土木 工程 英文 外文 文獻 翻譯 分析預(yù)應(yīng)力混凝土連續(xù)梁 畢業(yè)設(shè)計

1、分析預(yù)應(yīng)力混凝土連續(xù)梁 1緒論 這次會議是專門討論結(jié)構(gòu)分析的發(fā)展，而不是討論材料強度，但對材料的認識并用適當(dāng)?shù)募夹g(shù)分析結(jié)構(gòu)的組成，有助于有效地利用預(yù)應(yīng)力混凝土。預(yù)應(yīng)力混凝土結(jié)構(gòu)的設(shè)計通常是留給專家；粗心將會導(dǎo)致錯誤或花費更多時間用各種方法尋求解決的方案。有一些根本性的分歧在預(yù)應(yīng)力混凝土和其他材料之間。在沒有作用荷載下結(jié)構(gòu)依然是受力；可行的解決方案是有限的，在超靜定結(jié)構(gòu)，纜索外形的改變會引起不同的自應(yīng)力，所有這些要素都是受到徐變和溫度效應(yīng)的影響。如何判別這些問題和如何解決他們呢？自從在十九世紀(jì)末Hennebique對鋼筋混凝土進行了研究（庫薩克1984年） ，它表明了鋼筋和混凝土能更有效地結(jié)合起

2、來，如果鋼先預(yù)制然后把混凝土灌進去。開裂可以減少，如果可以很好的粘結(jié)在一起 ，這將增加剛度和提高耐久性。早期嘗試，所有失敗的原因是由于初始預(yù)應(yīng)力很快消失，留下的結(jié)構(gòu)必須具備一定的承受能力；關(guān)于這些情況Leonhardt和Abeles已做出了嘗試。這是Freyssinet對三座橋梁的觀察結(jié)果，它坐落在維希附近的Allier河上，1927年完成。用的是預(yù)應(yīng)力混凝土（ Freyssinet 1956年） 。只有Boutiron這座橋在二戰(zhàn)中保留下來（圖1 ） 。迄今，它一直假定混凝土的楊氏模量仍然是固定的，但他承認說由于變形的存在，這也解釋為何在早期的檢測預(yù)應(yīng)力已經(jīng)損失。 Freyssinet （圖

3、2 ）因為高強度鋼筋已予使用，所以發(fā)生徐變后仍然殘留有一些預(yù)應(yīng)力，而且同時使用了高質(zhì)量的混凝土，因此這可減少總體的徐變。關(guān)于Freyssinet的早期預(yù)應(yīng)力混凝土研究是被寫在其他地方。Figure 1: Boutiron Bridge， VichyFigure 2: Eugen Freyssinet大約在同一時間，這個工作也在英格蘭的BRE實驗室進行著（ （格蘭維爾1930年）和（ 1933 ） ） 。徐變的發(fā)現(xiàn)將歸功于誰，受到了爭論，但Freyssinet對預(yù)應(yīng)力混凝土的研究和成功的應(yīng)用是大家都公認的。還有相關(guān)問題需要討論，比如預(yù)應(yīng)力混凝土的工作機理是怎樣的？因為有好幾個的關(guān)于它的思維方式。

4、這些不同的哲學(xué)是在一定程度上的矛盾，當(dāng)然也包含年輕的工程師。它也反映，在某程度上，有很多種看法。容許應(yīng)力設(shè)計哲學(xué)認為，預(yù)應(yīng)力混凝土的一種方式，靠消除拉應(yīng)力避免開裂；目的是在徐變的損失后保持足夠的壓縮。由于徐變產(chǎn)生預(yù)應(yīng)力損失，這一理念源于Freyssinet的推理和主要的有效應(yīng)力的概念。極限強度哲學(xué)認為，預(yù)應(yīng)力的一種利用高鋼筋作為加固的方式。當(dāng)它用來作為加固時高強度鋼的高彈性應(yīng)變的能力無法被利用；如果鋼筋是先張法，大部分的應(yīng)變量在鋼筋粘接混凝土前之前已經(jīng)損失。這種方式的結(jié)構(gòu)設(shè)計通常設(shè)計為全橋處于永久荷載，但高活載下是允許裂紋。這種想法源于Dischinger從他1936年的研究和他1939年對奧

