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1、Unit 11 Unit 11 第第十一十一单单元元Steel MembersSteel Members钢钢构件构件Tension members are found in bridge and roof trusses , towers, bracing systems, and in situation where they are used as tie rods（连杆）.The selection of a section to be used as a tension member is one of the simplest problems encountered in desi
2、gn. As there is no danger of buckling, the designer needs only to compute the factored force（分解力）to be carried by the member and divide that force by a design stress to determine the effective cross-sectional area required1. Tension Members. Then it is necessary to select a steel section that provid
3、es the required area. Though these introductory calculations for tension members are quite simple, they do serve（完成）the important tasks of getting students started with design ideas and getting their “feet wet” regarding（涉足于）the massive LRFD Manual. 受拉构件在桥梁和屋架、塔、支撑系统以及用作连杆时被见到。用作受拉构件的截面选择是设计中遇到的最简单的
4、问题之一。因为没有屈曲的危险，设计者只需要计算由该构件承受的分解力，并将该力除以设计应力以确定所需的有效横截面面积。然后有必要选择一个钢截面，它提供了需要的面积。尽管这些关于受拉构件的介绍性的计算非常简单，但它们确实完成了这样一个重要的目标，即使学生开始拥有设计的概念，并使他们涉足于大量的LRFD手册。n nLoad Resistance Factor Design(LRFD)n n 钢结构设计规范钢结构设计规范(荷载抗力系数设计荷载抗力系数设计 )n nAllowable Stress Design (ASD) One of the simplest forms of tension mem
5、bers is the circular rod, but there is some difficulty in connecting it to many structures. The rod has been used frequently in the past, but has only occasional uses today in bracing systems, light trusses, and in timber construction. One important reason rods are not popular with designers is that
6、 they have been used improperly so often in the past that they have a bad name; however, if designed and installed correctly, they are satisfactory for many situations. 受拉构件最简单的形式之一是圆钢，但是将其与很多结构连接有一些困难。过去常常采用圆钢，但是如今只偶然用于支撑系统、轻质桁架以及木结构。圆钢不受设计者欢迎的一个重要原因是过去常常被不恰当地使用，以至于落得坏名声；但是如果正确地设计和安装，它们在很多情况下是令人满意的
7、。 The average size rod has very little stiffness and may quite easily sag under its own weight,injuring the appearance of the structure. The threaded rods formerly used in bridges often worked loose and rattled（发出嘎嘎声）.Another disadvantage of rods is the difficulty of fabricating them with the exact
8、lengths required and the consequent difficulties of installation. 通常尺寸的圆钢几乎没有刚度，并且在自重下很容易下垂，因而破坏了结构的外观。以前用于桥梁的有螺纹的圆钢常常松掉，并发出嘎嘎声。圆钢的另一个缺点是难以按需要的精确长度来制作，随之发生的是安装的困难。When rods are used in wind bracing, it is a good practice to produce initial tension in them, as this will tighten up the structure and r
9、educe rattling and swaying. To obtain initial tension the member may be detailed（设计）shorter than their required lengths, a method that gives the steel fabricator very little trouble.A common rule of thumb（单凭经验的方法）used is to detail the rods about 1/16 in. short for each 20 ft. of length. Another very
10、 satisfactory method involves tightening the rods with some sort of sleeve nut（轴套套螺母）or turnbuckle（套筒螺母）.Part 8 of the LRFD Manual provides detailed information for these devices.当圆钢被用作抗风支撑时，一个很好的做法是使它们产生初张力，因为这将拉紧结构，并减少发出嘎嘎声和摇晃。为获得初张力，杆件可以设计得比它们需要的长度短，该法对钢材的制作者来说几乎没什么麻烦。一个常用的经验法是设计该圆钢时每20英尺的长度缩短约1/
11、16英寸, 另一个非常令人满意的方法包括采用某种套筒螺母拉紧圆钢。LRFD手册的第八部分提供了有关这些方法的详细信息。The preceding discussion on rods should illustrate why rolled shapes（轧制型钢）such as angles have supplantedrods for most applications. In the early days of steel structures, tension members consisted of rods, bars,and perhaps cables.Today, alth
12、ough the use of cables is increasing for suspended-roof（悬索屋顶）structures, tension members usually consist of single angles, double angles, tees,channels（槽钢）,W sections（型钢）,or sections built up from plates（薄钢板）or rolled shapes. These members look better than the old ones, are stiffer, and are easier t
13、o connect. Another type of tension sectionoften used is the welded tension plate or flat bar（扁钢）,which is very satisfactory for use in transmission towers（发射塔）,signs（广告牌）,foot bridges（人行桥）,and similar structures.前面关于圆钢的讨论应该阐明为什么诸如角钢的轧制型钢已在多数应用中代替了圆钢。在早期的钢结构中，受拉构件包括圆钢、型钢以及可能是索。今天尽管索在悬索屋顶结构中的使用不断增加，受拉
14、构件通常包括单角钢、双角钢、T形钢、槽钢、W型钢，或由薄钢板或轧制型钢组合成的型钢。这些构件看上去比老的更好、更结实、更容易连接。另一种常用的受拉构件是焊接的受拉薄钢板或者是扁钢，它在用于发射塔、广告牌、人行桥以及类似的结构中是非常令人满意的。The tension members of steel roof trusses may consist of single angles as small as 21/2 2 1/4 for minor members. A more satisfactory member is made from two angles placed back to
15、 back with sufficient space between them to permit the insertion of plates(called gusset plates节点板)for connection purposes. Where steel sections（型钢）are used back-to-back in this manner, they should be connected every 4or 5 ft. to prevent rattling, particularly in bridge trusses. Single angles and do
16、uble angles are probably the most common types of tension members in use. Structural tees make very satisfactory chord members for welded trusses because web members can conveniently be connected to them.钢屋架的受拉构件由单角钢组成，对次要构件其尺寸可小至21/22 1/4 。一种较满意的构件是由两根背对背放置、中间有足够的间距允许插入金属板（称为节点板）以用于连接的角钢制成。在型钢采用背对背
17、的方式处，它们应该每隔4或5英尺连接一下以免发出嘎嘎声，特别是在桥梁桁架中。单角钢和双角钢可能是受拉构件中最常用的类型。对焊接桁架用结构T形钢可得到满意的弦杆，因为腹杆能方便地与它们连接起来。 For bridges and large roof trusses tension members may consist of channels, W or S shapes, or even sections built up from some combination of angles, channels, and plates. Single channels are frequently
18、used, as they have little eccentricity and are conveniently connected. Although, for the same weight, W sections are stiffer than S sections, they may have a connection disadvantage in their varying depths. For instance, the W12 79, W12 72, and W12 65 all have slightly different depths (12.38 in., 1
19、2.25 in., and 12.12 in., respectively) while the S sections of a certain nominal size all have the same depths. For instance, the S12 50, the S12 40.8 and the S12 35 all have 12.00 in. depths.对桥梁和大型屋架，受拉构件可以由槽钢、W型钢或S型钢，或者甚至由角钢、槽钢和薄钢板的某种组合而成的型钢组成。单槽钢常常被采用，因为它们几乎没有偏心，且容易连接。尽管相同重量的W型钢比S型钢更结实，但W型钢由于其变化的
20、厚度可能存在连接上的不利条件。例如W12 79、 W12 72以及W12 65都有略微不同的厚度（分别为12.38英寸、12.25英寸以及12.12英寸），而有着某个名义尺寸的S型钢都有相同的厚度。例如，S12 50、S12 40.8 以及S12 35，其厚度都为12英寸。 Although single structural shapes are a little more economical than built-up sections, the latter are occasionally used when the designer is unable to obtain suff
21、icient area or rigidity from single shapes. Where built-up sections are used it is important to remember that field（现场）connections will have to be made and paint applied; therefore, sufficient space must be available to accomplish these things.尽管单个结构型钢比组合的型钢稍微更经济一些，但是当设计者采用单个型钢不能够得到足够的面积或刚度时，偶然也会采用后
22、者。在采用组合型钢处，要记住很重要的一点是将不得不进行现场连接，并进行涂漆；因此，必须获得足够的空间来完成这些事情。n nMembers consisting of more than one section need to be tied together. Tie plates(also called tie bars) located at various intervals or perforated cover plates serve to hold the various pieces in their correct positions. These plates serve
23、to correct any unequal distribution of loads between the various parts. They also keep the slenderness ratios (to be discussed) of the individual parts within limitation and they may permit easier handling of the built-up members.Long individual members such as angles may be inconvenient to handle d
24、ue to flexibility,but when four angles are laced together into one member, as shown in Fig. 11-1, the member has considerable stiffness. None of the intermittent tie plates may be considered to increase the effective areas of the sections. As they do not theoretically carry portions of the force in
25、the main sections, their sizes are usually governed by specifications and perhaps by some judgment on the designers part. Perforated cover plates are an exception to this rule, as part of their areas can be considered as being effective in resisting axial load. 由几个截面组成的构件需要连接在一起。以不同的间隔设置的连接板（也称为连杆）或
26、多孔盖板用以保持不同的构件均在其恰当的位置上。这些板用以调整不同部分之间的荷载分配的不平衡。它们也使单个部分的长细比（将要讨论）保持在限制的范围内，这样他们可以允许较容易地处理组合构件。长长的单个构件如角钢，由于易弯性可能处理时有困难，但是当四根角钢绑扎成一根构件时，如图11-1所显示的，该构件具有相当大的刚度。可以不考虑间断的连接板对截面的有效面积的增加。因为他们理论上不承受主截面中的部分力，它们的尺寸通常由规范以及可能根据设计者方面的某些判断来决定。多孔盖板则是该规则的例外，因为它们的部分面积在抵抗轴向荷载时可认为是有效的。 A few of the various types of te
27、nsion members in general use are illustrated in Fig. 11-1. In this figure the dotted lines represent the intermittent tie plates or bars used to connect the shapes.常用的不同类型的一些受拉构件被举例在图11-1中。在该图中虚线代表了用以连接型钢的间断的连接板或连杆。 Steel cables are made with special steel alloy wire ropes（特种合金钢丝绳） which are cold-dr
28、awn to the desired diameter. The resulting wires with strengths of about 200,000 to 250,000 psi can be economically used for suspension bridges, cable supported（悬索）roofs, ski lifts（运送滑雪者上山坡的吊索设备）, and other similar applications. 钢索是由冷拉至需要直径的特种合金钢丝绳制成的。形成的具有强度约为200,000到250,000 psi的钢丝能经济地用于悬索桥、悬索屋顶、运送
29、滑雪者上山坡的吊索设备以及其他类似的应用。 Normally, to select a cable tension member the designer uses a manufacturers catalog. From the catalog the yield stress of the steel and the cable size required for the design force are determined. It is also possible to select clevises（马蹄钩）or other devices to use for connector
30、s（连接器）at the cable ends.通常，为选择索的受拉构件，设计者采用制造商的产品目录。从产品目录中可以确定钢材的屈服应力和设计力所需要的索的尺寸。也有可能选择马蹄钩或其他的装置用作索端的连接器。2.Axially Loaded Compression Members There are several types of compression members, the column being the best known.Among the other types are the top chords of trusses, bracing members, the comp
31、ression flanges of rolled beams and built-up beam sections,and members that are subjected simultaneously to bending and compressive loads. Columns are usually thought of as being straight vertical members whose lengths are considerably greater than their thicknesses. Short vertical members subjected
32、 to compressive loads are often called struts（支柱）or simply compression members; however, the terms column and compression member will be used interchangeably in the pages that follow.有多种受压构件，其中柱子是最知名的。在其他的类型中有桁架的上弦杆、支撑杆件、轧制梁和组合梁截面的受压翼缘以及同时承受弯曲荷载和压力荷载的构件。柱子通常被认为是直的竖向构件，其长度比它的厚度大得多。承受压力的短的竖向构件常常称为支柱或简
33、单地称为受压构件；但是术语柱子和受压构件在下面的页面中将被交替地使用。 There are three general modes by which axially loaded columns can fail. These are flexural buckling, local buckling and torsional buckling. These modes of buckling are briefly defined below. (1)Flexural buckling (also called Euler buckling欧拉屈曲) is the primary type
34、 of buckling. Members are subject to flexure or bending when they become unstable. (2)Local buckling occurs when some part or parts of the cross section of a column are so thin that they buckle locally in compression before the other modes of buckling can occur. The susceptibility（敏感性）of a column to
35、 local buckling is measured by the width-thickness ratios of the parts of its cross section. (3)Torsional buckling may occur in columns that have certain cross-sectional configurations（外形）. These columns fail by twisting(torsion) or by a combination of torsional and flexural buckling.轴向受力的柱子发生失效有三种一
36、般的模式。它们是弯曲屈曲、局部屈曲和扭转屈曲。这些屈曲模式简单地定义如下：（1）弯曲屈曲（也称为欧拉屈曲）是主要的屈曲类型。当构件变得不稳定时，它们易于弯曲。（2）局部屈曲发生在柱子某部分的横截面太薄了以至于在其他屈曲模式发生之前它们便受压局部屈曲。柱子对局部屈曲的敏感性可以通过该部分的横截面的宽厚比来测得。（3）扭转屈曲可以发生在具有某种横截面外形的柱子中。这些柱子由于扭曲（扭转）或扭转屈曲与弯曲屈曲的组合而失效。 The longer a column becomes for the same cross section the greater becomes its tendency t
37、o buckle and the smaller becomes the load it will support. The tendency of a member to buckle is usually measured by its slenderness ratio, which has previously been defined as the ratio of the length of the member to its least radius of gyration（回转半径）. The tendency to buckle is also affected by suc
