分析预应力混凝土连续梁-外文翻译

1、分析预应力混凝土连续梁梁克里斯burgoyne 2005年3月2 6日1绪论这次会议是专门讨论结构分析的发展，而不是讨论材料强度，但对材料的认 识并用适当的技术分析结构的组成，有助于有效地利用预应力混凝土。预应力混 凝土结构的设计通常是留给专家；粗心将会导致错误或花费更多时间用各种方法 寻求解决的方案。有一些根本性的分歧在预应力混凝土和其他材料之间。在没有作用荷载下结 构依然是受力；可行的解决方案是有限的，在超静定结构，缆索外形的改变会引 起不同的自应力，所有这些要素都是受到徐变和温度效应的影响。如何判别这些 问题和如何解决他们呢？自从在十九世纪末hennebique对钢筋混凝土进行了研究（库

2、萨克1984年）， 它表明了钢筋和混凝土能更有效地结合起来，如果钢先预制然后把混凝土灌进去。 开裂可以减少，如果可以很好的粘结在一起，这将增加刚度和提高耐久性。早期 尝试，所有失败的原因是由于初始预应力很快消失，留下的结构必须具备一定的 承受能力；关于这些情况leonhardt和abeles已做出了尝试。这是freyssinet对三座桥梁的观察结果，它坐落在维希附近的alli er河上， 1927年完成。用的是预应力混凝土（ freyssinet 1956年）。只有boutiron这 座桥在二战中保留下来（图1 ）。迄今，它一直假定混凝土的杨氏模量仍然是i古i 定的，但他承认说由于变形的存在，

3、这也解释为何在早期的检测预应力已经损失。 freyssinet （图2 ）因为高强度钢筋已予使用，所以发生徐变后仍然残留有一些 预应力，而且同时使用了高质量的混凝土，因此这可减少总体的徐变。关于 freyssinet的早期预应力混凝土研究是被写在其他地方。figure 1: boutiron bridge, vichyfigure 2: eugen freyssinet大约在同一时间，这个工作也在英格兰的bre实验室进行着（格兰维尔1930 年）和（1933 ）。徐变的发现将归功于谁，受到了争论，但freyssinct对 预应力混凝土的研究和成功的应用是人家都公认的。还有相关问题需要讨论，比如

4、预应力混凝土的工作机理是怎样的？因为有好 儿个的关于它的思维方式。这些不同的哲学是在一定程度上的矛盾，当然也包含 年轻的工程师。它也反映，在某程度上，有很多种看法。容许应力设计哲学认为，预应力混凝土的一种方式，靠消除拉应力避免开裂； 目的是在徐变的损失后保持足够的压缩。由于徐变产生预应力损失，这一理念源 于freyssinet的推理和主要的有效应力的概念。极限强度哲学认为，预应力的一种利用高钢筋作为加固的方式。当它用来作 为加固时高强度钢的高弹性应变的能力无法被利用；如果钢筋是先张法，大部分 的应变量在钢筋粘接混凝土前z前已经损失。这种方式的结构设计通常设计为全 桥处于永久荷载，但高活载下是允

5、许裂纹。这种想法源于dischinger从他1936年的研究和他1939年对奥厄大桥的研究工作中得出（schaonberg和菲克特1939 年）,以及finstcrwaldcr （ 1939年）。这主要是一种极限荷载的想法。部分 预应力来自这些想法。t.y提幽加载平衡的哲学，利用预应力对永久荷载的反效果（林1963） o缆 索的下垂对梁产生上升的力，导致梁产生反作用力。显然，除非这被作为恒载的 重量，这个负载才可以被平衡掉，然而在这恒载作用下梁只有净轴向预应力和不 会有任何的倾向，向上或向下徐变。这三个哲学都有其看法，至于这些中哪个是最根本的，他们敞开激烈的辩论。2断面设计从一开始就被承认，预