5、厄大橋的研究工作中得出（SchÄonberg和菲克特1939年） ，以及Finsterwalder（ 1939年） 。這主要是一種極限荷載的想法。部分預(yù)應(yīng)力來自這些想法。T.Y提出加載平衡的哲學(xué)，利用預(yù)應(yīng)力對永久荷載的反效果（林1963） 。纜索的下垂對梁產(chǎn)生上升的力，導(dǎo)致梁產(chǎn)生反作用力。顯然，除非這被作為恒載的重量，這個負載才可以被平衡掉，然而在這恒載作用下梁只有凈軸向預(yù)應(yīng)力和不會有任何的傾向，向上或向下徐變。這三個哲學(xué)都有其看法，至于這些中哪個是最根本的，他們敞開激烈的辯論。2斷面設(shè)計從一開始就被承認，預(yù)應(yīng)力混凝土要檢查兩個狀態(tài)：正常使用負荷和極限狀態(tài)負荷。對于鋼結(jié)構(gòu)，和那些鋼筋

6、混凝土，應(yīng)進行承載能力下允許應(yīng)力設(shè)計和極限載荷下的極限強度設(shè)計。舊規(guī)范是根據(jù)在正常工作負荷下的容許應(yīng)力規(guī)定的；新規(guī)范是使用短期的極限荷載。不同負荷的方式用于這兩種規(guī)范，而是對于一個結(jié)構(gòu)，通過其中一種負荷就可能通過另一種負荷。對于預(yù)應(yīng)力混凝土，這些想法不太對的，由于結(jié)構(gòu)是高應(yīng)力的，即使沒有負荷。少量增加負荷，可以帶來一些應(yīng)力超過極限，而大量增加負載可能會超過其他的極限。設(shè)計師應(yīng)當(dāng)考慮不同的工作負荷和極限荷載的能力；并都需要進行驗算。在每種負荷的情況下，設(shè)計師通常要檢查拉伸和壓縮應(yīng)力，無論在頂部還是底部。關(guān)鍵結(jié)構(gòu)都能正常使用，但也不是一概而論，對于中跨度和部分超過一般尺寸，其他部位有可能成為關(guān)鍵結(jié)

7、構(gòu)。當(dāng)纜索的斷面形狀被定下來。應(yīng)力在任何位置都是由三個部分組成，其中通常有不同于其他兩個的特性；特性的一致是至關(guān)重要的。若P是預(yù)應(yīng)力強度，e是其偏心率，A是橫截面積，Z是其彈性模量，而M是作用力矩，然后ft 和 fc 是允許的抗拉強度和抗壓強度。因此，對于任何組合的P和M，設(shè)計師都用四分之一來處理。隨著時間的推移預(yù)應(yīng)力強度會改變，這是由于蠕變的原因，設(shè)計師通常是至少面臨著三種預(yù)應(yīng)力和力矩的組合； 在徐變衰減之前，第一次施加作用力矩。在徐變衰減之后，最大的作用力矩。在徐變衰減之前，最小的作用力矩。Figure 4: GustaveMagnel其他的組合，可能需要在更復(fù)雜的情況下。在任一截面上至少

8、要滿足12種不同的情況，但由于一個截面有六變數(shù)，有兩個預(yù)應(yīng)力需要給定，但問題很難給定，這不能明顯的看出哪些情況是多余的。在沒有經(jīng)驗的工程師手中，設(shè)計過程可能很冗長。不過可以通過設(shè)計預(yù)應(yīng)力值區(qū)分出各設(shè)計斷面。考慮應(yīng)力的極限狀態(tài)，對于不同負荷情況下，預(yù)應(yīng)力的影響可以被忽略，留下的表達形式：這些不等式，不是太困難，這樣截面的最小容許尺寸就可以確定。只要一個合適的截面已擬定，結(jié)構(gòu)的預(yù)應(yīng)力就可以設(shè)計。極限應(yīng)力可以重新排列到表單中： 這些在一個圖表上的偏心預(yù)應(yīng)力強度，由一系列的散點線形成。提供了不同情況的滿足狀態(tài)，這些約束線將永遠留下一個區(qū)，顯示所有可行的組合的P和E 。最經(jīng)濟的設(shè)計，是根據(jù)預(yù)應(yīng)力的包絡(luò)圖