38、h factors as the types of end connections, eccentricity of load application, imperfection（缺陷）of column material, initial crookedness（弯曲）of column, residual stresses from manufacture, etc. 相同横截面的柱子越长，则屈曲的趋势越大，它能承受的荷载将越小。构件屈曲的趋势通常根据其长细比来测定，它在先前已定义为构件的长度与它最小的回转半径之比。屈曲的趋势也受到诸如端部连接的类型、荷载施加的偏心距、柱子材料的缺陷、柱子
39、的初始弯曲、制造引起的残余应力等因素的影响。 The loads supported by a building column are applied by the column section above（在.上方）and by the connections of other members directly to the column. The ideal situation is for the loads to be applied uniformly across the column, with the center of gravity（重心）of the loads coin
40、ciding with（与.一致）the center of gravity of the column. Furthermore, it is desirable（希望）for the column to have no flaws（缺陷）, to consist of a homogeneous（均匀的）material, and to be perfectly straight, but these situations are obviously impossible to achieve. 建筑物中的柱子承受的荷载是由其上方的柱子部分和直接与柱子相连的其他构件施加的。理想的情况是该荷
41、载均匀地施加在柱子上，荷载的重心与柱子的重心一致。而且希望柱子没有缺陷、由均匀的材料组成以及是完全笔直的，但是这些情形显然不可能达到。 Loads that are exactly centered（居中）over a column are referred to as axial or concentric（同轴的）loads. The dead loads may or may not be concentrically placed over an interior building column and the live loads may never be centered. For
42、 an outside column the load situation is probably even more eccentric（偏心）, as the center of gravity of the loads will usually fall well on（恰好落在）the inner side of the column. In other words, it is doubtful that a perfect axially loaded column will ever be encountered in practice. 在柱子上精确居中的荷载称为轴向或同轴荷载
43、。恒载可能或不一定同轴地置于建筑屋内部的柱子上，而活载可能永远也不会居中。外部柱子的荷载情形甚至可能更偏心，因为荷载的重心通常恰好落在柱子的内侧。换句话说，在实际中曾遇到一个完全轴向受荷的柱子是令人怀疑的。The other desirable situations are also impossible to achieve because of the following: imperfections of cross-sectional dimensions, residual stresses, holes punched for bolts, erection stresses, a
44、nd transverse loads. It is difficult to take into account all of these imperfections in a formula.由于下列的原因，其他希望的情形也是不可能达到：横截面尺寸的缺陷；残余应力；螺栓冲孔；安装应力；横向荷载。很难在一个公式中考虑所有的这些缺陷。Slight（微小的）imperfections in tension members and beams can be safely disregarded（忽略）as they are of little consequence（后果）. On the oth
45、er hand（相反）, slight defects（缺陷）in columns may be of major significance（重大意义）. A column that is slightly bent at the time it is put in place（就位）may have significant（很大的）bending moments equal to the column load times the initial lateral deflection. 受拉构件和梁中微小的缺陷可以安全地忽略掉，因为它们几乎没有什么后果。相反，柱子中微小的缺陷可能意义重大。柱
46、子就位时的轻微弯曲可能产生很大的弯距，它等于柱子上的荷载乘以初始的横向挠度。 Obviously, a column is a more critical（关键的）member in a structure than is a beam or tension member because minor（较小的） imperfections in materials and dimensions mean a great deal. The fact can be illustrated by a bridge truss that has some of its members damaged
47、by a truck. The bending of tension members probably will not be serious as the tensile loads will tend to straighten（使.伸直）those members; but the bending of any compression members is a serious matter（问题）, as compressive loads will tend to magnify（扩大）the bending in those members. 显然，比起梁或受拉构件，结构中的柱子是较
48、为关键的构件，因为材料和尺寸中较小的缺陷意味着很多。该事实可通过一个桥梁桁架来说明，其有一些被卡车损坏的构件。受拉构件的弯曲可能不是严重的问题，因为拉力往往使这些构件伸直；但是任何受压构件的弯曲则是一个严重的问题。因为压力往往扩大了这些构件中的弯曲。 The preceding（前述的）discussion should clearly show that column imperfections cause them to bend and the designer must consider stresses due to those moments as well as due to a
49、xial loads. 前述的讨论应该清楚地表明是柱子的缺陷使它们弯曲，并且设计者必须考虑由于这些弯距和轴向力引起的应力。The spacing（间距）of columns in plan establishes（确定）what is called a bay（开间）. For instance, if the columns are 20 ft. on center in one direction and 25 ft. in the other direction the bay size is 20 ft 25 ft. Larger bay sizes increase the user
50、s flexibility（灵活性）in space planning. As to economy, a detailed study by John Ruddy indicates that when shallow spread footings（扩展基础）are used, bays with length-to-width ratios of about 1.25 to 1.75 and areas of about 1000 sq ft. are the most cost efficient（费用最经济）. When deep foundations are used, his
51、study shows that larger bay areas are more economical. 平面上柱子的间距确定了什么是一个开间。例如如果柱子在某个方向的中心距为20英尺，在另一个方向的中心距为25英尺，则开间尺寸为20 英尺25英尺。较大的开间尺寸加大了使用者在空间布置时的灵活性。就经济性而言，John Ruddy 进行的详细研究表明，当采用浅的扩展基础时，长宽比约为1.25至1.75的开间、面积约为1000平方英尺是费用最经济的。当采用深基础时，他的研究显示较大的开间面积更经济。Type of Beams Beams are usually said to（被认为） be
52、 members that support transverse loads. They are probably thought of as being used in horizontal positions and subjected to gravity of vertical loads; but there are frequent exceptions rafters（椽子）, for example.3. Beams梁梁的种类 梁通常被认为是支撑横向荷载的构件。它们可能被认为是用于水平位置，并且承受竖向的重力荷载；但是常常有例外-例如椽子。 Among the many typ
53、es of beams are joists（搁栅）, lintels（过梁）, spandrels（托梁）, stringers（纵梁）, and floor beams（横梁）. Joists are the closely spaced beams supporting the floors and roofs of building, while lintels are the beams over openings in masonry walls such as windows and doors.A spandrel beam supports the exterior wall
54、s of buildings and perhaps part of the floor and hallway（走廊）loads. The discovery that steel beams as a part of a structural frame could support masonry walls (together with the development of passenger elevators) is said to（据说）have permitted（使.成为可能）the construction of todays “skyscrapers”. Stringers
55、 are the beams in bridge floors（桥面）running parallel to the roadway（车道） ,whereas floor beams are the larger beams in many bridge floors which are perpendicular to the roadway of the bridge and are used to transfer the floor loads（板面荷载） from the stringers to the supporting girders（大梁）or trusses. The t
56、erm girder is rather loosely（不严格）used but usually indicates a large beam and perhaps one into which smaller beams are framed（构成）. These and other types of beams are discussed in the sections（章节）to follow.在很多梁的类型中有搁栅、过梁、托梁、纵梁和横梁。搁栅是支撑建筑物楼面和屋面的密布梁，而过梁是在砌体墙中诸如窗洞和门洞以上的梁。托梁支撑建筑物的外墙以及可能部分的楼面和走廊的荷载。据说发现钢梁作
57、为结构框架的一部分能支撑砌体墙（加上载人电梯的发展）使今天的摩天大楼的建造成为可能。纵梁是桥面中平行于车道布置的梁，而横梁是很多桥面中垂直于桥梁车道的较大的梁，被用来将纵梁上的板面荷载传递至支撑大梁或桁架。术语大梁的采用是相当的不严格，但通常显示了一根较大的梁，或许是一根由较小的梁构成的大梁。这些和其他类型的梁在下面的章节中进行讨论。Sections Used as Beams The W shapes will normally prove to be the most economical beam sections（型钢梁）and they have largely replaced c
58、hannels and S sections for beam usage. Channels are sometimes used for beams subjected to light loads, such as purlins（檩条）, and in places where clearances available（可利用的净空）require narrow flanges. They have very little resistance to lateral forces and need to be braced. The W shapes have more steel c
59、oncentrated in their flanges than do S beams and thus have larger moments of inertia and resisting moments for the same weights. They are relatively wide（较宽）and have appreciable lateral stiffness. (The small amount of space（范围）devoted to （供.用）S beams in the LRFD Manual clearly shows how much their u
60、se has decreased from former years（前些年）. They are today used primarily for special situation as where narrow flange widths are desirable, or where shearing forces are very high, or where the greater flanges thickness next to the web may be desirable where lateral bending occurs as perhaps with（就象）cr
61、ane rails.)梁的断面W型钢通常证明是最经济的型钢梁，而且作为梁的使用，它们已经大量地代替了槽钢和S型钢。槽钢有时用作支撑轻负荷的梁如檩条，以及用在可利用的净空需要狭窄翼缘的位置处。它们对横向力几乎没有抵抗力，因此需要被支撑。W型钢的钢材比S型钢梁更多的集中在它们的翼缘上，这样同样重量时就有较大的惯性矩和抵抗弯距。它们较宽，并有明显的横向刚度。（在LRFD手册中供S型钢梁用的少量的范围清楚地显示了它们的使用从前些年开始已经降低了多少。今天它们主要被用于特殊的情况如需要狭窄的翼缘宽度处，或者剪力很大处，或者紧接着腹板处发生横向弯曲可能需要较大的翼缘厚度处，大概就象吊车轨道。） Anoth
62、er common type of beam section is the open web joist（空腹搁栅）or bar joist（型钢搁栅）. This type of section which is commonly used to support floor and roof slabs is actually a light shop-fabricated parallel chord truss（平行弦桁架）. It is particularly economical for long spans and light loads.另一个普通的梁截面的类型是空腹搁栅或型钢
63、搁栅。这种通常用来支撑楼面板和屋面板的断面类型实际上是一个轻质的工厂制造的平行弦桁架。它在大跨度和轻负荷时特别经济。作业练习 通过一篇Reading Material的学习，进一步了解钢构件的截面形式及其特点，以及冷加工后的钢构件的特点。Cracking Load and Ultimate Moment 开裂荷载和极限弯矩开裂荷载和极限弯矩 It has been shown that a variation in the external load It has been shown that a variation in the external load acting on a acti
64、ng on a prestressedprestressed beam results in a change in the location of the beam results in a change in the location of the pressure linepressure line（压力线）压力线）for beams in the elastic range. This is a for beams in the elastic range. This is a fundamental principle of fundamental principle of pres
65、tressedprestressed construction. In a normal construction. In a normal prestressedprestressed beam, this shift in the location of the pressure line beam, this shift in the location of the pressure line continues at a relatively uniform rate as the external load is increased, continues at a relativel
66、y uniform rate as the external load is increased, to the point where cracks develop in the tension fiber. After the to the point where cracks develop in the tension fiber. After the cracking load has been exceeded, the rate of movement in the pressure cracking load has been exceeded, the rate of mov
67、ement in the pressure line decreases as additional load is applied, and a significant increase line decreases as additional load is applied, and a significant increase in the stress in the in the stress in the prestressingprestressing tendon and the resultant concrete force tendon and the resultant
68、concrete force begins to take place. begins to take place. Action Under Overload-Cracking Load超载（超载（-开裂荷载）下的反应开裂荷载）下的反应 This change in the action of the internal moment This change in the action of the internal moment continues until all movement of the pressure line ceases. The moment continues unt
69、il all movement of the pressure line ceases. The moment caused by loads that are applied thereaftercaused by loads that are applied thereafter（其后）其后）is offsetis offset（抵消）抵消）entirely by a corresponding and proportional change in the internal entirely by a corresponding and proportional change in the
70、 internal forces, just as in reinforced-concrete construction. This fact, that the forces, just as in reinforced-concrete construction. This fact, that the load in the elastic range and the plastic range is carried by actions that load in the elastic range and the plastic range is carried by actions
71、 that are fundamentally different, is very significant are fundamentally different, is very significant and rendersand renders（使使. .变变得）得）strength computations essential for all designs in order to ensure strength computations essential for all designs in order to ensure that adequate safety factors
72、 exist. This is true even though the stresses that adequate safety factors exist. This is true even though the stresses in the elastic range may conform toin the elastic range may conform to（符合）符合）a recognizeda recognized（公认的）公认的）elastic design criterion.elastic design criterion. 已经显示作用在一根预应力梁上的外部荷载
73、的变化已经显示作用在一根预应力梁上的外部荷载的变化会导致梁在弹性阶段时其压力线位置的变化。这是预应力结构会导致梁在弹性阶段时其压力线位置的变化。这是预应力结构的基本规律。在一根普通的预应力梁中，随着外力的增加，其的基本规律。在一根普通的预应力梁中，随着外力的增加，其压力线位置以一个相对均匀的速度不断移动直至受拉纤维形成压力线位置以一个相对均匀的速度不断移动直至受拉纤维形成开裂的位置。在已经超过开裂荷载后，随着附加荷载的施加，开裂的位置。在已经超过开裂荷载后，随着附加荷载的施加，压力线移动的速度便会降低，且使预应力钢筋束中的应力和合压力线移动的速度便会降低，且使预应力钢筋束中的应力和合成的混凝土
74、力开始发生显著的增加。内部弯矩的作用不断变化成的混凝土力开始发生显著的增加。内部弯矩的作用不断变化直到所有压力线的移动都停止。其后施加的荷载引起的弯矩完直到所有压力线的移动都停止。其后施加的荷载引起的弯矩完全通过相应的、且按比例的内力变化来抵消，正如在钢筋混凝全通过相应的、且按比例的内力变化来抵消，正如在钢筋混凝土的结构中。这个事实，即弹性阶段和塑性阶段的力由基本不土的结构中。这个事实，即弹性阶段和塑性阶段的力由基本不同的作用来传送是非常重要的，且使强度计算变得对所有的设同的作用来传送是非常重要的，且使强度计算变得对所有的设计都是必要的，以确保存在足够的安全系数。这是正确的，即计都是必要的，以
