外文翻译 (4)

西安科技大学高新学院毕业设计（论文）

外文翻译

学生姓名：韩挺

院（系）：建工学院

专业班级：土木工程

指导教师：冯琪

完成日期：

8-2简支梁布局

一个简单的预应力混凝土梁由两个危险截面控制：最大弯矩截面和端截面。这两部分设计好之后，中间截面一定要单独检查，必要时其他部位也要单独调查。最大弯矩截面在以下两种荷载阶段为控制情况，即传递时梁受最小弯矩M G的初始阶段和最大设计弯矩M T时的工作荷载阶段。而端截面则由抗剪强度、支承垫板、锚头间距和千斤顶净空所需要的面积来决定。所有的中间截面是由一个或多个上述要求，根它们与上述两种危险截面的距离来控制。对于后张构件的一种常见的布置方式是在最大弯矩截面采用诸如I形或T形的截面，而在接近梁端处逐渐过渡到简单的矩形截面。这就是人们通常所说的后张构件的端块。对于用长线法生产的先张构件，为了便于生产，全部只用一种等截面，其截面形状则可以为I形、双T形或空心的。在第5 、 6 和7章节中已经阐明了个别截面的设计，下面论述简支梁钢索的总布置。

梁的布置可以用变化混凝土和钢筋的办法来调整。混凝土的截面在高度、宽度、形状和梁底面或者顶面的曲率方面都可以有变化。而钢筋只在面积方面有所变化，不过在相对于混凝土重心轴线的位置方面却多半可以有变化。通过调整这些变化因素，布置方案可能有许多组合，以适应不同的荷载情况。这一点是与钢筋混凝土梁是完全不同的，在钢筋混凝土梁的通常布置中，不是一个统一的矩形截面便是一个统一的T形，而钢筋的位置总是布置得尽量靠底面纤维。

首先考虑先张梁，如图 8-7，这里最好采用直线钢索，因为它们在两个台座之间加力比较容易。我们先从图（a）的等截面直梁的直线钢索开始讨论。这样的布置都很简单，但这样一来，就不是很经济的设计了，因为跨中和梁端的要求会产生冲突。通常发生在跨度中央的最大弯矩截面中的钢索，最好尽量放低，以便尽可能提供最大力臂而提供最大的内部抵制力矩。当跨度中央的梁自重弯矩M G相当大时，就可以把c.g.s布置在截面核心范围以下很远的地方，而不致在传递时在顶部纤维中引起拉应力。然而对于梁端截面却有一套完全不同的要求。由于在梁端没有外力矩，因为在最后的时刻，安排钢索要以c.g.s与 c.g.c在结束区段一致，如此同样地获得克服压力分配的方法。无论如何，如果张应力在最后不能承受，放置 c.g.s. 是必需紧排的，而且紧排的不能太远，避免张拉应力超过应力允许值。

图8-7 布局预应力梁

同时满足跨中和梁端两种截面的布局需求这是不可能的，举例来说，如（ a ），如果 c.g.s.全都放在核心下界处，那么这对梁端截面来说，已经是容许的最低点，面对跨中截面来说，则还没有达到足够大的力矩臂来提供令人满意的内部抵抗力矩。如果 c.g.s.紧排在下面位置，在中跨处的抵抗力就可以达到要求了，但是最后压力分配将不太容易，此外，过大的反挠度也可能导致这样的布局，由于预应力在整个光纤内受到负面弯曲。尽管有这些不对的地方，但这往往是最简单的布局，特别是一些短跨。

对于直线钢索等截面的混凝土梁，有可能获得比（a）更理想的布置，只要变化一下梁的底面形状，如在图8-7里的（ b ）和（ c ） ; （b）中的底面是折线的，而（ c ）中则是弧线的。对于这两种布置，对c.g.s.在跨中可以尽量放在低的位置，而在两端可以保持c.g.s不变，如果梁的底面可以任意改动，这样就有可能获得最适合于荷载情况的曲线。举例来说，一个抛物线底面最适合于匀布荷载。虽然这两个布置有效地抵抗应力分布，但是有三个缺点，首先，在（a）处模板要

更加复杂；第二，由于建筑或功能的原因，弧形或折线形的底面往往不切合实用；第三，它们在长线法预应力台座上都很难生产出来。

只要有可能变化混凝土梁的顶面，那么就可以有利地采用图 8-7( d ），（ e ）那样的布置方案。这样在最需要高度的跨中具有良好的高度，而且在梁端截面可以得到一个共轴的或者近乎共轴的预加应力。因为高度在梁端截面减少，所以一定要经常检查。例如（ d ）,也应该注意危险截面可能不在跨中，宁可布置在一些远离它的点，在最大值附近高度略微有点降低。梁（ d ）在模板方面要比（ e ）项中具有弧线形顶面的梁简单。