9、，通常是對右手邊的圖，那里的設(shè)計是在所允許的拉應(yīng)力范圍內(nèi)。縱軸允許的偏心值用圖面直接與橫截面比較，如圖 5所示。不等式（ 3 ）沒有提到結(jié)構(gòu)的尺寸，但這些實際范圍也可以顯示出來。一個好的設(shè)計師懂得如何改變設(shè)計方案和負載方式。改變這兩個最高和最低彎矩，但保持在一定的范圍內(nèi)，同時，提高和降低可行的區(qū)域。使得彎矩變得更加合理，這樣梁的受力更有利。在一般，隨著跨徑的加大，相對于活荷，恒載的彎矩值的比例將增加。有一個交叉點將達到較經(jīng)濟又滿足結(jié)構(gòu)受力要求； Guyon 認為這個極限狀態(tài)為臨界跨徑。短跨度在兩端將受拉應(yīng)力。而更長的跨度將受到偏心率和在底部拉應(yīng)力的限制。不過，這并不需要的增加大量的彎矩，此時壓

10、應(yīng)力將控制在梁底最大極限彎矩之內(nèi)。當(dāng)需要更大的跨徑和要求可行區(qū)域盡可能的向下移動時，將使得結(jié)構(gòu)變成取決于在兩板之間的壓應(yīng)力。3 連續(xù)梁設(shè)計靜定梁是相對比較簡單的；工程師會根據(jù)特殊的斷面進行設(shè)計，正如上文所述。許多狀況會出現(xiàn)，這就意味著設(shè)計師要考慮的不僅僅是一個是控制截面，梁是作為一個整體參與受力的。這些都是由于若干因素相互作用的，如徐變，溫度效應(yīng)和施工順序的影響。這是這些想法以論文的形式慢慢發(fā)展。1951年鄭家富和維特在倫敦舉行解決連續(xù)性問題的會議?；驹瓌t和專業(yè)術(shù)語早被使用，但用現(xiàn)代的眼光去處理和分析技術(shù)是不尋常的，而其中一個被關(guān)注的難題是估算預(yù)應(yīng)力損失。3.1 次內(nèi)力由于預(yù)應(yīng)力鋼索錨在梁上

11、會造成結(jié)構(gòu)的偏斜。不同于靜定梁可以不受約束的移動，位移將導(dǎo)致支承反力重新分配并引起附加內(nèi)力。這些都是常被稱為次內(nèi)力，其值并不總是小，但也并不總是不好的。Freyssinet橋位于Luzancy橫跨馬恩，始建于1941年，但直到1946年才完工，它常常被認為是一簡支梁，但它其實是建立在作為一個兩鉸拱上，借助于扁千斤頂和楔塊調(diào)整支承反力 。這種方法被應(yīng)用在同一條河上所建造的后來的和較大的橋梁。在1946年Magnel建造了比利時斯克萊恩河上第一座混合的連續(xù)梁橋（圖7 ）。纜索幾乎是直的，但它調(diào)整板的位置以便纜索更能接近中跨的梁底面。即使直線型鋼絲束下垂的次內(nèi)力比較大，大約50%的負彎矩由恒載和活載

12、所引起。只有知道纜索變形才能得出次內(nèi)力，有了次內(nèi)力才能進行纜索的設(shè)計。Guyon提出了吻合線的概念。符合吻合線時是沒有次內(nèi)力矩，es和ep是重合的，所有的內(nèi)力線都是它本身的吻合線。設(shè)計師面臨著一個稍微簡單的問題； 纜索的布置不僅要滿足偏心率的要求而且也要協(xié)調(diào)一致。這也是一個重要的問題，可根據(jù)許多種不同組合的荷載作用在梁上的彎矩圖進行設(shè)計，為了纜索的自重，梁本身也應(yīng)是一吻合線。這樣的受力是理想的，但它與結(jié)構(gòu)實際所受的力是有區(qū)別的。逐步地調(diào)整可找出一組比較理想的受力使得它接近理想線的彎矩圖。3.2 溫度的影響所有結(jié)構(gòu)都會發(fā)生溫度變化，但溫度變化對預(yù)應(yīng)力混凝土連續(xù)梁橋結(jié)構(gòu)的影響，比起其他結(jié)構(gòu)更加明顯

13、。當(dāng)我們進行計算時，溫度分布圖沿梁的厚度可分成三部分。第一種是由于結(jié)構(gòu)縱向膨脹引起的；第二種是彎曲導(dǎo)致梁的撓度和和作用在連續(xù)梁上的彎矩；而第三種是橫截面上自平衡的一組受力。作用物彎矩是可以估算的，對于預(yù)應(yīng)力混凝土梁自平衡引起的受力也是一個重要的問題。梁通常地是高蓄熱物質(zhì)，這就意味著每天的溫度變化不傳到結(jié)構(gòu)的核心部位。結(jié)果是溫度的不均勻分布導(dǎo)致沿梁不同厚度產(chǎn)生自平衡應(yīng)力。如果結(jié)構(gòu)的中心處于高溫而表面處于低溫，那么在夜間，梁的頂部和底部表面將產(chǎn)生相當(dāng)大的拉應(yīng)力。如果靠改變截面或預(yù)加壓力來克服溫度產(chǎn)生的拉應(yīng)力是非常的不經(jīng)濟。3.3 施工順序的影響預(yù)應(yīng)力混凝土往往被用于較長的大跨度橋梁結(jié)構(gòu)，它們常常是