75、确保存在足够的安全系数。这是正确的，即使弹性阶段的应力可能符合公认的弹性设计准则。使弹性阶段的应力可能符合公认的弹性设计准则。 It should be noted that the load deflection curve is close to It should be noted that the load deflection curve is close to a straight line up to the cracking load and that the curve becomes a straight line up to the cracking load and t
76、hat the curve becomes progressivelyprogressively（逐渐）逐渐）more curved as the load is increased above the more curved as the load is increased above the cracking load. The curvaturecracking load. The curvature（弯曲）弯曲）of the load-deflection curve for of the load-deflection curve for loads over the crackin
77、g load is due toloads over the cracking load is due to（由于由于. .所造成的）所造成的）the change the change in the basic internal resisting moment action that counteractsin the basic internal resisting moment action that counteracts（抵消）抵消）the applied loads, as described above, as well as to plastic strains that t
78、he applied loads, as described above, as well as to plastic strains that begin to take place in the steel and the concrete when stressed to high begin to take place in the steel and the concrete when stressed to high levelslevels（受到很大压力）受到很大压力）. . 应该注意到荷载挠度曲线在开裂荷载以内是接近直线应该注意到荷载挠度曲线在开裂荷载以内是接近直线的，且在超过
79、开裂荷载后，该曲线随着荷载的增加逐渐变得更弯的，且在超过开裂荷载后，该曲线随着荷载的增加逐渐变得更弯曲。正如上面所描述的，当超过开裂荷载时，其荷载曲。正如上面所描述的，当超过开裂荷载时，其荷载- -挠度曲线的挠度曲线的弯曲是由于抵消施加荷载的基本内部抵抗弯矩作用的变化以及当弯曲是由于抵消施加荷载的基本内部抵抗弯矩作用的变化以及当受到很大压力时钢筋和混凝土中开始发生的塑性应变所造成的。受到很大压力时钢筋和混凝土中开始发生的塑性应变所造成的。 In some structures it may be essential that the flexural In some structures it
80、 may be essential that the flexural members remain crack free even under significant overloads. This may members remain crack free even under significant overloads. This may be due to the structures being exposed to exceptionally corrosive be due to the structures being exposed to exceptionally corr
81、osive atmospheres during their useful life. In designing atmospheres during their useful life. In designing prestressedprestressed members members to be used in special structures of this type, it may be necessary to to be used in special structures of this type, it may be necessary to compute the l
82、oad that causes cracking of the tensile flange in order to compute the load that causes cracking of the tensile flange in order to ensure that adequate safety against cracking is provided by the design. ensure that adequate safety against cracking is provided by the design. The computation of the mo
83、ment that will cause cracking is also The computation of the moment that will cause cracking is also necessary to ensure compliance necessary to ensure compliance withsomewithsome design criteria design criteria（criterioncriterion的的复数形式）复数形式）. . 在一些结构中，保持受弯构件不开裂可能是在一些结构中，保持受弯构件不开裂可能是必要的，甚至在明显的超载下。这可
84、能是由于结构在它必要的，甚至在明显的超载下。这可能是由于结构在它们的有效寿命期间被暴露在特别腐蚀的空气中的原因。们的有效寿命期间被暴露在特别腐蚀的空气中的原因。当设计预应力构件用于这种类型的特殊结构时，可能有当设计预应力构件用于这种类型的特殊结构时，可能有必要计算引起受拉翼缘开裂的荷载，以确保该设计提供必要计算引起受拉翼缘开裂的荷载，以确保该设计提供足够抵抗开裂的安全性。也有必要计算会导致开裂的弯足够抵抗开裂的安全性。也有必要计算会导致开裂的弯矩，以确保符合一些设计标准。矩，以确保符合一些设计标准。 Many tests have demonstrated that the load-defl
85、ection Many tests have demonstrated that the load-deflection curves of curves of prestressedprestressed beams are approximately linear up to and beams are approximately linear up to and slightly in excess of the load that causes the first cracks in the tensile slightly in excess of the load that cau
86、ses the first cracks in the tensile flange. (The linearity is a function of the rate at which the load is flange. (The linearity is a function of the rate at which the load is applied.) For this reason, normal elastic-design relationships can be applied.) For this reason, normal elastic-design relat
87、ionships can be used in computing the cracking load by simply determining the load used in computing the cracking load by simply determining the load that results in a net tensile stress in the tensile flange (that results in a net tensile stress in the tensile flange (prestressprestress minus minus
88、 the effects of the applied loads) that is equal to the tensile strength of the effects of the applied loads) that is equal to the tensile strength of the concrete. It is customary to assume that the flexural tensile strength the concrete. It is customary to assume that the flexural tensile strength
89、 of the concrete is equal to the modulus of ruptureof the concrete is equal to the modulus of rupture（断裂模量）断裂模量）of the of the concrete when computing the cracking load.concrete when computing the cracking load. 很多试验证明，在引起受拉翼缘最初开裂的很多试验证明，在引起受拉翼缘最初开裂的荷载以内或稍微超过时，预应力梁的荷载荷载以内或稍微超过时，预应力梁的荷载- -挠度曲线是近挠度曲线是近
90、似直线的。（直线性是荷载施加速度的函数。）因此，似直线的。（直线性是荷载施加速度的函数。）因此，通过简单地确定导致受拉翼缘中产生一个净的受拉应力通过简单地确定导致受拉翼缘中产生一个净的受拉应力的荷载（预应力减去施加荷载的效应的荷载（预应力减去施加荷载的效应 ），普通的弹性设），普通的弹性设计关系式能用来计算开裂荷载，其值等于混凝土的抗拉计关系式能用来计算开裂荷载，其值等于混凝土的抗拉强度。当计算开裂荷载时，习惯上假定混凝土的受弯抗强度。当计算开裂荷载时，习惯上假定混凝土的受弯抗拉强度等于混凝土的断裂模量。拉强度等于混凝土的断裂模量。 It should be recognized It sho
91、uld be recognized thatha t the performance of t the performance of bondedbonded（有粘结的）有粘结的）prestressedprestressed member is actually a function member is actually a function of the transformed section rather than the of the transformed section rather than the grossconcretegrossconcrete section. secti
92、on. If it is desirable to make a precise estimate of the cracking load, If it is desirable to make a precise estimate of the cracking load, such as is required in some research work, this effect should be such as is required in some research work, this effect should be considered.considered. 应该承认有粘结
93、的预应力构件的性能实际上是一应该承认有粘结的预应力构件的性能实际上是一个换算截面的函数，不是混凝土毛截面的函数。如果想要对个换算截面的函数，不是混凝土毛截面的函数。如果想要对开裂荷载作一精确估计，例如在一些研究工作中需要的，该开裂荷载作一精确估计，例如在一些研究工作中需要的，该影响应该被考虑。影响应该被考虑。Principles of Ultimate Moments Capacity for Bonded members 有粘结构件极限弯矩能力的规则有粘结构件极限弯矩能力的规则 When When prestressedprestressed flexural members that ar
94、e flexural members that are stronger in shear and bond than in bending are loaded to failure, stronger in shear and bond than in bending are loaded to failure, they fail in one of the following modesthey fail in one of the following modes: : 当剪切和粘结比弯曲强的预应力受弯构件受荷当剪切和粘结比弯曲强的预应力受弯构件受荷失效时，它们会以下列方式中的一种失效
95、：失效时，它们会以下列方式中的一种失效：（1） Failure at cracking load In very lightly prestressed members, the cracking moment may be greater than the moment the member can withstand in the cracked condition and, hence, the cracking moment is the ultimate moment. This condition is rare and is most likely to occur in mem
96、bers that are prestressed concentrically with small amounts of steel. It can also occur in hollow or solid prestressed concrete members that have relatively low levels of reinforcing. Determination of the possibility of this type of failure is Determination of the possibility of this type of failure
97、 is accomplished by comparing the estimated moment accomplished by comparing the estimated moment that would cause cracking to the estimated ultimate that would cause cracking to the estimated ultimate moment, computed as described below. When the moment, computed as described below. When the estima
98、ted cracking load is larger than the computed estimated cracking load is larger than the computed ultimate load, this type of failure would take place if ultimate load, this type of failure would take place if the member were subjected to the required loads. the member were subjected to the required
99、 loads. Because this type of failure is brittle failure, it occurs Because this type of failure is brittle failure, it occurs without warning designs that would yieldwithout warning designs that would yield（产生）产生）this mode of failure should be avoided.this mode of failure should be avoided.（1 1）开裂荷载
100、下的失效开裂荷载下的失效 在施加非常少量预在施加非常少量预应力的构件中，其开裂弯矩可能大于构件在开裂状态下能应力的构件中，其开裂弯矩可能大于构件在开裂状态下能承受的弯矩，因此，开裂弯矩为极限弯矩。这种情况是很承受的弯矩，因此，开裂弯矩为极限弯矩。这种情况是很少的，且在构件中最可能发生用少量钢筋同心地施加预应少的，且在构件中最可能发生用少量钢筋同心地施加预应力。在空心或实心的预应力混凝土构件中也会出现相对低力。在空心或实心的预应力混凝土构件中也会出现相对低等级的钢筋。等级的钢筋。 通过比较引起开裂的弯矩估计值与按下面描通过比较引起开裂的弯矩估计值与按下面描述（的方法）计算的极限弯矩估计值来确定这
101、种失效的可述（的方法）计算的极限弯矩估计值来确定这种失效的可能性。当估计的开裂荷载大于计算的极限荷载，则如果构能性。当估计的开裂荷载大于计算的极限荷载，则如果构件承受要求的荷载，这种失效将会发生。由于这种失效是件承受要求的荷载，这种失效将会发生。由于这种失效是脆性失效，因此其发生时没有警告脆性失效，因此其发生时没有警告- -产生这种失效方式的设产生这种失效方式的设计应该被避免。计应该被避免。（2）Failure due to rupture of steel In lightly reinforced members subjected to ultimate load, the ultima
102、te strength of the steel may be attained before the concrete has reached a highly plastic state. This type of failure is occasionally encountered in the design of structures with very large compression flanges in comparison to the amount of prestressing steel, such as a composite bridge stringer（纵梁）
103、. Computation of the ultimate moment of a member subject to this type of failure can be done with a high precision. The method of computation, as well as the determination of which members are subject to this mode of failure, is described below.（2 2）钢筋断裂引起的失效钢筋断裂引起的失效 在少量加筋并承在少量加筋并承受极限荷载的构件中，钢筋的极限强度
104、可能在混凝土达受极限荷载的构件中，钢筋的极限强度可能在混凝土达到高度塑性状态之前就达到。这种失效在与预应力筋的到高度塑性状态之前就达到。这种失效在与预应力筋的数量相比有很大受压翼缘的结构设计中会偶然遇到，如数量相比有很大受压翼缘的结构设计中会偶然遇到，如一个复合的桥梁纵梁。可以高精度地计算易遭受这种失一个复合的桥梁纵梁。可以高精度地计算易遭受这种失效的构件的极限弯矩。这种计算方法以及确定哪根杆件效的构件的极限弯矩。这种计算方法以及确定哪根杆件易遭受这种失效方式将在下面描述。易遭受这种失效方式将在下面描述。（3）Failure due to strain The usual underreinf
105、orced，prestressed structure that are encountered in practice are of such proportions that, if loaded to ultimate, the steel would be stressed well into（早已进入）the plastic range and the member would evidence（显示）large deflection. Failure of the member will occur when the concrete Failure of the member w
106、ill occur when the concrete attains the maximum strain that it is capable of attains the maximum strain that it is capable of withstanding. It is important to understand that withstanding. It is important to understand that research intoresearch into（. .的调查）的调查）the ultimate bending the ultimate bend
107、ing strength of reinforced and strength of reinforced and prestressedprestressed concrete has concrete has led most investigators to the conclusion that concrete, led most investigators to the conclusion that concrete, of the qualityof the quality（特性）特性）normally encountered in normally encountered i
108、n prestressedprestressed work work（工程）工程）fails when the limiting fails when the limiting strain of 0.003 is attained in the concrete. strain of 0.003 is attained in the concrete. Since the ultimate bending capacity is limited by strain rather than stress in the concrete, it is a function of the elas
109、tic moduli（modulus的复数形式,模量）of the concrete and steel. The magnitude of the ultimate moment for members of this category can also be predicted, as a rule, within the normal tolerance（正常的允许误差）expected in structural design. The ultimate moment of underreinforced sections cannot be predicted with the sa
110、me precision as the lightly reinforced members described above, since the ultimate moments of underreinforced members are a function of the elastic properties of the steel and the effective stresses in the prestressing steel, whereas the ultimate moment capacities of lightly reinforced members are n
111、ot.（3 3）应变引起的失效应变引起的失效 在实践中遇到通常配筋不在实践中遇到通常配筋不足的预应力结构具有这样的尺寸，以至于如果加荷至极限，钢筋足的预应力结构具有这样的尺寸，以至于如果加荷至极限，钢筋的应力早已进入塑性范围，而该构件将显示出很大的挠度。当混的应力早已进入塑性范围，而该构件将显示出很大的挠度。当混凝土达到其能承受的最大应变时，该构件将发生失效。明白对预凝土达到其能承受的最大应变时，该构件将发生失效。明白对预应力钢筋混凝土的极限抗弯强度的调查已经导致多数调查者得到应力钢筋混凝土的极限抗弯强度的调查已经导致多数调查者得到了结论，即当混凝土达到了结论，即当混凝土达到 0.003 0.