6、应力混凝土要检查两个状态：正常使用负荷和极限状 态负荷。对于钢结构，和那些钢筋混凝土，应进行承载能力下允许应力设计和极 限载荷下的极限强度设计。旧规范是根据在正常工作负荷下的容许应力规定的； 新规范是使用短期的极限荷载。不同负荷的方式用于这两种规范，而是对于一个 结构，通过其中一种负荷就可能通过另一种负荷。figure 3: load dehection curve对于预应力混凝土，这些想法不太对的，由于结构是高应力的，即使没有负 荷。少量增加负荷，可以带来一些应力超过极限，而人量增加负载可能会超过其 他的极限。设计师应当考虑不同的工作负荷和极限荷载的能力；并都需要进行验 算。在每种负荷的情况

7、下，设计师通常要检查拉仲和压缩应力，无论在顶部述是 底部。关键结构都能正常使用，但也不是一概而论，对于中跨度和部分超过一般 尺寸，其他部位有可能成为关键结构。当缆索的断面形状被定下来。应力在任何位置都是由三个部分组成，其中通常有不同于其他两个的特性； 特性的一致是至关重要的。若p是预应力强度，e是其偏心率，a是横截面积，z是其弹性模量，而m是 作用力矩，然后ft和fc是允许的抗拉强度和抗压强度。因此，对于任何组合的p和m,设计师都用四分之一来处理。随着时间的推移预应力强度会改变，这是由于蠕变的原因，设计师通常是至 少面临着三种预应力和力矩的组合；在徐变衰减z前，第一次施加作用力矩。在徐变衰减之

8、后，最大的作用力矩。在徐变衰减之前，最小的作用力矩。figure 4: gustave magnel其他的组合，可能需要在更复杂的情况下。在任一截面上至少要满足12种不 同的情况，但由于一个截面有六变数，有两个预应力需要给定，但问题很难给定, 这不能明显的看出哪些情况是多余的。在没有经验的工程师手屮，设计过程可能 很冗长。不过可以通过设计预应力值区分出各设计断面。考虑应力的极限状态，对于不同负荷情况下，预应力的影响可以被忽略，留下的表达形式:moment rangepermissible stress range这些不等式，不是太困难，这样截面的最小容许尺寸就可以确定。只要一个合适的截面己拟定

9、，结构的预应力就可以设计。极限应力可以重新排列到表单中：这些在一个图表上的偏心预应力强度，由一系列的散点线形成。提供了不同 情况的满足状态，这些约束线将永远留下一个区，显示所有可行的组合的p和e。 最经济的设计，是根据预应力的包络图，通常是对右手边的图，那里的设计是在 所允许的拉应力范围内。cover zone乙冬 bottom"figure 5: magiiel diagrain纵轴允许的偏心值用图面育接与横截面比较，如图5所示。不等式（3 ）没 有提到结构的尺寸，但这些实际范围也可以显示出来。一个好的设计师懂得如何改变设计方案和负载方式。改变这两个最高和最低 弯矩，但保持在一定的

10、范阖内，同时，提高和降低可行的区域。使得弯矩变得更 加合理，这样梁的受力更有利。在一般，随着跨径的加大，相对于活荷，恒载的 弯矩值的比例将增加。有一个交叉点将达到较经济又满足结构受力要求；guyon 认为这个极限状态为临界跨径。短跨度在两端将受拉应力。而更长的跨度将受到 偏心率和在底部拉应力的限制。不过，这并不需要的增加大量的弯矩，此时压应 力将控制在梁底最大极限弯矩之内。当需要更大的跨径和要求可行区域尽可能的向下移动时，将使得结构变成取 决于在两板之间的压应力。3连续梁设计静定梁是相对比较简单的；工程师会根据特殊的断面进行设计，正如上 文所述。许多状况会出现，这就意味着设计师要考虑的不仅仅是