美国的大多数先张预制工厂沿张拉台座埋设有锚头，以便于先张法梁的力筋也可以折曲，如图8-7的（f）、（g）。倘若梁必须是等截面的直梁，而且倘若梁自

重弯矩M G的确大得有必要作这种额外花费的弯曲的话，那么这样做也可能是经济的。不过必须设法减少力筋的弯曲所引起的预应力的摩擦损失。例如，在末端就先张拉，然后再受拉弯曲。

显然，从上述讨论中，许多布置都是可能的。只有一些基本的形式在这方面介

绍了，变化的组合需要自行设计。正确的布置结构将取决于当地的条件和实际需求

以及理论上的思考。

图8-8 使钢筋后张的梁的布局

但是，对于适筋梁，像图8-8，没有必要保持弯矩包络图是直线，因为稍微弯

曲或弧线形的力筋同直线力筋一样可以轻松张拉。因此，在等截面直梁中，力筋往往弯曲，例如在图8-8.(a)处。把力筋弯曲将会允许 c.g.s.在梁两端和跨中以及其他各点的截面中都获得有利的位置。

只要不要求用直线的底面，那么就常常可以采用如图 8-8( b ）所示的把弧线形或折曲的力筋配合弧线或折线底面一同使用。这样可以使力筋弯曲得小些，从而降低摩擦力。弧线的或折曲的钢索也可以配合变高度梁使用。如在（ c ）处。有时发现同时使用直线的和弧线的力筋颇为有利，如图（ d ）所示。

沿长度方向改变钢筋面积的布置方案偶尔也是可取的。这样的梁必须经过专门设计，而它所必须用到的细节构造却可能抵消掉所节省的钢材。在图8-8（e）中，一些钢索被向上弯曲而且布置在最高的边缘。在(f) 处，一些钢索在底部的边缘中被省略。这些布置方案虽然可以节省一些钢材，不过除了像用在承受重荷载的很长跨度的梁上那样能节约大量钢材的情况之外，可能不值得的采用。

8-3 钢索的纵断面

我们在上一节已经讨论了，简支梁的布置是受到最大弯矩和梁端两种截面控制，因而在这两种截面设计哈之后，介于其间的其他截面就往往可以通过观察来确定。然而，有时沿梁长度方向的中间点上也可能出现危险截面，乃至在许多情况中宜于为钢索确定容许的并且理想的纵断面。要做到这一点，c.g.s.在限制区的位置是首先需要确定的，然后再布置钢索，使其重心保持在限定区之内。

描述的方法在这里是为简支梁，但它也可作为解决更为复杂布局的方法，如悬臂梁和连续跨越梁，检查电缆的位置是不容易确定的。方法是图解式的；c.g.s.在给定的限制地域里面，生产时一定要通过井然有序且没有张应力的过程。压应力混凝土中没有检查这个的方法。据推测，布局的具体方法和地区的预应力钢已经确定时只有形象的c.g.s.的位置。

在谈到图8-9时，在确定具体的布局部分时，我们开始计算他们克恩点，从而产生两个克恩线，一个顶部和底部的一个，如（ c ）处。请注意，对于变截面，这些克恩线将被弯曲，但为方便起见，他们将表现出连续的数字以代表梁截面。

因为光缆装载显示在（a）处, 在（ b ）处最低和最高的时刻梁负荷载和总的工作负荷分别被标记为M G和M T。为了根据工作负荷，压力中心的C线，将不属于上述顶端克恩线，很明显，c.g.s.必须位于下方顶端克恩处。

a 1=M

T

/F (8-1)

图8-9 c. g. s.的限制区域

如果c.g.s.属于上述上限在任何地点，然后在C线相应的M T和预应力F载上述顶端克恩线处，底部光缆将造成严重受压。

同样，为了使C线不低于底部克恩线，c.g.s.线不得低于定位底部克恩线的位置。如果c.g.s.定位高于下限，这里看到的C线将高于底部克恩线，这样就不会产生顶端光纤梁下的负荷和初始预应力。

因此，它可以清楚地看到限制区c.g.s.给出了阴影面积图, 如图8-9（c），为了将根据梁负荷下的工作负荷不存在。然而，个别的腱可能被放在任何的位置，如

此就当做 c.g.s. 保持在所有的电缆中的限制地域里面。

位置和宽度的限制区往往说明是否是适当和经济的设计,如图8-10。如果上限的一些部分外面或者在底部的光纤附近落下，在（a）处, 预应力F或光缆的深度在那一部分应该被增加。另一方面，如果它属于上述底部纤维，在（ b ）中，预应力梁高度是可以降低的。如果穿越下限，在（ C ）中，这意味着，如果是可以做到没有c.g.s.提供的位置，然后在F或预应力梁深入时必须增加，以降低下限。另一方面，将讨论后，该例题中显示图8-10（c）可能是非常令人满意的是，允许布局在拉应力混凝土。