112、003的极限应变时，具有在预应力工程的极限应变时，具有在预应力工程中常遇性能的混凝土会失效，这点很重要。由于极限抗弯能力受中常遇性能的混凝土会失效，这点很重要。由于极限抗弯能力受到混凝土中的应变而不是应力的限制，因此，它是混凝土和钢筋到混凝土中的应变而不是应力的限制，因此，它是混凝土和钢筋弹性模量的函数。作为一个规律，这类构件极限弯矩的大小也能弹性模量的函数。作为一个规律，这类构件极限弯矩的大小也能被预测在结构设计所预期的正常的允许误差范围内。被预测在结构设计所预期的正常的允许误差范围内。 配筋不足截配筋不足截面的极限弯矩不能以与上面描述的少量配筋的构件相同的精度来面的极限弯矩不能以与上面描述
113、的少量配筋的构件相同的精度来预测，因为配筋不足的构件的极限弯矩是钢筋弹性性能和预应力预测，因为配筋不足的构件的极限弯矩是钢筋弹性性能和预应力钢筋中的有效应力的函数，而少量配筋构件的极限弯矩能力则不钢筋中的有效应力的函数，而少量配筋构件的极限弯矩能力则不是。是。（4）Failure due to crushing of the concrete Flexural members that have relatively large amounts of prestressing steel or relatively small compressive flanges are referred
114、to as being overreinforced。Overreinforced members, when loaded to destruction, do not attain the large deflections associated with underreinforced members the steel stresses do not exceed the yield point and failure is the result of the concrete being crushed. Computation of the ultimate moments of
115、overreinforced members is done by a trial and error procedure，involving assumed strain patterns，as well as by empirical relationships。（4 4）混凝土压碎引起的失效）混凝土压碎引起的失效 有着相对大量有着相对大量预应力筋或相对小的受压翼缘的受弯构件称为是超配筋的。预应力筋或相对小的受压翼缘的受弯构件称为是超配筋的。当受荷至破坏的超配筋构件没有达到与配筋不足构件有关当受荷至破坏的超配筋构件没有达到与配筋不足构件有关联的大挠度联的大挠度- -钢筋的应力没有超过屈服点
116、，因而失效是混钢筋的应力没有超过屈服点，因而失效是混凝土被压碎的结果。通过试算过程以及经验关系式来计算凝土被压碎的结果。通过试算过程以及经验关系式来计算超配筋构件的极限弯矩，包括假定应变模式。超配筋构件的极限弯矩，包括假定应变模式。 It must be emphasized that there is no clear It must be emphasized that there is no clear distinction between the different classifications of failure listed distinction between the d
117、ifferent classifications of failure listed above. For convenience of design, certain parameters, which are above. For convenience of design, certain parameters, which are a function of the percentage of steel, are used by different a function of the percentage of steel, are used by different authori
118、tiesauthorities（权威）权威）to distinguish between the different types of to distinguish between the different types of failure that would be anticipatedfailure that would be anticipated（预测）预测）. . 必须强调在上面列出的不同的失效类别之间没有必须强调在上面列出的不同的失效类别之间没有明显的区别。为了便于设计，通过不同的权威采用某些参数明显的区别。为了便于设计，通过不同的权威采用某些参数（这些参数是钢筋百分率的函数）
119、来区别被预测的不同类型（这些参数是钢筋百分率的函数）来区别被预测的不同类型的失效。的失效。 In order to simplify the explanation of the theory related to the computation of the ultimate moments, a rectangular section will be assumed throughout the derivation, in order to eliminate the variable（变化因素）of flange width which is frequently encountere
120、d with I or T sections. In addition, the following assumptions, some of which differ slightly from those contained in ACI-318, are made: 为了简化与极限弯矩计算有关的理论的解释，在整个推导的过程中将假定一个矩形截面，以消除翼缘宽度的变化因素，其常常被遇到是I或T形截面。而且，作以下假定，其中一些稍许不同于ACI-318中包括的假定：Plane sections are assumed to remain plane.The stress-strain prop
121、erties of the steel are smooth curves without a definite yield point.The limiting strain of the concrete is equal to 0.0034, regardless of the strength of the concrete.The steel and concrete are completely bonded.假定平截面依然是平面的；假定平截面依然是平面的；钢筋的应力钢筋的应力- -应变特点是光滑的曲线，上面没有确定的屈应变特点是光滑的曲线，上面没有确定的屈服点；服点；混凝土的极限
122、应变等于混凝土的极限应变等于0.00340.0034，不考虑混凝土的强度；，不考虑混凝土的强度；钢筋与混凝土是完全粘结的；钢筋与混凝土是完全粘结的；The stress diagram of the concrete at failure is such that the average concrete stress is 0.80fc and the resultant of the stress in the concrete acts at a distance from the extreme fiber equal to 0.42 of the depth of the compr
123、ession block.The strain in the top fiber under prestress alone is equal to zero.The section is subject to pure bending.The analysis is for the condition of static loads of short duration（持续时间）.在混凝土失效时的应力图中，平均的混凝土应力为在混凝土失效时的应力图中，平均的混凝土应力为0.80 0.80 fcfc，而混凝土中的应力合力则作用在离端部纤维的距离为而混凝土中的应力合力则作用在离端部纤维的距离为0.
124、420.42倍的受压区深度处；倍的受压区深度处；仅在预应力作用下顶部纤维的应变等于零；仅在预应力作用下顶部纤维的应变等于零；截面易遭受纯弯；截面易遭受纯弯；分析是针对静力荷载在短的持续时间下的情况。分析是针对静力荷载在短的持续时间下的情况。 As we stated above, the relationships that were developed are applicable to rectangular sections. These relationships are equally accurate for flanged sections, provided the neutr
125、al axis of the section at ultimate is within the limits of the flange. If the neutral axis falls outside of the flange area, the same strains distribution applied as in the case of rectangular sections, but due to the variable width of the section, the distance to the resultant of the compressive bl
126、ock must be calculated. To facilitate（方便）the calculation of the location of the resultant, the compression block can be assumed to be rectangular rather than curved without introducing significant error（导致重大错误）.正如我们上面所正如我们上面所述述，那些被提出的关系式适用于矩形截，那些被提出的关系式适用于矩形截面。假如在极限状态时截面的中性轴落在翼缘的边界之面。假如在极限状态时截面的中性轴落
127、在翼缘的边界之内，则这些关系式对有翼缘的截面同样得准确。如果中内，则这些关系式对有翼缘的截面同样得准确。如果中性轴落在翼缘区域的外面，则采用与矩形情况中相同的性轴落在翼缘区域的外面，则采用与矩形情况中相同的应变分布，但是由于截面宽度的变化，必须计算（中性应变分布，但是由于截面宽度的变化，必须计算（中性轴）至压力区合力的距离。为了方便计算合力的位置，轴）至压力区合力的距离。为了方便计算合力的位置，可以假定受压区是矩形的，而不是弯曲的，这不会导致可以假定受压区是矩形的，而不是弯曲的，这不会导致重大的错误。重大的错误。 When small quantities of non-prestressed
128、 reinforcement are used in combination with small quantities of prestressed reinforcement, the additional ultimate moment due to the non-prestressed reinforcement can be calculated. For larger amounts of non-prestressed reinforcement or for members with high steel indices（index的复数形式，率）, the moment s
129、hould be determined by trial and error from the basic strain patterns. 当采用少量的非预应力钢筋再加上少量的预应力钢筋，则可以计算由于非预应力钢筋引起的附加的极限弯矩。对较多数量的非预应力钢筋或具有高钢筋率的构件，其弯矩应该根据基本的应变模式通过试算来确定。Examination willExamination will show that small show that small variations invariations in the effective the effective prestressprestre
130、ss have no significant effect on the ultimate strength of have no significant effect on the ultimate strength of prestressedprestressed members. It is important to note that even if errors are made in members. It is important to note that even if errors are made in estimating the losses of estimatin
131、g the losses of prestressprestress, in estimating the stressing, in estimating the stressing（施加应施加应力）力）friction, or even if the stressing is not carried out to a high friction, or even if the stressing is not carried out to a high precision in the field due to poor workmanshipprecision in the field
132、due to poor workmanship（低劣的手艺）低劣的手艺）, the , the effect on the ultimate moment is generally small for flexural members effect on the ultimate moment is generally small for flexural members with bonded tendons.with bonded tendons. 研究显示有效预应力的微小变化对预应力构件的极限研究显示有效预应力的微小变化对预应力构件的极限强度没有显著的影响。很重要地注意到，即使错误地估计
133、了预应强度没有显著的影响。很重要地注意到，即使错误地估计了预应力的损失和施加应力的摩擦，或即使在现场由于低劣的手艺而没力的损失和施加应力的摩擦，或即使在现场由于低劣的手艺而没有高精度地施加应力，对有粘结钢筋束的受弯构件极限弯矩的影有高精度地施加应力，对有粘结钢筋束的受弯构件极限弯矩的影响通常也是小的。响通常也是小的。Principles of Ultimate Moment Capacity for Unbonded Members 无粘结的构件极限弯矩能力的规则无粘结的构件极限弯矩能力的规则BecauseBecause the the prestressingprestressing ten
134、dons can slip (with respect to the concrete) tendons can slip (with respect to the concrete) during loading of an during loading of an unbondedunbonded member, the relationships for ultimate member, the relationships for ultimate moment capacity do not apply moment capacity do not apply to unbondedt
135、o unbonded beams. Because the beams. Because the tendons can slip with respect to the concrete, other variablestendons can slip with respect to the concrete, other variables（变量）变量）affect the ultimate moment capacity of affect the ultimate moment capacity of unbondedunbonded prestressedprestressed co
136、ncrete concrete members.members. 由于在对无粘结的构件加荷期间，施加预应力的钢筋束会相由于在对无粘结的构件加荷期间，施加预应力的钢筋束会相对于混凝土滑移，因此极限弯矩能力的关系式不适用于无粘结的对于混凝土滑移，因此极限弯矩能力的关系式不适用于无粘结的梁。由于该钢筋束会相对于混凝土滑移，因此另外的变量影响了梁。由于该钢筋束会相对于混凝土滑移，因此另外的变量影响了无粘结的预应力混凝土构件的极限弯矩能力。无粘结的预应力混凝土构件的极限弯矩能力。 Variables that affect the ultimate moment capacity of an Varia
137、bles that affect the ultimate moment capacity of an unbondedunbonded beam, but which do not affect bonded beams in beam, but which do not affect bonded beams in the same manner or not at the same manner or not at allall, , include the following:include the following:Magnitude of the effective stress
138、 in the tendons.Magnitude of the effective stress in the tendons.Span to depth ratioSpan to depth ratio（跨高比）跨高比）. .Characteristics of the materials.Characteristics of the materials.Form of loading (shape of the bending moment diagram).Form of loading (shape of the bending moment diagram).ProfileProf
139、ile（断面）断面）of the of the prestressingprestressing tendon. tendon.Friction coefficient between the Friction coefficient between the prestressingprestressing steel and steel and ductduct（导管）导管）. .Amount of bonded non-Amount of bonded non-prestressedprestressed reinforcing. reinforcing. 影响无粘结的梁的极限弯矩能力，但
140、不影响或者根影响无粘结的梁的极限弯矩能力，但不影响或者根本不影响相同方式下的有粘结的梁的变量包括如下：本不影响相同方式下的有粘结的梁的变量包括如下：钢筋束中的有效应力大小；钢筋束中的有效应力大小；跨高比；跨高比；材料特性；材料特性；加荷方式（弯矩图的形状）；加荷方式（弯矩图的形状）；施加预应力的钢筋束的断面；施加预应力的钢筋束的断面；在施加预应力的钢筋和导管之间的摩擦系数；在施加预应力的钢筋和导管之间的摩擦系数；有粘结的非预应力钢筋的数量。有粘结的非预应力钢筋的数量。 A method of computing the ultimate strength of A method of comp
141、uting the ultimate strength of prestressedprestressed members (with members (with unbondedunbonded tendons) that takes into tendons) that takes into account theaccount the variables listed above has been proposed by Pannell. This variables listed above has been proposed by Pannell. This method is ba