11、一个是控制截面，figure 6: liizancy bridge梁是作为一个整体参与受力的。这些都是由于若干因素相互作用的，如徐变，温 度效应和施工顺序的影响。这是这些想法以论文的形式慢慢发展。1951年郑家富 和维特在伦敦举行解决连续性问题的会议。基本原则和专业术语早被使用，但用 现代的眼光去处理和分析技术是不寻常的，而其中一个被关注的难题是估算预应 力损失。3. 1次内力由于预应力钢索锚在梁上会造成结构的偏斜。不同于静定梁可以不受约束的 移动，位移将导致支承反力重新分配并引起附加内力。这些都是常被称为次内力， 其值并不总是小，但也并不总是不好的。freyssinet桥位于luzancy横

12、跨马恩，始建于1941年，但直到1946年才完 工，它常常被认为是一简支梁，但它其实是建立在作为一个两较拱上，借助于扁 千斤顶和楔块调整支承反力。这种方法被应用在同一条河上所建造的后來的和较 大的桥梁。figure 7: sclayn bridge在1946年magnel建造了比利时斯克莱恩河上第一座混合的连续梁桥（图7 ）。 缆索几乎是直的，但它调整板的位置以便缆索更能接近中跨的梁底面。即使直线 型钢丝束下垂的次内力比较大，大约50%的负弯矩由恒载和活载所引起。只有知道缆索变形才能得出次内力，有了次内力才能进行缆索的设计。guyon 提岀了吻合线的概念。符合吻合线时是没有次内力矩，es和ep

13、是重合的，所有的 内力线都是它本身的吻合线。设计师面临着一个稍微简单的问题；缆索的布置不仅要满足偏心率的要求而 且也要协调一致。这也是一个重要的问题，可根据许多种不同组合的荷载作用在 梁上的弯矩图进行设计，为了缆索的自重，梁本身也应是一吻合线。这样的受力 是理想的，但它与结构实际所受的力是有区别的。逐步地调整可找出一组比较理 想的受力使得它接近理想线的弯矩图。3. 2温度的影响所有结构都会发生温度变化，但温度变化对预应力混凝土连续梁桥结构的影 响，比起其他结构更加明显。当我们进行计算时，温度分布图沿梁的厚度可分成 三部分。第一种是由于结构纵向膨胀引起的；第二种是弯曲导致梁的挠度和和作 用在连续

14、梁上的弯矩；而第三种是横截面上自平衡的一组受力。作用物弯矩是可以估算的，对于预应力混凝土梁自平衡引起的受力也是一个 重要的问题。梁通常地是高蓄热物质，这就意味着每天的温度变化不传到结构的 核心部位。结果是温度的不均匀分布导致沿梁不同厚度产生自平衡应力。如果结 构的中心处于高温而表面处于低温，那么在夜间，梁的顶部和底部表面将产牛相 当大的拉应力。如果靠改变截面或预加压力来克服温度产生的拉应力是非常的不 经济。3. 3施工顺序的影响预应力混凝土往往被用于较长的大跨度桥梁结构，它们常常是按是顺序施工 的。在施工的末期挠曲力矩是不同于成桥的整体弯矩。举例来说，用平衡悬臂施 工法从主桥墩两边扩建，这样结

15、构就不可避免产生弯曲挠度。当两悬臂梁端合拢 在一起使得它们完全地连续。预应力钢索被布置在顶板上以便抵抗悬臂是的下弯 挠度，预应力钢索通过连接使其连续以便抵抗后期的弯曲挠度。设计师不得不考虑临时的情况以及施加时产生的附加弯矩，这些都是施工过 程所引起的。弯矩可以是很大的，由于他们是恒载支撑的再分布导致的，因此附 加力矩是遵从相同的规律。设计师有意地选择使用连续的缆索去引起附加力矩以 减少负弯矩。当结构处于单独结构情形时，通过利用临时预应力钢索可以导致更大的次弯 矩，它随支撑条件移动而改变。比如一跨接一跨的结构，对于在跨径的桥梁每次 修建一跨，在建设期间，它有吋必需引进临时缆索于以抵抗下垂弯矩。将