14、按是順序施工的。在施工的末期撓曲力矩是不同于成橋的整體彎矩。舉例來說，用平衡懸臂施工法從主橋墩兩邊擴建，這樣結(jié)構(gòu)就不可避免產(chǎn)生彎曲撓度。當(dāng)兩懸臂梁端合攏在一起使得它們完全地連續(xù)。預(yù)應(yīng)力鋼索被布置在頂板上以便抵抗懸臂是的下彎撓度，預(yù)應(yīng)力鋼索通過連接使其連續(xù)以便抵抗后期的彎曲撓度。設(shè)計師不得不考慮臨時的情況以及施加時產(chǎn)生的附加彎矩，這些都是施工過程所引起的。彎矩可以是很大的，由于他們是恒載支撐的再分布導(dǎo)致的，因此附加力矩是遵從相同的規(guī)律。設(shè)計師有意地選擇使用連續(xù)的纜索去引起附加力矩以減少負彎矩。當(dāng)結(jié)構(gòu)處于單獨結(jié)構(gòu)情形時，通過利用臨時預(yù)應(yīng)力鋼索可以導(dǎo)致更大的次彎矩，它隨支撐條件移動而改變。比如一跨接

15、一跨的結(jié)構(gòu)，對于在跨徑的橋梁每次修建一跨，在建設(shè)期間，它有時必需引進臨時纜索于以抵抗下垂彎矩。將纜索穿進兩跨之間，可一旦它發(fā)生位移，結(jié)構(gòu)受力就更加復(fù)雜，應(yīng)力也不會平衡，這影響是不能忽略的。3.4 徐變的影響最后需要考慮的是徐變的影響，F(xiàn)reyssinet發(fā)現(xiàn)用預(yù)應(yīng)力混凝土可以減少由于徐變所引起強度損失。在簡支梁中徐變的發(fā)生使得一些預(yù)應(yīng)力損失和增加梁的撓度，這可能需要被考慮的，但是它不影響彎矩分配，所以設(shè)計時相對比較簡單。如果結(jié)構(gòu)是不確定的，支撐條件重新分配可能會改變撓曲力矩。如果混凝土是一塊塊同時預(yù)制，那么結(jié)構(gòu)的有效模量將均勻地變化，在這種情況下強度將可能不會重新分配。然而如果混凝土具有不同的

16、老化程度，那么對于允許彎矩重新分配的結(jié)構(gòu)，在不同部位產(chǎn)生的徐變大小也不一樣?，F(xiàn)在大家都認為發(fā)生徐變都接近整體狀態(tài)，設(shè)計者可以取這當(dāng)做設(shè)計參考和把這整體的狀態(tài)當(dāng)做梁工作的極限狀態(tài)，這簡化了設(shè)計過程。英格蘭對沿梁不同高度的溫度效應(yīng)變化進行了研究，徐變是隨溫度變化而變的，結(jié)構(gòu)較熱的那側(cè)發(fā)生徐變的速度比冷的那側(cè)快，它可以顯著地改變荷載分布。這個研究最初被應(yīng)用到船舶護外殼上，船舶護外殼沿殼厚溫度變化可以超過100度。這個研究是利用穩(wěn)態(tài)的這一概念。雖然應(yīng)力沒有再分布但是徐變?nèi)匝永m(xù)著。近年來，認為沿船橋甲板的厚度較小溫度變化是可能發(fā)生的，它大概5度左右，這也是值得注意的影響。發(fā)生徐變的速度取決于結(jié)構(gòu)不同部位

17、混凝土的老化程度。4、結(jié)論：要成功的設(shè)計預(yù)應(yīng)力混凝土連續(xù)梁不能脫離對結(jié)構(gòu)的分析，自從第一個超靜定結(jié)構(gòu)被建造，這個方法已經(jīng)發(fā)展起來。在同一期間這種結(jié)構(gòu)分析方法也是非常值得我們深思。設(shè)計師不能一味的使用分析程序而忽略預(yù)應(yīng)力混凝土的工作機理。外文文獻翻譯原文Analysis of Continuous Prestressed Concrete BeamsChris BurgoyneMarch 26, 20051、 IntroductionThis conference is devoted to the development of structural analysis rather than t