142、sed upon experimental data and is considered method is based upon experimental data and is considered slightly conservative.slightly conservative. Pannell Pannell已经建议用以计算考虑上述列出变量的（具已经建议用以计算考虑上述列出变量的（具有无粘结的钢筋束的）预应力构件极限强度的方法。该有无粘结的钢筋束的）预应力构件极限强度的方法。该法是基于试验数据，并且考虑时稍有保守。法是基于试验数据，并且考虑时稍有保守。It It should b
143、e recognized that the ultimate moment capacity of a should be recognized that the ultimate moment capacity of a member stressed with member stressed with unbondedunbonded tendons, unlike members with tendons, unlike members with bonded tendons, may be bonded tendons, may be adversely affectedadverse
144、ly affected by by unintentional unintentional variationsvariations in the effective in the effective prestressprestress. Hence, it is considered . Hence, it is considered prudentprudent（谨慎的）谨慎的）to exertto exert（给予）给予）more care in estimating the more care in estimating the losses of losses of prestre
145、ssprestress and in supervising and in supervising（监控）监控）the stressingthe stressing（加压）加压）of of unbondedunbonded members than would be considered necessary for members than would be considered necessary for bonded members, in order to assure the desired results are obtained.bonded members, in order t
146、o assure the desired results are obtained. 应该承认，不象具有有粘结的钢筋束的构件，受到应该承认，不象具有有粘结的钢筋束的构件，受到无粘结的钢筋束施加应力的构件的极限弯矩能力，可能无粘结的钢筋束施加应力的构件的极限弯矩能力，可能会反过来受到有效应力不经意的变化的影响。因此，为会反过来受到有效应力不经意的变化的影响。因此，为了确保获得期望的结果，比起需谨慎考虑有粘结的构件了确保获得期望的结果，比起需谨慎考虑有粘结的构件而言，在估计预应力损失和监控无粘结的构件加压时更而言，在估计预应力损失和监控无粘结的构件加压时更加予以小心谨慎，这被认为是谨慎的（做法）。
147、加予以小心谨慎，这被认为是谨慎的（做法）。Structural Analysis 结构分析 A structureA structure consistsconsists ofof a series ofa series of connected parts used to connected parts used to support loadssupport loads. . Notable Notable examples include buildings, bridges, examples include buildings, bridges, towers, tanks, and
148、 dams. Thetowers, tanks, and dams. The processprocess of creating any of of creating any of these structures requiresthese structures requires planningplanning, analysis, design, and , analysis, design, and construction. Structural analysisconstruction. Structural analysis consists ofconsists of a a
149、 varietyvariety ofof mathematical proceduresmathematical procedures for determiningfor determining suchsuch quantities quantities asas the member forces and various structuralthe member forces and various structural displacementsdisplacements as a as a structure responds to its loads. Estimating rea
150、listic loads for structure responds to its loads. Estimating realistic loads for thethe structure structure considering considering its use and location is often a part its use and location is often a part of structural analysis. of structural analysis. 结构由一系列相连的用以支撑荷载的构件组成。显著的例子包括建筑、桥梁、塔、水箱和大坝等。建造这
151、些结构中的任何一个的过程需要规划、分析、设计和建造。结构分析包括各种各样的数学程序以确定诸如当一个结构对荷载有响应时构件的力和不同结构位移的大小。根据结构的使用和位置来估计它的实际荷载经常是结构分析的一部分。 Only two assumptions are made regarding the Only two assumptions are made regarding the materials used in the structures of this chapter. First, materials used in the structures of this chapter.
152、First, the material has athe material has a linearlinear stress-strain relationshipstress-strain relationship. . Second, there is no difference in the material behavior Second, there is no difference in the material behavior when stressed in tensionwhen stressed in tension vis-a-visvis-a-vis（与与. .相比
153、）相比）compression. compression. n n关于本章结构中所用的材料只作了两点假设。首先，材料具有线性的应力应变关系。其次，材料的性能在受拉和受压时没有区别。The frames and trusses studied are plane structural systems. It will be assumed that there is adequate bracing perpendicular to the plane so that no member will fail due to an elastic instability. The very impo
154、rtant consideration regarding such instability will be left for the specific design course. n n研究的框架和桁架是平面结构体系。假定垂直于研究的框架和桁架是平面结构体系。假定垂直于平面的方向有足够的支撑，因而构件不会因为弹平面的方向有足够的支撑，因而构件不会因为弹性失稳而失效。一个非常重要的关于这种失稳的性失稳而失效。一个非常重要的关于这种失稳的考虑留待具体的设计过程。考虑留待具体的设计过程。All structures are assumed to undergo only small All st
155、ructures are assumed to undergo only small deformations as they are loaded.deformations as they are loaded. As a As a consequence, consequence, we assume no change in the we assume no change in the position or direction of a forceposition or direction of a force as a result ofas a result of structur
156、alstructural deflectionsdeflections（变位）变位）. Finally, since . Finally, since linear elastic materials and small displacement linear elastic materials and small displacement are assumed, the are assumed, the principle of superposition will apply in all cases. will apply in all cases. 假定所有的结构在它们加荷时只经历小
157、的变形。因此，我们假定当结构变位时荷载的位置与方向不变。最后，因为假定了线弹性材料和小位移，叠加原理将适用于所有的情况。n nThus the displacements or internal forces thatThus the displacements or internal forces that arisearise fromfrom two different forces systems appliedtwo different forces systems applied one at a one at a timetime（一次一个）（一次一个）may bemay be
158、added algebraicallyadded algebraically（几（几何相加）何相加）to determine the structures response when to determine the structures response when both both system(ssystem(s) are applied simultaneously.) are applied simultaneously. 这样当两种不同的力系同时施加时，可以由不这样当两种不同的力系同时施加时，可以由不同的力系一次施加一个引起的位移或内力几何相加同的力系一次施加一个引起的位移或内力几
159、何相加来确定结构的响应。来确定结构的响应。 In the real sense In the real sense an exact analysis of a structure an exact analysis of a structure can never be carried out since estimates always have can never be carried out since estimates always have to be made of the loadings and the strength of the to be made of the l
160、oadings and the strength of the materialsmaterials composing composing the structure. Furthermore,the structure. Furthermore, points points of application of application for the loadings must also be estimated. for the loadings must also be estimated. It is important,It is important, thereforetheref
161、ore, that the structural engineers, that the structural engineers develop develop the ability tothe ability to model model oror idealize idealize a structure so a structure so that he or she can perform a practical force analysis of that he or she can perform a practical force analysis of the member
162、s.the members. 真正意义上对一个结构准确的分析是永远也不可能进行的，因为总是不得不估计荷载和构成结构的材料的强度。而且，必须估计荷载的作用点。因此，结构工程师有能力模拟一个结构或使其理想化很重要，这样，他或她能对构件进行实际的力的分析。 Structural members are joined together in various Structural members are joined together in various waysways depending ondepending on the the intentintent of the designer. Th
163、e two types of of the designer. The two types of joints most often specified are the joints most often specified are the pin connection and and the fixed joint. A pin-connected joint allows some freedom for. A pin-connected joint allows some freedom for slightslight rotation, whereas the fixed joint
164、 allows no rotation, whereas the fixed joint allows no relative rotation between the connected members. 结构构件根据设计者的意图采用不同的方式连在一起。最常规定的两种节点是铰接节点和固定节点。铰接节点允许有一些轻微的转动自由，而固定节点不允许相连的构件有相对的转动。n nIn reality, however, all connectionsIn reality, however, all connections exhibit exhibit some stiffness some sti
165、ffness toward joint rotations,toward joint rotations, owingowing toto friction friction and material and material behavior. When selecting a particular model for eachbehavior. When selecting a particular model for each support support or joint, the engineer mustor joint, the engineer must be aware o
166、fbe aware of how the how the assumptions will affect the actualassumptions will affect the actual performance performance of the of the member and whether the assumptions are reasonable for member and whether the assumptions are reasonable for the structural design.the structural design.n n但是，事实上由于摩
167、擦和材料的特性使所有的连接对但是，事实上由于摩擦和材料的特性使所有的连接对节点的转动显现出一些刚度。当为每一个支座或节点节点的转动显现出一些刚度。当为每一个支座或节点选择一个特定的模型时，工程师必须知道该假设将如选择一个特定的模型时，工程师必须知道该假设将如何影响构件的实际运行，以及该假设是否对结构的设何影响构件的实际运行，以及该假设是否对结构的设计是合理的。计是合理的。 In reality, all structural supports actuallyIn reality, all structural supports actually exertexert（产生）（产生）distr
168、ibuteddistributed surface loads surface loads on their contacting members. Theon their contacting members. The resultantsresultants（合力）（合力） of these load distributions are often of these load distributions are often idealized as theidealized as the concentrated forces and moments, sinceand moments,
169、since the the surface areasurface area over which the distributed load acts is over which the distributed load acts is considerably smaller than the total surface area of the considerably smaller than the total surface area of the connecting members.connecting members. 实际上，所有的结构支座在它们接触的构件上产生分布的面荷载。这
170、些荷载分布的合力常常理想化为集中力和弯矩，因为分布荷载作用的表面面积比相连的构件的总的表面面积小很多。The ability toThe ability to reducereduce an actual structurean actual structure toto an idealized form can an idealized form can only be gained by experience. In engineering practice, if it only be gained by experience. In engineering practice, if
171、it becomes becomes doubtful doubtful as toas to how to model ahow to model a structure orstructure or transfertransfer the loadsthe loads toto the members, it is best to consider several the members, it is best to consider several idealized structures and loadings and then design the actual idealize