16、缆索穿 进两跨之间，可一旦它发生位移，结构受力就更加复杂，应力也不会平衡，这影 响是不能忽略的。3. 4徐变的影响最后需要考虑的是徐变的影响，freyssinet发现用预应力混凝土可以减少由 于徐变所引起强度损失。在简支梁中徐变的发生使得一些预应力损失和增加梁的 挠度，这可能需要被考虑的，但是它不影响弯矩分配，所以设计时相对比较简单。如果结构是不确定的，支撑条件重新分配可能会改变挠曲力矩。如果混凝土 是一块块同吋预制，那么结构的有效模量将均匀地变化，在这种情况下强度将可 能不会重新分配。然而如果混凝土具有不同的老化程度，那么对于允许弯矩重新分配的结构， 在不同部位产生的徐变大小也不一样。现在大

17、家都认为发生徐变都接近整体状态, 设计者可以取这当做设计参考和把这整体的状态当做梁工作的极限状态，这简化 了设计过程。英格兰对沿梁不同高度的温度效应变化进行了研究，徐变是随温度变化而变 的，结构较热的那侧发生徐变的速度比冷的那侧快，它可以显著地改变荷载分布。 这个研究最初被应用到船舶护外壳上，船舶护外壳沿壳厚温度变化可以超过100 度。这个研究是利用稳态的这一概念。虽然应力没有再分布但是徐变仍延续着。 近年来，认为沿船桥甲板的厚度较小温度变化是可能发生的，它大概5度左右， 这也是值得注意的影响。发生徐变的速度取决于结构不同部位混凝土的老化程度。4、结论：要成功的设计预应力混凝土连续梁不能脱离对

18、结构的分析，自从第一个超静 定结构被建造，这个方法已经发展起来。在同一期间这种结构分析方法也是非常 值得我们深思。设计师不能一味的使用分析程序而忽略预应力混凝土的工作机理。外文文献翻译原文analysis of continuous prestressed concrete beamschris burgoynemarch 26, 20051、introductionthis conference is devoted to the development of structural analysis rather than the strength of materials, but the

19、 effective use of prestressed concrete relies on an appropriate combination of structural analysis techniques with knowledge of the material behaviou匚 design of prestressed concrete structures is usually left to specialists; the unwary will either make mistakes or spend inordinate time trying to ext

20、ract a solution from the various equations.there are a number of fundamental differences between the behaviour of prestressed concrete and that of other materials. structures are not unstressed when unloaded; the design space of feasible solutions is totally bounded； in hyperstatic structures, vario

21、us states of self-stress can be induced by altering the cable profile, and all of these factors get influenced by creep and thermal effects. how were these problems recognised and how have they been tackled?ever since the development of reinforced concrete by hennebique at the end of the 19th centur

22、y (cusack 1984), it was recognised that steel and concrete could bemore effectively combinedif thesteelwaspretensioned, puttingthe concrete intocompression. cracking couldbereduced, if not prevented altogether, which would increase stiffness and improve durability. early attempts all failed because

23、the initial prestress soon vanished, leaving the structure to be- have as though it was reinforced; good descriptions of these attempts are given by leonhardt (1964) and abeles (1964).it was freyssineti's observations of the sagging of the shallow arches on three bridges that he had just complet

24、ed in 1927 over the river allier near vichy which led directly to prestressed concrete (freyssinet 1956). only the bridge at boutiron survived wwii (fig i). hitherto, it had been assumed that concrete had a youngs modulus which remained fixed, but he recognised that the de- ferred strains due to cre

25、ep explained why the prestress had been lost in the early trials. freyssinet (fig. 2) also correctly reasoned that high tensile steel had tobe used, so that some prestress would remain after the creep had occurred, and also that high quality concrete should be used, since this minimised the total am

26、ount of creep. the history of freyssinetis early prestressed concrete work is written elsewherefigure 1: boutiron bridge, vichyfigure 2: eugen freyssinetat about the same time work was underway on creep at the bre laboratory in england (glanville 1930) and (1933). it is debatable which man should be

