衢州學(xué)院本科畢業(yè)設(shè)計(jì)(論文)外文翻譯

1、衢州學(xué)院本科畢業(yè)設(shè)計(jì)(論文)外文翻譯 譯文：受扭構(gòu)件的強(qiáng)度及變形Dr.A.美赫.普拉薩德8.1引言鋼筋混凝土結(jié)構(gòu)中的扭轉(zhuǎn)現(xiàn)象常常是由于構(gòu)件之間的連續(xù)性而產(chǎn)生的。由于這個(gè)原因，扭轉(zhuǎn)問(wèn)題在本世紀(jì)前半葉相對(duì)來(lái)說(shuō)就未曾受到足夠的重視,而在設(shè)計(jì)中忽視扭轉(zhuǎn)問(wèn)題看來(lái)好象也沒(méi)有造成什么嚴(yán)重后果。在最近十至十五年內(nèi)，研究活動(dòng)的大幅度增長(zhǎng)顯著提高了對(duì)這個(gè)問(wèn)題的理解。目前世界各地巳經(jīng)或正在對(duì)混凝土中扭轉(zhuǎn)問(wèn)題的很多方面進(jìn)行探討。第一次重要的、組織起來(lái)的，把這方面的知識(shí)和研究成果匯集起來(lái)的轉(zhuǎn)動(dòng)是由士ACI主辦的專題討論會(huì)。專題討論會(huì)文集還對(duì)許多有價(jià)值的開創(chuàng)性系作進(jìn)行了回顧.到目前力止，大多數(shù)關(guān)于扭轉(zhuǎn)的規(guī)范參考文獻(xiàn)都從各

2、向同性勻質(zhì)彈性材料的性能中 借用的概念為依據(jù)的?，F(xiàn)行的ACI規(guī)范第一次包含了關(guān)于扭轉(zhuǎn)的設(shè)計(jì)建議。這些建議是以相當(dāng)數(shù)置的實(shí)驗(yàn)資料為基礎(chǔ)的，但是在綜合了更多的得自現(xiàn)代研究成果的資料之后，這些建議大概還要進(jìn)一步修改。扭轉(zhuǎn)現(xiàn)象可能是由于一階效應(yīng)或二階效應(yīng)的結(jié)果而產(chǎn)生的一階扭轉(zhuǎn)情況是發(fā)生在外荷載不能由扭轉(zhuǎn)以外的另一種方式來(lái)承受的時(shí)候。在這種情況下，為了保持靜力平衡而需要的扭矩單一的確定出來(lái)。這種情況也可以稱為平衡扭轉(zhuǎn)。它主要是一個(gè)強(qiáng)度回題，因?yàn)槿绻ぞ貜?qiáng)度得不到滿足，機(jī)構(gòu)或其部分就會(huì)破壞。如圖8.1和8.8所示的沿著跨度通過(guò)懸臂承受偏心線荷載的簡(jiǎn)支梁和偏心受荷的箱形都截面梁是一階扭轉(zhuǎn)或平衡扭矩的例子。圖

3、8.1 一階扭轉(zhuǎn)或平衡扭轉(zhuǎn)的實(shí)例 在超靜定結(jié)構(gòu)扭轉(zhuǎn)現(xiàn)象就可能是由于連續(xù)住的要求作為二階效應(yīng)而產(chǎn)生的。在設(shè)計(jì)中忽略這種連續(xù)性就會(huì)導(dǎo)致過(guò)寬的裂縫，但不一定有更嚴(yán)重的后果。設(shè)計(jì)者常常都直覺(jué)地忽略這種二階扭轉(zhuǎn)效應(yīng)。支承板或次梁的框架邊梁就是這種情況的典型(見圖8.2 在具有剛性連接的空間結(jié)構(gòu)中幾乎沒(méi)有可能避免由干變形的協(xié)調(diào)性所引起的扭轉(zhuǎn)現(xiàn)象。某些堵如受邊梁彈性約一束的殼體之類的結(jié)構(gòu)較之其它結(jié)構(gòu)對(duì)這類扭轉(zhuǎn)就更為敏感。目的知識(shí)水平使我似有可能接近實(shí)際地估計(jì)在鋼筋混凝土超靜定結(jié)構(gòu)中的不同加載階段可能產(chǎn)生的扭轉(zhuǎn)效應(yīng)。混凝土結(jié)構(gòu)中的扭轉(zhuǎn)現(xiàn)象很少是在沒(méi)有其它作用的情況下發(fā)生的。通常都同時(shí)作用有彎矩、剪力和軸向力。