172、d structures and loadings and then design the actual structure so that it canstructure so that it can resist resist the loadings in all the idealized the loadings in all the idealized models.models.将一个实际的结构简化成一种理想的形式的能力只有通过将一个实际的结构简化成一种理想的形式的能力只有通过经验才能获得。在工程实践中，如果就怎样模拟一个结经验才能获得。在工程实践中，如果就怎样模拟一个结构或将荷
173、载传递给构件变得难以确定时，最好考虑几个构或将荷载传递给构件变得难以确定时，最好考虑几个理想的结构和荷载，然后设计实际的结构，使它在所有理想的结构和荷载，然后设计实际的结构，使它在所有理想的模型中都能抵抗荷载。理想的模型中都能抵抗荷载。 It may beIt may be recalled recalled from statics that a structure or one from statics that a structure or one of its members isof its members is in equilibriumin equilibrium（处于平衡）处
174、于平衡） when it when it maintains a balance of force and moment. When all the maintains a balance of force and moment. When all the forces in a structure can be determined strictly from these forces in a structure can be determined strictly from these equations, the structureequations, the structure is
175、 referred to asis referred to as statically determinate . Structures having more unknown forces . Structures having more unknown forces than availablethan available equilibrium equationsequilibrium equations are called statically are called statically indeterminate. indeterminate. n n从静力学可以回想起当一个结构或
176、它的一个构件维持从静力学可以回想起当一个结构或它的一个构件维持力和弯矩的平衡时即处于平衡状态。当一个结构中所力和弯矩的平衡时即处于平衡状态。当一个结构中所有的力能严格地根据这些方程式来确定，该结构称为有的力能严格地根据这些方程式来确定，该结构称为静定的。如果结构上未知的力比能得到的平衡方程多静定的。如果结构上未知的力比能得到的平衡方程多时称为超静定结构。时称为超静定结构。As a general rule, a structure canAs a general rule, a structure can be identified as beingbeing either staticall
177、y determinatestatically determinate or statically indeterminate statically indeterminate by drawingby drawing free-body diagrams of all its members, or of all its members, or selective parts of its members, and thenselective parts of its members, and then comparing the the total number of unknown re
178、active forcetotal number of unknown reactive force and momentand moment components（分量）（分量）with the total number of available the total number of available equilibrium equationsequilibrium equations. 作为一般的规律，一个结构可以通过画出所有作为一般的规律，一个结构可以通过画出所有构件或经选择的部分构件的隔离体图，然后比较未构件或经选择的部分构件的隔离体图，然后比较未知的反力和弯矩的分量总数目与可用的
179、平衡方程总知的反力和弯矩的分量总数目与可用的平衡方程总数目是否相等来确定其是静定结构还是超静定结构。数目是否相等来确定其是静定结构还是超静定结构。 In particular, if a structure is statically indeterminate, In particular, if a structure is statically indeterminate, thethe additional equationsadditional equations needed to solve for the unknown needed to solve for the unkn
180、own reactions reactions are obtained byare obtained by relatingrelating the applied loads and the applied loads and reactionsreactions toto the displacement orthe displacement or slopeslope（转角）转角）at different at different points on the structure. These equations, which are referred points on the str
181、ucture. These equations, which are referred to asto as compatibility equations（相容性方程或协调方程）相容性方程或协调方程）, must be equal in number to the, must be equal in number to the degree of indeterminacy（不确定次数）不确定次数）of the structure. of the structure. Compatibility equationsCompatibility equations involveinvolve（
182、涉及）涉及）the geometric and the geometric and physical properties of the structure.physical properties of the structure. 特别地，如果一个结构是超静定的，可以通过建立特别地，如果一个结构是超静定的，可以通过建立作用力和反力与结构不同点上的位移或转角的关系来得作用力和反力与结构不同点上的位移或转角的关系来得到用以求解未知反力所需的附加方程。这些称为相容性到用以求解未知反力所需的附加方程。这些称为相容性方程的方程式在数量上必须等于结构的不确定次数。相方程的方程式在数量上必须等于结构的不确
183、定次数。相容性方程涉及结构的几何和物理性能。容性方程涉及结构的几何和物理性能。 There are two fundamental methods of analysis There are two fundamental methods of analysis for trusses: for trusses: the method of joints and and the method of sections. Both. Both startstart withwith a free-body a free-body diagram of the trussdiagram of the
184、 truss as a wholeas a whole, from which the , from which the equilibrium equations are written and solved for theequilibrium equations are written and solved for the support reactions（支座反力）支座反力）. . 有两种分析桁架的基本方法：节点法和截面有两种分析桁架的基本方法：节点法和截面法。两种方法基本上都从桁架的隔离体图着手，法。两种方法基本上都从桁架的隔离体图着手，根据它可以写出平衡方程并求解支座反力。根据它
185、可以写出平衡方程并求解支座反力。 The method of joints: After the support reactions have The method of joints: After the support reactions have been found, a joint is selected that hasbeen found, a joint is selected that has no more than no more than two two members connecting for which the axial forces are members
186、connecting for which the axial forces are unknown. The free-body diagram of that joint is drawn, the unknown. The free-body diagram of that joint is drawn, the forces areforces are summed summed in two directions, and each sumin two directions, and each sum is is equated to equated to zero. zero. 节点
187、法：节点法：求出支座反力后，选择一个节点，与其连接的轴求出支座反力后，选择一个节点，与其连接的轴向力未知的构件不超过两根。画出节点的隔离体图，将向力未知的构件不超过两根。画出节点的隔离体图，将力在两个方向上进行合计，每个方向（力）的合计等于力在两个方向上进行合计，每个方向（力）的合计等于零。零。When drawing the free-body diagram, it is a good idea to assume that the unknown forces are tensions and to show show them so on the free-body diagram b
188、y exerting a pull on the joint. When this is assumed, the resulting sign sign of the unknowns when evaluated evaluated will match match the conventional conventional + + for tension and for compression. 当画出隔离体图时，有个好主意是假定未知力是拉力，并在当画出隔离体图时，有个好主意是假定未知力是拉力，并在隔离体图上通过对该节点施加一个拉力来表示。这样假定隔离体图上通过对该节点施加一个拉力来表示
189、。这样假定后，未知力计算结果的符号将与习惯的正为拉力负为压力后，未知力计算结果的符号将与习惯的正为拉力负为压力相符。相符。Once a joint has been analyzed, its members become knowns, and adjacent jointsadjacent joints, which mightmight havehave had three or more unknowns, can then be solved since some of these unknowns have become knowns. This process process c
190、ontinues from joint to joint, each time selecting a joint whose number of unknown members does not exceed 2.vv一旦一个节点已经被分析，其上的构件成为已知构件，相邻的节点可能曾经有三个或更多的未知力，但因为其中的一些已经成为已知，因此也能求出。这个过程从一个节点到另一个节点连续进行，每次选择的节点其上未知构件（力）的数量不超过两根。 Almost Almost all all truss truss systems systems areare configuredconfigured（
191、装装配配）so so that that analysis analysis using using the the method method of of joints joints must must begin begin at at one one end end andand proceed proceed joint joint by by joint joint toward toward the the other other end. end. If If it it is is necessary necessary to to evaluate evaluate the
192、the forces forces carried carried by by a a membermember locatedlocated somesome distance distance fromfrom the the ends, ends, the the method method of of joints joints requires requires the the calculation calculation of of the the forces in many members before the desired one is reached. forces i
193、n many members before the desired one is reached. 几乎所有的桁架体系是装配的，因此采用节点法进行几乎所有的桁架体系是装配的，因此采用节点法进行的分析必须从一个端点开始，并一个节点连着一个节点地的分析必须从一个端点开始，并一个节点连着一个节点地朝另一个端点继续进行。如果有必要计算位于端部一定距朝另一个端点继续进行。如果有必要计算位于端部一定距离的构件上的力，节点法需要在到达这根要求（计算）的离的构件上的力，节点法需要在到达这根要求（计算）的构件之前计算很多构件中的力。构件之前计算很多构件中的力。The method of sections pro
194、vides a means means for a direct calculation in these cases. After the support reactions have been calculated the truss is cut cut through through (analyticallyanalytically) so that one part of the truss is completely severedsevered fromfrom the rest. When this is done, no more than three unknown me
195、mbers should be cut. If If possible possible the cut cut should pass pass throughthrough the member or members whose internal forces are to be found. 在这些情况下截面法提供了一个直接计算的方法。当求出支在这些情况下截面法提供了一个直接计算的方法。当求出支座反力后，桁架（在分析上）被切开，从而一部分桁架同座反力后，桁架（在分析上）被切开，从而一部分桁架同其余部分完全分离。当这样切开时，应该切出不超过三个其余部分完全分离。当这样切开时，应该切出不超过
196、三个构件的力是未知的。如果可能，切口应穿过将要求解内力构件的力是未知的。如果可能，切口应穿过将要求解内力的构件。的构件。A free-body diagram of the part of the truss on on one one side side ofof this section is drawn, and the internal forces are found through the equilibrium equations. Since the system system of of forcesforces on the free-body diagram is a p
197、lane non-concurrentnon-concurrent（非共点）force system, three equilibrium equations may be written and solved for the three unknowns.画出在截面一边的桁架部分的隔离体图，并通过画出在截面一边的桁架部分的隔离体图，并通过平衡方程式求解内力。由于隔离体图上的力系平衡方程式求解内力。由于隔离体图上的力系是平面非共点的，因而可以写出三个平衡方程是平面非共点的，因而可以写出三个平衡方程式并求出三个未知力。式并求出三个未知力。 Influence lines have importa
198、nthave important application application for for the design of structures that resist largethe design of structures that resist large live loads. An influence line. An influence line represents represents the variation ofthe variation of eithereither the reaction, shear, moment,the reaction, shear,
199、moment, oror deflection at adeflection at a specificspecific point in a memberpoint in a member asas concentrated force concentrated force moves over the member. moves over the member. 影响线在设计抵抗大量活荷载的结构时有着重要的应用。影响线在设计抵抗大量活荷载的结构时有着重要的应用。一根影响线代表着当集中力在构件上移动时构件上一一根影响线代表着当集中力在构件上移动时构件上一个特定点的反力、剪力、弯矩或挠度的变化
200、。个特定点的反力、剪力、弯矩或挠度的变化。Once this line isOnce this line is constructedconstructed（作图）（作图）, one can, one can tell at a tell at a glance glance where a live load should be placed on the where a live load should be placed on the structure so that itstructure so that it creates creates the greatest influen
201、ce at the the greatest influence at the specified point. Furthermore, thespecified point. Furthermore, the magnitude magnitude of theof the associatedassociated （相关的）（相关的）reaction, shear, moment, or reaction, shear, moment, or deflection at the point can then be calculated from thedeflection at the