27、 given credit for the discovery of creep but freyssinet clearly gets the credit for successfully using the knowledge to prestress concrete.there are still problems associated with understanding how prestressed concrete works, partly because there is more than one way of thinking about it. these diff

28、erent philosophies are to some extent contradictory, and certainly confusing to the young engineer. it is also reflected, to a certain extent, in the various codes of practice.permissible stress design philosophy sees prestressed concrete as a way of avoiding cracking by eliminating tensile stresses

29、; the objective is for sufficient compression to remain after creep losses. untensioned reinforcement, which attracts prestress due to creep, is anathema. this philosophy derives directly from freyssinets logic and is primarily a working stress concept.ultimate strength philosophy sees prestressing

30、as a way of utilising high tensile steel as reinforcement. high strength steels have high elastic strain capacity, which could not be utilised when used as reinforcement; if the steel is pretensioned, much of that strain capacity is taken out before bonding the steel to the concrete. structures desi

31、gned this way are normally designed to be in compression everywhere under permanent loads, but allowed to crack under high live load. the idea derives directly from the work of dischinger (1936) and his work on the bridge at aue in 1939 (schonberg and fichter 1939), as well as that of finsterwalder

32、(1939). it is primarily an ultimate load concept. the idea of partial prestressing derives from these ideas.the load-balancing philosophy, introduced by t.y. lin, uses prestressing to counter the effect of the permanent loads (lin 1963). the sag of the cables causes an upward force on the beam, whic

33、h counteracts the load on the beam. clearly, only one load can be balanced, but if this is taken as the total dead weight, then under that load the beam will perceive only the net axial prestress and will have no tendency to creep up or down.these three philosophies all have their champions, and hea

34、ted debates take place between them as to which is the most fundamental.2、section designfrom the outset it was recognised that prestressed concrete has to be checked at both the working loadandthe ultimate load. forsteelstructures,andthose made from reinforced concrete, there is a fairly direct rela

35、tionship between the load capacity underanallowable stressdesign, andthat attheultimate load under an ultimate strength design. older codes were based on permissible stresses at the working load; new codes use moment capacities at the ultimate load. different load factors are used in the two codes,

36、but a structure which passes one code is likely to be acceptable under the othe匚figure 3: load deflection curvefor prestressed concrete, those ideas do not hold, since the structure is highly stressed, even when unloaded. a small increase of load can cause some stress limits to be breached, while a

37、large increase in load might be needed to cross other limits. the designer has considerable freedom to vary both the working load and ultimate load capacities independently; both need to be checked.a designer normally has to check the tensile and compressive stresses, in both the top and bottom fibr

38、e of the section, for every load case. the critical sections are normally, but not always, the mid-span and the sections over piers but other sections may become critical , when the cable profile has to be determined.the stresses at any position are made up of three components, one of which normally

39、 has a different sign from the other two; consistency of sign convention is essential.if p is the prestressing force and e its eccentricity, a and z are the area of the cross-section and its elastic section modulus, while m is the applied moment, then where ft and fc are the permissible stresses in

40、tension and compression.thus, for any combination of p and m , the designer already has four equalities to deal with.the prestressing force differs over time, due to creep losses, and a designer is usually faced with at least three combinations of prestressing force and moment; the applied moment at

41、 the time the prestress is first applied, before creep losses occur, the maximum applied moment after creep losses, and the minimum applied moment after creep losses.figure 4: gustave magnelother combinations may be needed in more complex cases. there are at least twelve inequalities that have to be

42、 satisfied at any cross-section, but since an i-section can be defined by six variables, and two are needed to define the prestress, the problem is over-specified and it is not immediately obvious which conditions are superfluous. in the hands of inexperienced engineers, the design process can be ve

43、ry long-winded. however, it is possible to separate out the design of the cross-section from the design of the prestress. by considering pairs of stress limits on the same fibre, but for different load cases, the effects of the prestress can be eliminated, leaving expressions of the form:z<moment