图8-10 限制c.g.s.的不利位置

8-2, Simple Beam Layout

The layout of a simple prestressed-concrete beam is controlled by two critical sections: the maximum moment and the end sections. After these sections are designed, intermediate ones can often be determined by inspection but should be separately investigated when necessary. The maximum moment section is controlled by two loading stages, the initial stage at transfer with minimum moment M G acting on the beam and the working-load stage with maximum design moment M T. The end sections are controlled by area required for share resistance, bearing plates, anchorage spacings, and jacking clearances. All intermediate sections are designed by one or more of the above requirements, depending on their respective distances from the above controlling sections.

A common arrangement for posttensioned members is to employ some shape, such as I

or T, for the maximum moment section and to round it out into a simple rectangular shape near the ends. This is commonly referred to as the end block for posttensioned members. For pretensioned members, produced on a long line process, a uniform I, double-T, or cored section is employed throughout, in order to facilitate production. The design for individual sections having been explained in Chapters 5, 6, and 7,the general cable layout of simple beams will now be discussed.

The layout of a beam can be adjusted by varying both the concrete and the steel. The section of concrete can be varied as to its height, width, shape, and the curvature of its soffit or extrados. The steel can be varied occasionally in its area but mostly in its position relative to the centroidal axis of concrete. By adjusting these variables, many combinations of layout are possible to suit different loading conditions. This is quite different from the design of reinforced-concrete beams, where the usual layout is either a uniform rectangular section or a uniform T-section and the position of steel is always as near the bottom fibers as is possible.

Consider first the pretensioned beams, Fig. 8-7.Here straight cables are preferred, since they can be more easily tensioned between two abutments. Let us start with a straight cable in a straight beam of uniform section, (a).This is simple as far as form and workmanship are concened, But such a section cannot often be economically designed, because of the conflicting requirements of the midspan and end sections. At the maximum moment section generally occurring at midspan, it is best to place the cable as near the bottom as possible in order to provide the maximum lever arm for the internal resisting moment. When the M G at midspan is appreciable, it is possible to place the c. g. s. much below the kern without producing tension in the top fibers at transfer. The end section, however, presents an entirely different set of requirements. Since there is no external moment at the end, it is best to arrange the tendons so that the c. g. s. will coincide with the c. g. c. at the end section, so as to obtain a uniform stress distribution.

In any case, it is necessary to place the c. g. s. within the kern if tensile stresses are not permitted at the ends, and not too far outside the kern to avoid tension stress in excess of

allowable values.

It is not possible to meet the conflicting requirements of both the midspan and the end sections by a layout such as ( a ). For example, if the c. g. s. is located all along the lower kern point, which is the lowest point permitted by the end section, a satisfactory lever arm is not yet attained for the internal resisting moment at midspan. If the c. g. s. is located below the kern, a bigger lever arm is obtained for resisting the moment at midspan, but stress distribution will be more unfavorable at the ends. Besides, too much camber may result from such a layout, since the entire length of the beam is subjected to negative bending due to prestress. In spite of these objections, this simple arrangement is often used, especially for short spans.

Fig 8-7. Layouts for pretensioned beams.

For a uniform concrete section and a straight cable, it is possible to get a more desirable layout than ( a ) by simple varying the soffit of the beam, as in Fig. 8-7( b ) and ( c ); ( b ) has a bent soffit, while ( c ) has a curved one. For both layouts, the c. g. s. at midspan can be depressed as low as desired, while that at the ends can be kept near the c.

g. c. If the soffit can be varied at will, it is possible to obtain a curvature that will best fit the given loading condition; for example, a parabolic soffit will suit a uniform loading. While these two layouts are efficient in resisting moment and favorable in stress distribution, they possess three disadvantages. First, the formwork is more complicated than in ( a ). Second, the curved or bent soffit is often impractical in a structure, for architectural or functional reasons. Third, they cannot be easily produced on a long-line

pretensioning bed.

When it is possible to vary the extrados of concrete, a layout like Fig. 8-7( d ) or ( e ) can be advantageously employed. These will give a favorable height at midspan, where it is most needed, and yet yield a concentric or nearly concentric prestress at end section. Since the depth is reduced for the end sections, they must be checked for share resistance. For ( d ), it should also be noted that the critical section may not be at midspan but rather at some point away from it where the depth has decreasd appreciably while the external moment is still near the maximum. Beam ( d ), however, is simple in formwork than ( e ), which has a curved extrados.