18、he strength of materials, but the effective use of prestressed concrete relies on an appropriate combination of structural analysis techniques with knowledge of the material behaviour. Design of prestressed concrete structures is usually left to specialists; the unwary will either make mistakes or s

19、pend inordinate time trying to extract 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

20、； in hyperstatic structures, various 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 Henne

21、bique at the end of the 19th century (Cusack 1984), it was recognised that steel and concrete could be more effectively combined if the steel was pretensioned, putting the concrete into compression. Cracking could be reduced, if not prevented altogether, which would increase stiffness and improve du

22、rability. Early attempts all failed because 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 Freyssinetis observations of the sagging of the shallow arches on

23、 three bridges that he had just completed in 1927 over the River Allier near Vichy which led directly to prestressed concrete (Freyssinet 1956). Only the bridge at Boutiron survived WWII (Fig 1). Hitherto, it had been assumed that concrete had a Youngs modulus which remained fixed, but he recognised

24、 that the de- ferred strains due to creep explained why the prestress had been lost in the early trials. Freyssinet (Fig. 2) also correctly reasoned that high tensile steel had to be used, so that some prestress would remain after the creep had occurred, and also that high quality concrete should be

25、 used, since this minimised the total amount of creep. The history of Freyssinetis early prestressed concrete work is written elsewhere Figure 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 (1

26、933). It is debatable which man should be 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

27、 one way of thinking about it. These different 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

28、 cracking by eliminating tensile stresses; 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.Ultima

29、te strength philosophy sees prestressing 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 t

30、he steel to the concrete. Structures designed 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

31、 1939), as well as that of Finsterwalder (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

32、 causes an upward force on the beam, which 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 philo

33、sophies all have their champions, and heated 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 load and the ultimate load. For steel structures, and those made from re

34、inforced concrete, there is a fairly direct relationship between the load capacity under an allowable stress design, and that at the ultimate 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 lo

35、ad. Different load factors are used in the two codes, but a structure which passes one code is likely to be acceptable under the other.For 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

36、to be breached, while a 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

37、 the top and bottom fibre 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

38、, one of which normally 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 p

39、ermissible stresses in tension and compression.Thus, for any combination of P and M , the designer already has four in- 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 mo

40、ment; the applied moment at 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: GustaveMagnelOther combinations may be needed in more complex cases. There are at least twelve in

41、equalities that have to be satisfied at any cross-section, but since an I-section can be defined by six variables, and two are needed to define theprestress, the problem is over-specified and it is not immediately obvious which conditions are superfluous. In the hands of inexperienced engineers, the

42、 design process can be very 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 expression

43、s of the form:These inequalities, which can be evaluated exhaustively with little difficulty, allow the 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 limits can all

44、 be rearranged into the form:By 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 feasible combinations of P and e. T

45、he 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, as shown in Fig. 5. Inequalities

46、(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 the loadings alter the Magnel diagram. Changing both the maximum and minimum bending moments, but keeping the range the same, ra

47、ises 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.5) moves outside the physical li

48、mits 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 governed by the limiting eccentricity and tensile stresses in the bottom fibre. However, it does not take a la

49、rge increase in moment ，at which point compressive stresses will govern in the bottom fibre under maximum moment.Only when much longer spans are required, and the feasible region moves as far down as possible, does the structure become governed by compressive stresses in both fibres.3、 Continuous be

50、amsThe design of statically determinate beams is relatively straightforward; the engineer can work on the basis of the design of individual cross-sections, as outlined above. A number of complications arise when the structure is indeterminate which means that the designer has to consider, not only a

51、 critical section,but also the behaviour of the beam as a whole. These are due to 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 add

52、ressed at a conference in London (Andrew and Witt 1951). 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 for

53、ce.3.1 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. These are often termed Secondary

54、Moments, but they are not always small, or Parasitic Moments, but they are not always bad. Freyssinets bridge across the Marne at Luzancy, started in 1941 but not completed until 1946, is often thought of as a simply supported beam, but it was actually built as a two-hinged arch (Harris 1986), with

55、support reactions adjusted by means of flat jacks and wedges which were later grouted-in (Fig.6). The same principles were applied in the later and larger beams built over the same river. Magnel built the first indeterminate beam bridge at Sclayn, in Belgium (Fig.7) in 1946. The cables are virtually

56、 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 moments are large; about 50% of the hogging moment at the central support caused by dead and live load.The secondary 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 conco