attached to joint A3 on one of their ends, and to the ground on the other ends. The peak displacements obtained experimentally and analytically (Model A) are 0.242 in (6.1 mm) and 0.252 in (6.4 mm), respectively, which differ only by about 4%. The experimental and analytical times corresponding to peak displacement are 0.069 s and 0.066 s, respectively. The analytical results show apermanent displacement of about 0.208 in (5.3 mm), which is about 14% smaller than the corresponding experimental value of 0.242 in (6.1 mm).Fig. 8 compares vertical displacement histories of joint A3 in the second floor estimated analytically based on Models A and B. As can be seen, modeling infills with struts (Model B) results in a maximum vertical displacement of joint A3 equal to about 0.45 in (11.4 mm), which is approximately 80% larger than the value obtained from Model A. Note that the results obtained from Model A are in close agreement with experimental results (see Fig. 7), while Model B significantly overestimates the deformation of the structure. If the maximum vertical displacement were larger, the infill walls were more severely cracked and the struts were more completely formed, the difference between the results of the two models (Models A and B) would be smaller.Fig. 9 compares the experimental and analytical (Model A) displacement of joint A2 in the second floor. Again, while the first peak vertical displacement obtained experimentally and analytically are in good agreement, the analytical permanent displacement under estimates the experimental value.Analytically estimated deformed shapes of the structure at the maximum vertical displacement based on Model A are shown in Fig. 10 with a magnification factor of 200. The experimentally measured deformed shape over the end regions of beams A1–A2 and A3–B3 in the second floorare represented in the figure by solid lines. A total of 14 potentiometers were located at the top and bottom of the end regions of the second floor beams A1–A2 and A3–B3, which were the most critical elements in load redistribution. The beam top and corresponding bottom potentiometer recordings were used to calculate rotation between the sections where the potentiometer ends were connected. This was done by first finding the difference between the recorded deformations at the top and bottom of the beam, and then dividing the value by the distance (along the height of the beam section) between the two potentiometers. The expected deformed shapes between the measured end regions of the second floor beams are shown by dashed lines. As can be seen in the figures, analytically estimated deformed shapes of the beams are in good agreement with experimentally obtained deformed shapes.Analytical results of Model A show that only two plastic hinges are formed indicating rebar yielding. Also, four sections that did not have negative (top) reinforcement, reached cracking moment capacities and therefore cracked. Fig. 10 shows the locations of all the formed plastic hinges and cracks.。