Most pretensioning plants in the United States have buried anchors along the stressing beds so that the tendons for a pretensioned beam can be bent, Fig. 8-7( f ) and ( g ). It may be economical to do so ,if the beam has to be of straight and uniform section, and if the M G is heavy enough to warrant such additional expense of bending. Means must be provided to reduce the frictional loss of prestress produced by the bending of the tendons. For example, the tendons may be tensioned first from the ends and then bent at the harping points.

It is evident from the above discussion that many different layouts are possible. Only some basic forms are described here, the variations and combinations being left to the discretion of the designer. The correct layout for each structure will depend upon the local conditions and the practical requirements as well as upon theoretical considerations.

Most of the layouts for pretensioned beams can be used for posttensioned ones as well. But, for posttensioned beams, Fig. 8-8, it is not necessary to keep the tendons straight, since slightly bent or curved tendons can be as easily tensioned as straight ones. Thus, for a beam of straight and uniform section, the tendons are very often curved as in Fig. 8-8( a ). Curving the tendons will permit favorable positions of c. g. s. to be obtained at both the end and midspan sections, and other points as well.

Fig 8-8. Layouts for posttensioned beams.

A combination of curved or bent tendons with curved or bent soffits is frequently used, Fig. 8-8( b ), when straight soffits are not required. This will permit a smaller curvature in the tendons, thus reducing the friction. Curved or bent cables are also combined with beams of variable depth, as in ( c ). Combinations of straight and curved tendons are sometimes found convenient, as in ( d ).

Variable steel area along the length of a beam is occasionally preferred. This calls for special design of the beam and involves details which may offset its economy in weight of steel. In Fig. 8-8( e ), some cables are bent upward and anchored at top flanges. In ( f ), some cables are stopped part way in the bottom flange. These arrangements will save some steel but may not be justified unless the saving is considerable as for very long spans carrying heavy loads.

8-3 Cable Profiles

We stated in the previous section that the layout of simple beams is controlled by the maximum moment and end sections so that, after these two sections are designed, other sections can often be determined by inspection. It sometimes happens, however, that intermediate points along the beam may also be critical, and in many instances it would be desirable to determine the permissible and desirable profile for the tendons. To do this, a limiting zone for the location of c. g. s. is first obtained, then the tendons are arranged so that their centroid will lie within the zone.

The method described here is intended for simple beams, but it also serves as an introduction to the solution of more complicated layouts, such as cantilever and continuous spans, where cable location cannot be easily determined by inspection. The method is a graphical one; giving the limiting zone within which the c. g. s. must pass in order that no tensile stresses will be produced. Compressive stresses in concrete are not checked by this method. It is assumed that the layout of the concrete sections and the area of prestressing steel have already been determined. Only the profile of the c. g. s. is to be located.

Referring to Fig . 8-9, having determined the layout of concrete sections, we proceed to compute their kern points, thus yielding two kern lines, one top and one bottom, ( c ) . Note that for variable sections, these kern lines would be curved, although for convenience they are shown straight in the figure representing a beam with uniform cross section.

For a beam loaded as shown in ( a ), the minimum and maximum moment diagrams for the girder load and for the total working load respectively are marked as M G and M T

in ( b ). In order that, under the working load, the center of pressure, the C-line, will not fall above the top kern line, it is evident that the c. g. s. must be located below the top kern at least a distance

a1=M T/F (8-1)

Fig 8-9. Location of limiting zone for c. g. s.

If the c. g. s. falls above that upper limit at any point, then the C-line corresponding to moment M T and prestress F will fall above the top kern, resulting in tension in the bottom fiber.

Similarly, in order that the C-line will not fall below the bottom kern line, the c. g. s. line must not be positioned below the bottom kern by a distance greater than which gives the lower limit for the location of c. g. s. If the c. g. s. is positioned above that lower limit, it is seen that the C-line will be above the bottom kern and there will be no tension in the top fiber under the girder load and initial prestress F0.

Thus, it becomes clear that the limiting zone for c. g. s. is given by the shaded area in Fig. 8-9( c ), in order that no tension will exist both under the girder load and under the working load. The individual tendons, however, may be placed in any position so long as the c. g. s. of all the cables remains within the limiting zone.

The position and width of the limiting zone are often an indication of the adequacy

and economy of design, Fig. 8-10. If some portion of the upper limit falls outside or too near the bottom fiber, in ( a ), either the prestress F or the depth of beam at that portion should be increased. On the other hand, if it falls too far above the bottom fiber, in ( b ), either the prestress or the beam depth can be reduced. If the lower limit crosses the upper limit, in ( C ), it means that no zone is available for the location of c. g. s. , and either the prestress F or the beam depth must be increased or the girder moment must be increased to depress the lower limit if that can be done. On the other hand, as will be discussed later, the case shown in Fig. 8.10( c ) may be very satisfactory when are allowing tensile stress in concrete.

Fig 8-10. Undesirable positions for c. g. s. zone limits.