4、大量較為近期的研究工，作都曾試圖確定扭轉(zhuǎn)與結(jié)構(gòu)上的其它作用之間的相互影響規(guī)律。由于包含的參數(shù)很多，要確切地估量這一綜合性能的所有方面就還需要做一些努力。圖8.2 超靜定結(jié)構(gòu)中的扭轉(zhuǎn)8.2承受扭矩的素混凝土 鋼筋混凝土的受扭性能在開始開裂以前可以取對(duì)素混凝土的研究作為基礎(chǔ).因?yàn)殇摻钤谶@個(gè)時(shí)候所起的作用是可以忽略不計(jì)的。8.2.1彈性性能介紹的眾所周知的方法.圣維南(St, Venant)的古典解可以用于一般的矩形混凝土截面。干是最大的扭轉(zhuǎn)剪應(yīng)力vt便發(fā)生在長(zhǎng)邊的中點(diǎn)，并可由下式求得: （8.1）式中: T作用于截面的扭矩 x,y矩形截面的外輪廓尺寸，x0.5時(shí)(即扭轉(zhuǎn)作用較為顯著時(shí))，觀察到的是

5、脆性破壞.而當(dāng)彎矩較為顯著時(shí)(即Tm/Mm0.5時(shí))，就可望產(chǎn)生較為具有延性的破壞。梁的抗扭強(qiáng)度只有在增加腹筋的情況下才能提高?？箯濅摻畹臄?shù)量看來(lái)對(duì)混凝土截面的抗扭能力沒(méi)有影響。 在T形和L形梁中，翼緣的挑出部分對(duì)抗扭強(qiáng)度是起作用的。這已通過(guò)獨(dú)立梁得到證實(shí)。當(dāng)翼緣是樓板的一部分時(shí)，它的有效寬度是難以確定的。當(dāng)由千于版中負(fù)彎矩的作用面有可能如圖8.9所示沿邊梁形成一條屈服線時(shí)，翼緣的一大部分看來(lái)就不大可能再提供什么抗扭強(qiáng)度了。在這種情況下只依靠矩形截面就比較合理。8.4無(wú)腹筋梁中伯扭轉(zhuǎn)與剪切顯然就疊加的意義來(lái)說(shuō)由扭矩和剪應(yīng)力所引起的剪應(yīng)力在矩形梁截面的一邊是相加，而在對(duì)面一邊則是相減。這樣接著產(chǎn)

6、生的臨界斜拉應(yīng)力又會(huì)受到混凝土中彎曲拉應(yīng)力的進(jìn)一步影響，因?yàn)椴豢赡苤蛔饔眉袅Χ瑫r(shí)卻沒(méi)有彎矩產(chǎn)生?，F(xiàn)在還沒(méi)有聽說(shuō)已經(jīng)研究出了一個(gè)在考慮彎曲作用的情況下對(duì)剪切與扭轉(zhuǎn)的相互作用進(jìn)行分析的十分合理的理論.由子這個(gè)原因就必須依靠由試驗(yàn)得到的經(jīng)驗(yàn)數(shù)據(jù)。在設(shè)置的抗彎鋼筋多于需要的條件下，就有可通過(guò)實(shí)驗(yàn)來(lái)研究剪扭聯(lián)合作用時(shí)的破壞判別條件.通常在這類試驗(yàn)中都要在荷載增大直至破壞的過(guò)程中使扭矩與剪力的比值維持不變，然而實(shí)際上卻可能是一種作用首先發(fā)生，并在另一種作用顯著增大之前就使構(gòu)件產(chǎn)生了與其作用相應(yīng)的裂分布圖形。因此在分析試驗(yàn)結(jié)果方而權(quán)且偏于保守是合理的。 圖8.10繪出了在典型的扭一剪共同作用試臉中獲得的試

7、驗(yàn)點(diǎn)子的散布倩況，它還表明只要選用了足夠低的剪切.斜向開裂和扭轉(zhuǎn)斜向開裂應(yīng)力值，一條圓弧形的相互作用曲線(對(duì)這一組特定試驗(yàn)進(jìn)行了公稱化處理)是可以用于設(shè)計(jì)的。對(duì)于這些不設(shè)腹筋的梁來(lái)說(shuō)，由公式7.5和公式8.8計(jì)算出來(lái)的、對(duì)途中所繪出的那些試驗(yàn)點(diǎn)子形成了近似下限的剪應(yīng)力和扭轉(zhuǎn)剪應(yīng)力值分別為 這個(gè)圓弧形相互作用關(guān)系曲線是現(xiàn)行ACI規(guī)范條文的基礎(chǔ)。為了方便起見，可以把已開裂截面在極限荷載時(shí)所承受的相互作用的剪力值和扭矩值用名義應(yīng)力表示為： （8.14）式中:vtm在極限情況下引起的由混凝土承受的名義扭轉(zhuǎn)應(yīng)力，由公式8.8給出；Vm-在極限情況下引起的由棍凝土承受的剪應(yīng)力，由公式7.5給出。圖8.10