44、 rangepermissible stress rangethese inequalities, which can be evaluated exhaustively with little difficulty, allowthe minimum size of the cross-section to be determined.once a suitable cross-section has been found, the prestress can be designed using a construction due to magnel (fig.4). the stress

45、 limits can all be reaitanged into the form:71e<+c/z + m)a pby plotting these on a diagram of eccentricity versus the reciprocal of the prestressing force, a series of bound lines will be formed. provided the inequalities (2) are satisfied, these bound lines will always leave a zone showing all f

46、easible combinations of p and e. the most economical design, using the minimum prestress, usually lies on the right hand side of the diagram, where the design is limited by the permissible tensile stresses.plotting the eccentricity on the vertical axis allows direct comparison with the crosssection,

47、 as shown in fig. 5. inequalities (3) make no reference to the physical dimensions of the structure, but these practical cover limits can be shown as wella good designer knows how changes to the design and theloadings alter the magnel diagram. changing both the maximum and minimum bending moments, b

48、ut keeping the range the same, raises and lowers the feasible region. if the moments become more sagging the feasible region gets lower in the beam.in general, as spans increase, the dead load moments increase in proportion to the live load. a stage will be reached where the economic point (a on fig

49、.5) moves outside the physical limits of the beam; guyon (1951a) denoted the limiting condition as the critical span. shorter spans will be governed by tensile stresses in the two extreme fibres, while longer spans will be governedbythe limitingeccentricityand tensile stresses in the bottomfibre. ho

50、wever, itdoesnot take alarge increase in moment，at which pointcompressive stresses will govern in the bottom fibre under maximum moment.only whenmuchlongerspans arerequired, and the feasibleregion moves asfardown aspossible,does the structure becomegoverned by compressive stresses in both fibres.3、c

51、ontinuous beamsthe designof statically determinate beams is relativelystraightforward;the engineer canwork on the basis of the design ofindividual cross-sections, as outlined above. a number of complications arise when the structure is indeterminate which means that the designer has. to consider, no

52、tonly a critical section, the interaction of a number of factors, such as creep, temperature effects and construction sequence effects- it is the development of these ideas which forms the core of this paper. the problems of continuity were addressed at a conference in london (andrew and witt 1951).

53、 the basic principles, and nomenclature, were already in use, but to modern eyes concentration on hand analysis techniques was unusual, and one of the principle concerns seems to have been the difficulty of estimating losses of prestressing force.figure 6: liizancy bridgebut also the behaviour of th

54、e beam as a whole. these are due to3.1 secondary momentsa prestressing cable in a beam causes the structure to deflect. unlike the statically determinate beam, where this motion is unrestrained, the movement causes a redistribution of the support reactions which in turn induces additional moments. t

55、hese are often termed secondary moments, but they are not always small, or parasitic moments, but they are not always bad.freyssinetbridge across the marne atluzancy, started in1941but not completed until 1946, is often thought of as a simply supported beam,butit was actually built asa two-hinged ar

56、ch (harris1986), with support reactions adjusted by means of flat jacks and wedges whichwerelater grouted-in (fig.6).the same principleswereapplied in thelaterand larger beams builtover the same rive匸magnel built the first indeterminate beam bridge at sclayn, in belgium (fig.7) in 1946. the cables a

57、re virtually straight, but he adjusted the deck profile so that the cables were close to the soffit near mid-span. even with straight cables the sagging secondary momentsfigure 7: sclavn bridgeare large; about 50% of the hogging moment at the central support caused by dead and live load.the secondar

58、y moments cannot be found until the profile is known but the cable cannot be designed until the secondary moments are known. guyon (1951b) introduced the concept of the concordant profile, which is a profile that causes no secondary moments; es and ep thus coincide. any line of thrust is itself a concordant profile.the designer is then faced w 让h a slightly simpler problem; a cable profile has to be chosen which not only satisfies the eccentricity limits (3) but is also concordant. that in