202、point can then be calculated from the ordinatesordinates（纵坐标）（纵坐标）of the influence-line diagram.of the influence-line diagram. 一旦画出这根线，任何人一眼便知活荷载应该置于一旦画出这根线，任何人一眼便知活荷载应该置于结构的哪个位置才能对这个特定的点引起最大的影响。结构的哪个位置才能对这个特定的点引起最大的影响。而且，这点上相关的反力、剪力、弯矩或挠度可从影响而且，这点上相关的反力、剪力、弯矩或挠度可从影响线图的纵坐标上计算出来。线图的纵坐标上计算出来。n nFor th
203、ese reasonsFor these reasons, influence lines, influence lines playplay an importantan important part inpart in the design of bridges,the design of bridges, industrial industrial crane railscrane rails（吊车轨道）（吊车轨道）, , conveyors,conveyors, and other structures where loadsand other structures where loa
204、ds move acrossmove across their their spanspan. Although the. Although the procedure procedure for constructing an for constructing an influence line is ratherinfluence line is rather basicbasic, one should clearly, one should clearly be aware be aware ofof the differencethe difference betweenbetwee
205、n constructing an influence lineconstructing an influence line andand constructing a shear or moment diagram.constructing a shear or moment diagram.因此，影响线在桥梁、工业吊车轨道、输送机和其它有荷载因此，影响线在桥梁、工业吊车轨道、输送机和其它有荷载在整个结构长度上移动的结构设计中扮演着重要的角色。在整个结构长度上移动的结构设计中扮演着重要的角色。虽然画出一条影响线的步骤是相当基本的，但任何人应该虽然画出一条影响线的步骤是相当基本的，但任何人应该
206、清楚地意识到画一条影响线与画一条剪力或弯矩图的区别。清楚地意识到画一条影响线与画一条剪力或弯矩图的区别。Influence lines represent the effect of a moving Influence lines represent the effect of a moving load onlyload only at at a specified point on a member,a specified point on a member, whereaswhereas shear and moment diagrams represent the effect of
207、 shear and moment diagrams represent the effect of fixed loadsfixed loads at at all points along the axis of the all points along the axis of the member.member.影响线只代表着移动荷载对构件上特定点的影响，而剪影响线只代表着移动荷载对构件上特定点的影响，而剪力和弯矩图代表固定荷载对沿着构件轴线的所有点的力和弯矩图代表固定荷载对沿着构件轴线的所有点的影响。影响。 Deflections of structures can occur fro
208、m variousDeflections of structures can occur from various sourcessources, , such assuch as loads, temperature, fabrication errors, or loads, temperature, fabrication errors, or settlement. In design, deflections must be limitedsettlement. In design, deflections must be limited in order in order toto
209、 prevent cracking ofprevent cracking of attached attached brittle materialsbrittle materials suchsuch asas concrete or plaster (concrete or plaster (石膏石膏) . Furthermore, a structure must ) . Furthermore, a structure must not vibrate ornot vibrate or deflectdeflect（变位）（变位）severelyseverely inin ordero
210、rder toto “appear” safe for its“appear” safe for its occupantsoccupants. More important,. More important, thoughthough, , deflections at specified points in a structure must be deflections at specified points in a structure must be computed if one is to analyze statically indeterminate computed if o
211、ne is to analyze statically indeterminate structures. structures. 结构的挠度可以因不同的原因而发生，如荷载、温结构的挠度可以因不同的原因而发生，如荷载、温度、制造错误或沉降。设计中，挠度必须加以限制以阻度、制造错误或沉降。设计中，挠度必须加以限制以阻止附属的脆性材料如混凝土或石膏的开裂。而且，为了止附属的脆性材料如混凝土或石膏的开裂。而且，为了向居住者显示安全性，结构不能严重地振动或变位。而向居住者显示安全性，结构不能严重地振动或变位。而更重要的是如果有人要分析超静定结构，必须计算出结更重要的是如果有人要分析超静定结构，必须计算
212、出结构中规定点的挠度。构中规定点的挠度。We We often often determine determine the the elastic elastic deflections deflections of of a a structure structure usingusing bothboth geometricalgeometrical andand energy methods. . Also, Also, the the methods methods ofof double integration（双双重重积积分分）are are used. used. The The
213、 geometrical geometrical methods methods include include thethe moment-area theorems（弯弯矩矩图图面面积积定定理理）and and thethe conjugate-beam method（共共轭轭梁梁法法）, , and and the the energyenergy methods methods to to be be considered considered areare basedbased onon virtual work（虚虚功功）andand CastiglianosCastigliano
214、s theoremtheorem（卡卡氏氏最最小小功功定定理理）. . Each Each of of these these methods has particular advantages or disadvantages.methods has particular advantages or disadvantages.我们通常采用几何法和能量法来确定结构的弹性我们通常采用几何法和能量法来确定结构的弹性挠度。也采用双重积分法。几何法包括弯矩图挠度。也采用双重积分法。几何法包括弯矩图面积定理和共轭梁法，而考虑的能量法是基于面积定理和共轭梁法，而考虑的能量法是基于虚功定理和卡式最小功定理
215、。每一种方法都有虚功定理和卡式最小功定理。每一种方法都有其特别的优缺点。其特别的优缺点。n nWe can determine the equation of the elastic curve by integration of equation d2v / dx2 = M / EI. Solution of this equation requires two successive successive integrations to obtain the deflection v of the elastic curve. For each integration, it is nece
216、ssary to introduce introduce a “ “constant of integration” ”（积分常数）, and then solvesolve forfor the constants to obtain a unique solutionunique solution for a particular particular problem. 我们可以通过对方程我们可以通过对方程d2v / dx2 = M / EId2v / dx2 = M / EI的积分来的积分来确定弹性曲线的方程。该方程的求解需要两个连续的积确定弹性曲线的方程。该方程的求解需要两个连续的积分
217、，以获得弹性曲线的挠度分，以获得弹性曲线的挠度v v。对每次积分，有必要引。对每次积分，有必要引入积分常数，求出该常数以获得一个特定问题的唯一解。入积分常数，求出该常数以获得一个特定问题的唯一解。n nVs second derivation with respect to x It It should should be be realized realized that that the the method method of of double double integration integration is is suitablesuitable onlyonly forfor e
218、lastic elastic deflectionsdeflections suchsuch thatthat the the beams beams slope slope is is very very small. small. Furthermore, Furthermore, the the method method considers only deflectionsconsiders only deflections duedue toto bending.bending.应该了解到双重积分法只适合于弹性变位，因而梁的应该了解到双重积分法只适合于弹性变位，因而梁的转角是非常小的
219、。而且，该法只考虑了由于弯曲引转角是非常小的。而且，该法只考虑了由于弯曲引起的挠度。起的挠度。 TheThe initial initial ideas ideas for for the the two two moment-area moment-area theorems theorems werewere developed developed by by Otto Otto Mohr Mohr and and laterlater stated stated formally formally by by Charles Charles E. E. Greene Greene in
220、in 1872. 1872. These These theorems theorems provide provide a a semi-graphical technique for for determining determining the the slope slope of of the the elastic elastic curve curve and and its its deflection deflection due due to to bending. bending. They They are are particularlyparticularly adv
221、antageous advantageous when when used used to to solve solve problems problems involving involving beams beams especially especially those those subjected subjected toto a a series series ofof concentrated concentrated loadings loadings or or havinghaving segments segments with differentwith differe
222、nt moment of inertia. . 最初的关于两个弯矩图面积定理的概念是由最初的关于两个弯矩图面积定理的概念是由Otto MohrOtto Mohr提出，后来由提出，后来由Charles E. GreeneCharles E. Greene在在18721872年正式加以确定。这些定理为确定弹性曲线由于年正式加以确定。这些定理为确定弹性曲线由于弯曲引起的转角和挠度提供了半图解的方法。当弯曲引起的转角和挠度提供了半图解的方法。当用以解决包括梁在内的问题，特别是那些承受一用以解决包括梁在内的问题，特别是那些承受一组集中加载的梁或有着不同惯性矩的梁段时，它组集中加载的梁或有着不同惯性矩的梁
223、段时，它们（指弯矩图面积定理）是特别得有利。们（指弯矩图面积定理）是特别得有利。Theorem Theorem 1: 1: TheThe change change in in slope slope between between any any two two points points on on the the elastic elastic curvecurve equalsequals the the area area of of the the M M / / EI EI diagram diagram between between these these two two p
224、oints. points. Theorem Theorem 2: 2: TheThe deviation deviation of of thethe tangent tangent at at point point B B on on the the elastic elastic curvecurve with with respect respect to to the the tangent tangent at at point point A A equals equals thethe “moment”“moment” of of the the M M / / EI EI
225、diagram diagram between between the the two two points points A A and and B B computedcomputed aboutabout point point A A (the (the point point on on the the elastic elastic curve),curve), where where the the deviation deviation t tA A/B/B is is to to be be determined.determined.定理定理1 1：弹性曲线上任何两点之间转
226、角的变化等于这：弹性曲线上任何两点之间转角的变化等于这两点之间的两点之间的M / EIM / EI图的面积。定理图的面积。定理2 2：弹性曲线上：弹性曲线上B B点的正切相对于点的正切相对于A A点的正切的偏差等于点点的正切的偏差等于点A A与点与点B B之间的之间的M / EIM / EI图对图对A A点（该点在弹性曲线上）的矩，点（该点在弹性曲线上）的矩，这里偏差这里偏差t tA A/B/B将被确定。将被确定。 The The conjugate-beam conjugate-beam method method was was firstfirst presentedpresented
227、by by Otto Otto Mohr Mohr in in 1860.1860. EssentiallyEssentially, , it it requiresrequires the the samesame amount amount of of computation computation asas the the moment-area moment-area theorems theorems to to determine determine a a beams beams slope slope or or deflection; deflection; however,
228、 however, this this methodmethod reliesrelies onlyonly onon the the principles principles of of statics statics and and hence hence its its application application will will be be moremore familiarfamiliar. . The The basis basis for for the the methodmethod comes comes fromfrom thethe similarity sim
229、ilarity betweenbetween bothboth dV/dxdV/dx = = - - andand d d2 2M/dxM/dx2 2 = = - - , , whichwhich relaterelate a a beams beams internal internal shear shear and and momentmoment toto its its applied applied loading, loading, and and d d /dx/dx = = M/EI M/EI and and d d2 2y/dxy/dx2 2 = = M/EI, M/EI,
230、 whichwhich relaterelate the the slope slope and and deflection of its elastic curvedeflection of its elastic curve toto the internal moment. the internal moment. 共共轭轭梁梁法法首首先先在在18601860年年由由Otto Otto MohrMohr提提出出。本本质质上上说说，它它与与弯弯矩矩图图面面积积定定理理一一样样在在确确定定梁梁的的转转角角或或挠挠度度上上需需要要相相同同的的计计算算量量；但但是是这这种种方方法法只只依依赖赖
231、于于静静力力学学的的原原理理，因因此此，它它的的应应用用更更常常见见。该该法法的的基基础础来来自自于于dV/dxdV/dx=-=- 和和d d2 2M/dxM/dx2 2=-=- 之之间间的的相相似似性性，它它将将梁梁的的内内部部剪剪力力和和弯弯矩矩与与它它施施加加的的荷荷载载联联系系起起来来，而而d d /dx/dx = = M/EIM/EI和和d d2 2y/dxy/dx2 2 = = M/EIM/EI将将弹弹性性曲曲线线的的转转角角和和挠挠度与内部弯矩联系起来。度与内部弯矩联系起来。 Note Note that that the the shear shear V V compares