8、 扭轉(zhuǎn)與剪力的相互作用原文:Strength and Deformationof Members with TorsionDr. A. Meher Prasad8.1 INTRODUCTION Torsion in reinforced concrete structures often arises from continuity between members. For this reason torsion received; relatively scant attention during the first half of this century, and the omissio

9、n from design considerations apparently had no serious consequences. During ;the last 10 to 15 years, a great increase in research activity has advanced the understanding of the problem significantly. Numerous aspects of torsion in concrete have been,and currently are being, examined in various part

10、s of the world. The first significant organized pooling of knowledge and research effort in this field was a symposium sponsored by the American Concrete Institute. The symposium volume also reviews much of the valuable pioneering work. Most code references to torsion to date have relied on ideas bo

11、rrowed from the behavior of homogeneous isotropic elastic materials. The current ACI code8.2 incorporates for the first time detailed design recommendations for torsion. These recommendations are based on a considerable volume of experimental evidence, but they are likely to be further modified as a

12、dditional information from current research efforts is consolidated. Torsion may arise as a result of primary or secondary actions. The case of primary torsion occurs when the external load has no alternative to being resisted but by torsion. In such situations the torsion, required to maintain stat

13、ic equilibrium, can be uniquely determined. This case may also be refer-red to as equilibrium torsion. It is primarily a strength problem because the structure, or its component, will collapse if the torsional resistance cannot be supplied. A simple beam, receiving eccentric line loadings along its

14、span,cantilevers and eccentrically loaded box girders, as illustrated in Figs. 8.1and 8.8, are examples of primary or equilibrium torsion. In statically indeterminate structures, torsion cart also arise as a secondary action from the requirements of continuity. Disregard for such continuity in the d

15、esign may lead to excessive crack widths but need not have more serious consequences. Often designers intuitively neglect such secondary torsional effects. The edge beams of frames, supporting slabs or secondary-beams, are typical of this situation (see Fig. 8.2). In a rigid jointed space structure

16、it is hardly possible to avoid torsion arising from the compatibility of deformations. Certain structures, such as shells elastically restrained by edge beams, are more sensitive to this type of torsion than are other. The present state of knowledge allows a realistic assessment. of the torsion that

17、 may arise in statically indeterminate reinforced concrete structures at various stages of the loading. Torsion in concrete structures rarely occurs. without other actions. Usually flexure, shear, and axial forces are also present. A great many of the more recent studies have attempted to establish

18、the laws of interactions that may exist between torsion and other structural actions. Because of the large number of parameters involved, some effort is still required to assess reliably all aspects of this complex behavior.8.2PLAIN CONCRETE SUBJECT TO TORSION The behavior of reinforced concrete in

19、torsion, before the onset of cracking,can be based ors the study of plain concrete because the contribution of rein-force ment at this stage is negligible.8.2.1 Elastic BehaviorFor the assessment of torsional effects in plain concrete, we can use the well-known approach presented inmost texts on str

20、uctural mechanics. The classical solution of St.Venant can be applied to the common rectangular concrete section. Accordingly, the maximum torsional shearing stress vt is generated at the middle of the long side and can be obtained fromwhere T=torsional moment at the section y,x =overall dimensions

21、of the rectangular section, x y t =a stress factor being a function y/x, as given in Fig. 8.3It may be equally as important to know the load-displacement relationship for the member. This can be derived from the familiar relationship.where t,= the angle of twist T = the applied torque, which may be

22、a function of the distance along the span G = the modulus in shear as defined in Eq. 7.37 C = the torsional moment of inertia, sometimes referred to as torsion constant or equivalent polar moments of inertia z = distance along memberFor rectangular sections, we havein which t, a coefficient dependen

23、t on the aspect ratio y/x of the section (Fig.8.3), allows for the nonlinear distribution of shear strains across the section. These terms enable the torsional stiffness of a member of length section. l to be defined as the magnitude of the torque required to cause unit angle of twist over this leng

24、th as In the general elastic analysis of a statically indeterminate structure, both the torsional stiffness and the flexural stiffness of members may be required.Equation 8.4 for the torsional stiffness of a member may be compared with the equation for the flexural stiffness of a member with far end

25、 restrained,defined as the moment required to cause unit rotation, 4EI/1, where EI =flexural rigidity of a section. The behavior of compound sections, T and L shapes, is more complex.However, following Bachs suggestion, it is customary to assume that a suitable subdivision of the section into its co

26、nstituent rectangles is an accept-able approximation for design purposes. Accordingly it is assumed that each ,rectangle resists a portion of the external torque in proportion to its torsional rigidity. As Fig. 8.4a shows, the overhanging parts of the flanges should be taken without overlapping. In