232、 compares with with the the slope slope , , the the moment moment MM comparescompares withwith the the displacement displacement y y and and the the intensity intensity of of the the external external load load comparescompares withwith the the area area under under the the M/EI M/EI diagram. diagra
233、m. ToTo make make use use ofof this this comparison comparison we we will will consider consider a a beam beam having having the the same same length length as as the the real real beam, beam, but but referred referred to to here here as as the the “conjugate beam”. “conjugate beam”. 注意剪力注意剪力V V与转角与
234、转角 相对应，弯矩相对应，弯矩MM与位移与位移y y相对相对应，而外力的强度应，而外力的强度 与与M/EIM/EI图下的面积相对图下的面积相对应。为了利用这些对应，我们将考虑一根与应。为了利用这些对应，我们将考虑一根与实际梁一样长的梁。但是这里称为共轭梁。实际梁一样长的梁。但是这里称为共轭梁。In general,In general, thoughthough, remember that if the real support allows , remember that if the real support allows a slope, the conjugate support m
235、usta slope, the conjugate support must develop develop a shear; and if a shear; and if the real support allows a displacement, the conjugate support the real support allows a displacement, the conjugate support must develop a moment, note that the conjugate beam is must develop a moment, note that t
236、he conjugate beam is “loaded” with the M/EI diagram,“loaded” with the M/EI diagram, in order toin order to conform to conform to the load on the real beam. the load on the real beam. 然而通常要记住如果实际的支座允然而通常要记住如果实际的支座允许一个转角，共轭的支座必须产生一个许一个转角，共轭的支座必须产生一个剪力；如果实际的支座允许一个位移，剪力；如果实际的支座允许一个位移，共轭的支座必须产生一个弯矩，注意共共轭
237、的支座必须产生一个弯矩，注意共轭梁用轭梁用M/EIM/EI图来加荷，以便与实际梁上图来加荷，以便与实际梁上的荷载一致。的荷载一致。We can thereforeWe can therefore state two theorems related to the two theorems related to the conjugate beam,conjugate beam, namely, Theorem 1: The slope at a , Theorem 1: The slope at a point in the real beam is equal to the shear at
238、 thepoint in the real beam is equal to the shear at the corresponding point in conjugate beam. Theorem 2: in conjugate beam. Theorem 2: The displacement of a point in the real beam is equal The displacement of a point in the real beam is equal to the moment at the corresponding point in the to the m
239、oment at the corresponding point in the conjugate beam.conjugate beam.因此，我们可以陈述与共轭梁相关的两种因此，我们可以陈述与共轭梁相关的两种定理，即，定理定理，即，定理1 1：实际梁上某一点的转：实际梁上某一点的转角等于共轭梁上相应点的剪力。定理角等于共轭梁上相应点的剪力。定理2 2：实际梁上某一点的位移等于共轭梁上相实际梁上某一点的位移等于共轭梁上相应点的弯矩。应点的弯矩。 For more complicated loadings or for structures such as For more complicat
240、ed loadings or for structures such as trusses and frame, it istrusses and frame, it is suggestedsuggested that energy methods that energy methods bebe used used for the computation. All energy methods are based on thefor the computation. All energy methods are based on the conservation of energy pri
241、nciple, which, which statesstates that that thethe work work done by all the external forces acting on a structure, done by all the external forces acting on a structure, UeUe, , is transformed into is transformed into internal work or or strain energy UI, which isUI, which is developed developed wh
242、en the structurewhen the structure deformsdeforms. . 对于较复杂的荷载或结构如桁架和框架，建议应对于较复杂的荷载或结构如桁架和框架，建议应该采用能量法来计算。所有的能量法是基于能量守恒该采用能量法来计算。所有的能量法是基于能量守恒原则，它规定了作用在结构上的所有外力作的功原则，它规定了作用在结构上的所有外力作的功UeUe转转化成内部功或结构变形时形成的应变能化成内部功或结构变形时形成的应变能UI UI 。 The principle of virtual workThe principle of virtual work was develo
243、ped by John was developed by John Bernoulli in 1717 and is sometimes referred to as theBernoulli in 1717 and is sometimes referred to as the unit-load method. It provides a. It provides a general means general means of obtaining the of obtaining the displacement and slope at a point on a structure,d
244、isplacement and slope at a point on a structure, be it be it a beam, a beam, frame, or truss. Before developing the principle of virtual frame, or truss. Before developing the principle of virtual work, it is necessary to make somework, it is necessary to make some generalgeneral statements statemen
245、ts regardingregarding the principle of work and energy. the principle of work and energy. 虚功原理在虚功原理在17171717年由年由John BernoulliJohn Bernoulli提出，有时称为单提出，有时称为单位荷载法。它提供了获得结构上某一点的位移和转角的一位荷载法。它提供了获得结构上某一点的位移和转角的一般的方法，不管该结构是梁、框架还是桁架。在提出虚功般的方法，不管该结构是梁、框架还是桁架。在提出虚功原理之前，关于功和能量的原理有必要作些一般规定。原理之前，关于功和能量的原理有必要作些一
246、般规定。+plus- minus multiplied bytimes divided by plus or minus is equal toequalsis is identically equal toidentically equals is approximately equal toapproximately equals二、常用数学符号的读法二、常用数学符号的读法(English reading for frequently-used mathematical symbols） x bar, the mean value of x the absolute value of xb
247、 prime b double primeb second primeb two primeb subscript oneb sub one b superscript twob super twox dot x two dotsfunction f of xDee x differential x the n th derivative of y with respect to xdelintegral between limits a and b bracket a plus b bracket closed the ratio of a to b x squarex squaredthe
248、 square of xthe second power of xx to the second powernth delintegral infinity the partial derivative of y with respect to x the square root of x the fifth root of x square x cubex cubedthe cube of xthe third power of x x to the third power log x to the base n Factorial x n n2061249980110061276n n3
249、3 砼剪力墙构件的行为状态砼剪力墙构件的行为状态 屈服状态和极限状态是砼剪力墙两个重要的行为状态。屈服状态和极限状态是砼剪力墙两个重要的行为状态。n n3.1 3.1 屈服状态和砼剪力墙的屈服变形屈服状态和砼剪力墙的屈服变形n n能量等效原理能量等效原理和和几何图法几何图法是确定构件屈服点常用的两种方法。是确定构件屈服点常用的两种方法。由由预制大型钢筋砼框架的节点与连接设计规范预制大型钢筋砼框架的节点与连接设计规范推荐的方推荐的方法如下：法如下：1 1）当荷载变形曲线有明显的转折时，转折点对应）当荷载变形曲线有明显的转折时，转折点对应的荷载作为屈服荷载的荷载作为屈服荷载FyFy，其对应的变形就
250、是屈服变形，其对应的变形就是屈服变形UyUy；2 2）对于没有明显转折点的）对于没有明显转折点的荷载变形曲线荷载变形曲线，可以找出曲线上，可以找出曲线上的极限荷载的极限荷载FucFuc，0.75Fuc0.75Fuc对应的水平线与对应的水平线与FuFu曲线的上升段相曲线的上升段相交于交于A A点，之后，点，之后，OAOA线段的延长线与线段的延长线与FucFuc对应的水平线相交对应的水平线相交于于B B点。最后，画出点。最后，画出B B点对应的垂直线，与曲线相交于点对应的垂直线，与曲线相交于E E点点（如图（如图3 3所示）。点所示）。点E E即即FuFu曲线的屈服点，其对应的荷载即屈曲线的屈服点
251、，其对应的荷载即屈服荷载，对应的变形即是构件对应的屈服变形。一些其它资服荷载，对应的变形即是构件对应的屈服变形。一些其它资料将最外层受拉钢筋的屈服点作为构件的屈服点。本文为安料将最外层受拉钢筋的屈服点作为构件的屈服点。本文为安全起见，将由以上两种方法得出的较小的屈服变形作为钢筋全起见，将由以上两种方法得出的较小的屈服变形作为钢筋砼剪力墙构件的屈服变形。砼剪力墙构件的屈服变形。n n3.23.2极限状态和砼剪力墙的极限变形极限状态和砼剪力墙的极限变形 以弯曲为主的延性钢筋砼剪力墙，本文认为若满足以下四个以弯曲为主的延性钢筋砼剪力墙，本文认为若满足以下四个条件之一，即达到了极限状态。条件之一，即达
252、到了极限状态。n n(1) (1) 纵向受拉筋达到极限拉应变纵向受拉筋达到极限拉应变 砼结构用钢砼结构用钢给出了常用的给出了常用的HPB235HPB235，HRB335HRB335，HRB400HRB400等级钢筋在最大力作用下的伸长率的下限。为安全起见，用等级钢筋在最大力作用下的伸长率的下限。为安全起见，用最大荷载下的伸长率作为钢筋的极限拉应变。最大荷载下的伸长率作为钢筋的极限拉应变。HPB235HPB235的极的极限拉应变是限拉应变是0.1000.100，HRB335HRB335和和HRB400HRB400的极限拉应变是的极限拉应变是0.0750.075。n n(2) (2) 砼达到极限压
253、应变砼达到极限压应变 根据作者的叙述，用下面两个标准去确定砼受压区的极限压根据作者的叙述，用下面两个标准去确定砼受压区的极限压应变，然后取小值作为极限压应变。标准应变，然后取小值作为极限压应变。标准1 1： 受压应力应变受压应力应变曲线的下降段的曲线的下降段的收敛点收敛点E E为砼的失效点，其对应的应变即砼为砼的失效点，其对应的应变即砼的极限压应变。通常来说，取应力峰值的的极限压应变。通常来说，取应力峰值的50%50%对应的点作为对应的点作为收敛点是合理的，即：收敛点是合理的，即： 标准标准2 2：作者的研究表明，配置普：作者的研究表明，配置普通箍筋的砼极限压应变不大于通箍筋的砼极限压应变不大
254、于0.0150.015，本文取其小于等于，本文取其小于等于0.0150.015n n（3 3）纵向受压钢筋达到屈曲应变）纵向受压钢筋达到屈曲应变n n纵筋发生屈曲，经常会使得砼保护层严重受损，纵筋发生屈曲，经常会使得砼保护层严重受损，同时，发生了大的同时，发生了大的粘结滑移粘结滑移，粘结力急剧减少。，粘结力急剧减少。没有了砼的约束，箍筋间的受压纵筋屈曲，核心没有了砼的约束，箍筋间的受压纵筋屈曲，核心砼的压应力显著减少。当砼的压应力显著减少。当箍筋间距箍筋间距相对较小时，相对较小时，钢筋的屈曲并不是砼剪力墙极限状态的控制因素。钢筋的屈曲并不是砼剪力墙极限状态的控制因素。n n（4 4）承载力降低
255、至峰值的）承载力降低至峰值的85%85%n n按照按照预制大型钢筋砼框架的节点与连接设计规预制大型钢筋砼框架的节点与连接设计规范范, ,在下降段取峰值的在下降段取峰值的85%85%对应的点作为砼剪力对应的点作为砼剪力墙的极限状态点墙的极限状态点. .n n在以上四个条件中，条件在以上四个条件中，条件3 3经常伴随着条件经常伴随着条件2 2发生，发生，它并不是控制因素，将条件它并不是控制因素，将条件1 1，2 2，4 4作为确定砼剪作为确定砼剪力墙的极限状态的准则。将其中的最小变形作为力墙的极限状态的准则。将其中的最小变形作为极限变形。极限变形。n n3.3 3.3 地震作用下的砼剪力墙的极限塑
256、性变形地震作用下的砼剪力墙的极限塑性变形n n屈服前，非弹性变形和砼剪力墙的结构破坏是很少屈服前，非弹性变形和砼剪力墙的结构破坏是很少见的，用屈服变形作为砼剪力墙在频遇地震作用下见的，用屈服变形作为砼剪力墙在频遇地震作用下的变形限值，以满足国家标准中抗震设计的的变形限值，以满足国家标准中抗震设计的“ “小震小震不坏不坏” ”是合理的。当砼剪力墙达到极限状态时，构是合理的。当砼剪力墙达到极限状态时，构件严重破坏，承载力明显下降。建议在大震作用下，件严重破坏，承载力明显下降。建议在大震作用下，用极限变形作为砼剪力墙的变形限值，以保证抗震用极限变形作为砼剪力墙的变形限值，以保证抗震设计中设计中“ “
257、大震不倒大震不倒” ”， 砼剪力墙的行为状态与塑性砼剪力墙的行为状态与塑性变形相近，所以塑性变形与屈服变形的差值，作为变形相近，所以塑性变形与屈服变形的差值，作为砼剪力墙的抗震作为指数。砼剪力墙的抗震作为指数。 因此，因此，频遇地震频遇地震下的塑下的塑性变形不大于性变形不大于0 0，大震作用大震作用下的塑性变形不大于极限下的塑性变形不大于极限塑性变形，用塑性变形，用参数参数a a表示塑性变形与屈服变形的差值。表示塑性变形与屈服变形的差值。强震下的塑性变形集中在对砼剪力墙的塑性变形限强震下的塑性变形集中在对砼剪力墙的塑性变形限值的计算。值的计算。国家网球中心新馆可开启屋盖的风国家网球中心新馆可开
258、启屋盖的风压分布压分布n n摘要：由于国家网球中心新馆可开闭屋盖自重轻、柔性大、摘要：由于国家网球中心新馆可开闭屋盖自重轻、柔性大、阻尼小，所以易受风载影响，风载是控制结构设计最重要阻尼小，所以易受风载影响，风载是控制结构设计最重要的荷载。本文用同步测压技术和计算流体力学数字模拟技的荷载。本文用同步测压技术和计算流体力学数字模拟技术，对国家网球中心新馆可开闭屋盖在开合时的平均风载术，对国家网球中心新馆可开闭屋盖在开合时的平均风载和脉动风载的风压分布进行了研究。平均风压依赖于可开和脉动风载的风压分布进行了研究。平均风压依赖于可开闭屋盖的表面形状和状态。表面形状的变化会导致形状系闭屋盖的表面形状和
259、状态。表面形状的变化会导致形状系数的巨大变化。不过，当可开闭屋盖处于状态不同时，最数的巨大变化。不过，当可开闭屋盖处于状态不同时，最大形状系数位于不同区域。作用在可开闭屋盖的风压分布大形状系数位于不同区域。作用在可开闭屋盖的风压分布密度概率并不适于高斯分布且比高斯分布更加密度概率并不适于高斯分布且比高斯分布更加sharpersharper，所，所以风压的脉冲效应是显著的。风载的均方根分布与形状系以风压的脉冲效应是显著的。风载的均方根分布与形状系数的增色方根分布相关，最大的均方根位于形状系数显著数的增色方根分布相关，最大的均方根位于形状系数显著变化的位置。基于风压的平均及脉冲分布，提出了非流线变
260、化的位置。基于风压的平均及脉冲分布，提出了非流线型空气动力学的途径型空气动力学的途径n n1 1 简介简介n n过去十年，中国已经修建或拟建大量的大跨屋顶结构。这过去十年，中国已经修建或拟建大量的大跨屋顶结构。这类屋顶结构一般具有自重轻、柔性大、小阻尼和自振频率类屋顶结构一般具有自重轻、柔性大、小阻尼和自振频率低。因此，大跨屋顶对风更加敏感，风荷载是结构设计中低。因此，大跨屋顶对风更加敏感，风荷载是结构设计中的主要控制荷载。可开闭屋盖是一种大跨屋顶，建筑形式的主要控制荷载。可开闭屋盖是一种大跨屋顶，建筑形式和状态的多样性使得可开闭屋盖上的风载更加复杂。和状态的多样性使得可开闭屋盖上的风载更加复
261、杂。n n国家网球中心新馆位于北京奥林匹克公园北区，将是国家网球中心新馆位于北京奥林匹克公园北区，将是20102010年中国网球公开赛的主比赛馆，国家网球中心新馆屋盖平年中国网球公开赛的主比赛馆，国家网球中心新馆屋盖平面形状为直径面形状为直径140m140m的圆形的圆形, ,在球形屋盖的中部设置投影尺在球形屋盖的中部设置投影尺寸为寸为70m70m70m70m的可开启屋盖。屋盖固定部分采用三层网壳的可开启屋盖。屋盖固定部分采用三层网壳结构，可开闭屋盖部分由预应力空间桁架组成。结构，可开闭屋盖部分由预应力空间桁架组成。n n由于国家网球中心新馆可开闭屋盖自重轻、柔性大、小阻尼，所以易受风载影响， 风荷载是结构设计中的主要控制荷载。本文用同步测压风洞试验和计算流体力学数字模拟技术，对国家网球中心新馆可开闭屋盖在开合时的风压分布特性进行了研究，包括平均风载和脉冲风载。