27、slabs forming the flanges of beams, the effective length of the contributing rectangle should not be taken as more than three times the slab thickness. For the case of pure torsion, this is a conservative approximation.Using Bachs approximation,8.5 the portion of the total torque T resisted by eleme

28、nt 2 in Fig. 8.4a isand the resulting maximum torsional shear stress is from Eq. 8.1 The approximation is conservative because the junction effect has been neglected. Compound sections in which shear must be subdivided in a different way.The elastic torsional shear stress flow can occur, as in box s

29、ections,Figure 8.4c illustrates the procedure.distribution over compound cross sections may be best visualized by Prandtls membrane analogy, the principles of which may be found in standard works concrete structures, we seldom encounter the on elasticity. In reinforced foregoing assumptions associat

30、ed with linear conditions under which the elastic behavior are satisfied.8.2.2 Plastic Behavior In ductile materials it is possible to attain a state at which yield in shear occur over the whole area of a particular cross section. If yielding occurs over the whole section, the plastic torque can be

31、computed with relative ease. Consider the square section appearing in Fig. 8.5, where yield in shear Vty has set in the quadrants. The total shear force V acting over one quadrant is The same results may be obtained using Nadais sand heap analogy. According to this analogy the volume of sand placed

32、over the given cross section is proportional to the plastic torque sustained by this section.the heap (or roof) over the rectangular section (see Fig. 8.6) has a height xv. where x = small dimension of the cross section.mid over the square section (Fig. 8.5) isThe volume of the heap over the oblong

33、section (Fig. 8.6) isIt is evident that ty=3 when x/y= I and O,y =2when x/y=0 It may be seen that Eq. 8.7 is similar to the expression obtained for elastic behavior, Eq. 8.1. Concrete is not ductile enough, particularly in tension, to permit a perfect plastic distribution of shear stresses. Therefor

34、e the ultimate torsional strength of a plain concrete section will be between the values predicted by the membrane (fully elastic) and sand heap (fully plastic) analogies. Shear stresses cause diagonal (principal) tensile stresses, which initiate, the failure. In the light of the foregoing approxima

35、tions and the variability of the tensile strength of concrete, the simplified design equation for the determination of the nominal ultimate sections, proposed by shear stress induced by torsion in plain concrete ACI 318-71, is acceptable:where x y. The value of 3 for t is or ty,3, is a minimum for t

36、he elastic theory and a maxi-mum for the plastic theory (see Fig. 8.3 and Eq. 8.7a). The ultimate torsional resistance of compound sections can be mated by the summation of the contribution of the constituent sections such as those in Fig. 8.4, the approximation is where x y for each rectangle. The

37、principal stress (tensile strength) concept would suggest that failure cracks should develop at each face of the beam along a spiral running at 450 to the beam axis. However, this is not possible because the boundary of the failure surface must form a closed loop. Hsu has suggested that bending occu

38、rs about an axis parallel to the planes that is at approximately 450 to the beam axis and of the long faces of a rectangular beam. This bending causes compression beam. The latter tension cracking eventually and tensile stresses in the 450 plane across the initiates a surface crack. As soon as flexu

39、ral occurs the flexural strength of the section is reduced, the crack rapidly propagates, and sudden failure follows. Hsu observed this sequence of failure with the aid of high-speed motion pictures. For most structures little use can be made of the torsional (tensile) strength of unreinforced concr

40、ete members. 8.2.3 Tubular Sections Because of the advantageous efficient in resisting distribution of shear stresses, tubular sections are most resisting torsion. They are widely used in bridge construction .Figure8.7 illustrates the basic forms used for bridge girders. The torsional properties of

41、the girders improve in progressing from Figs. 8.7a to 8.7g. When the wall thickness h is small relative to the overall dimensions of the section, uniform shear stress across the thickness can be assumed. By considering the moments exerted about a suitable point by the shear stresses,acting over infi

42、nitesimal elements of the tube section, as in Fig. 8.8a, the torque of resistance can be expressed.asThe product hvt = vo is termed the shear flow,.and this is constant; thus where Ao = the area enclosed by the center Jine of the tube wall (shaded area in Fig. 8.8). The concept of shear flow around

43、the thin wall tube is useful when the role of reinforcement in torsion is considered.The ACI code 8.2 suggests that the equation relevant to solid sections. 8.8, be used also for hollow sections, with the following modification when the wall thickness is not less than x/l0 (see Fig. 8.8c):where x y.

44、 Equation 8.9b follows from first principles and has the advantage of being applicable to both the elastic and fully plastic state of stress. The torque-twist relationship for hollow sections may be readily derived from strain energy considerations. By equating the work done by the applied torque (external work) to that of the shear stresses (internal work), the torsion constant CO for tubular sections can be found thus: Hence by equating the two expressions and using Eq. 8.9b, the relationship b