土木工程专业英语 中英文对照 unit5

1、Unit 5 第五单元Structural Analysis 结构分析教学目标了解结构分析的假定和几种方法了解结构分析中运用的几个定理熟悉结构力学中的专业词汇熟悉科技类文献中的常用句型熟悉as a consequence、 as a result、for these reasons、therefore 以及as a consequence of、as a result of 的含义；state 的不同用法；relate to、relate.to、be related to 的区别；be equal to、be equated to、equal 的用法； with respect to、rega

2、rding、considering、as to 的用法 A structure consists of由.组成a series of connected parts used to support loads. Notable显著的 examples include buildings, bridges, towers, tanks, and dams. The process过程of creating any of these structures requires planning规划, analysis, design, and construction施工. Structural an

3、alysis consists of 包括a variety of mathematical procedures数学程序for determining such quantities as the member forces and various structural displacements位移 as a structure responds to its loads. Estimating realistic loads for the structure considering根据its use and location is often a part of structural

4、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局部。 Only two assumptions are made regarding关于the materials used in the structures of this chapter. First, the material has a linear stress-stra

5、in relationship线性的应力-应变关系. Second, there is no difference in the material behavior when stressed in tension vis-a-vis与.相比compression. The frames and trusses studied are plane structural systems平面结构体系. It will be assumed that there is adequate bracing perpendicular to垂直于the plane so that no member wi

6、ll fail due to an elastic instability弹性失稳. The very important consideration regarding such instability will be left for the specific具体的design course. All structures are assumed to undergo only small deformations as they are loaded. As a consequence因此we assume no change in the position or direction o

7、f a force as a result of 由于structural deflections变位. Finally, since linear elastic materials and small displacement are assumed, the principle of superposition will apply in all cases. Thus the displacements or internal forces that arise from two different forces systems applied one at a time一次一个may

8、 be added algebraically几何相加to determine the structures response when both system(s) are applied simultaneously. 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。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。假定所有的结构在它们加荷时只经历小的变形。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

9、材料和小位移，叠加原理将适用于所有的情况。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来确定结构的响应。 In the real sense真正意义上an exact analysis of a structure can never be carried out since estimates always have to be made of the loadings and the strength of the materials composing构成the structure. Furthermore, points of applicati

10、on作用点for the loadings must also be estimated. It is important, therefore, that the structural engineers develop形成the ability to model模拟or idealize使.理想化a structure so that he or she can perform a practical force analysis of 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

11、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 ways depending on the intent意图of the designer. The two types of joints most often specified规定的are the pin connection and the fixed joint节点. A pin-connected joint allows some freedom for slight轻微rotation,

12、 whereas the fixed joint allows no relative rotation between the connected members. In reality, however, all connections exhibit显现some stiffness toward joint rotations, owing to friction摩擦and material behavior. When selecting a particular model for each support支座or joint, the engineer must be aware

13、of how the assumptions will affect the actual performance运行of the member and whether the assumptions are reasonable for the structural design. In reality, all structural supports actually exert产生distributed surface loads面荷载on their contacting members. The resultants合力 of these load distributions are

14、 often idealized as the concentrated forces集中力and moments, since the surface area 外表积over which the distributed load acts is considerably smaller than the total surface area of the connecting members. The ability to reduce an actual structure to将.简化为an idealized form can only be gained by experience

15、. In engineering practice, if it becomes doubtful不明确as to how to model a structure or transfer the loads to the members, it is best to consider several idealized structures and loadings and then design the actual structure so that it can resist抵抗the loadings in all the idealized models. 结构构件根据设计者的意图

16、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。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计是合理的。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外表面积比相连的构件的总的外表面积小很多。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构或将

17、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，使它在所有理想的模型中都能抵抗荷载。 It may be recalled回想from statics that a structure or one of its members is in equilibrium处于平衡 when it maintains a balance of force and moment. When all the forces in a structure can be determined strictly from these equations, the structure

18、is referred to as statically determinate静定的. Structures having more unknown forces than available equilibrium equations平衡方程are called statically indeterminate. As a general rule, a structure can be identified as确定being either statically determinate or statically indeterminate by drawing free-body di

19、agrams隔离体图of all its members, or selective parts of its members, and then comparing the total number of unknown reactive force and moment components分量with the total number of available equilibrium equations. 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

20、时称为超静定结构。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局部构件的隔离体图，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。 In particular, if a structure is statically indeterminate, the additional equations附加方程needed to solve for求解the unknown reactions反力are obtained by relating the applied loads and reactions to the displace

21、ment or slope转角at different points on the structure. These equations, which are referred to as compatibility equations相容性方程或协调方程, must be equal in number to the degree of indeterminacy不确定次数of the structure. Compatibility equations involve涉及the geometric and physical properties of the structure. 特别地，

22、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。相容性方程涉及结构的几何和物理性能。 There are two fundamental methods of analysis for trusses: the method of joints and the method of sections. Both start with从.着手a free-body diagram of the truss as a whole根本上, from which the eq

23、uilibrium equations are written and solved for the support reactions支座反力. 有两种分析桁架的根本方法：节点法和截面法。两种方法根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。 The method of joints: After the support reactions have been found, a joint is selected that has no more than不超过two members connecting for which the axial forces are u

24、nknown. The free-body diagram of that joint is drawn, the forces are summed合计in two directions, and each sum is equated to等于zero. When drawing the free-body diagram, it is a good idea to assume that the unknown forces are tensions and to show表示them so on the free-body diagram by their exerting a pul

25、l on对.施加拉力the joint. When this is assumed, the resulting sign符号of the unknowns when evaluated计算will match符合the conventional习惯的+ for tension and for compression. Once a joint has been analyzed, its members become knowns, and adjacent joints相邻节点, which might have had three or more unknowns, can then b

26、e solved since some of these unknowns have become knowns. This process过程continues from joint to joint, each time selecting a joint whose number of unknown members does not exceed 2.节点法：求出支座反力后，选择一个节点其上连接着轴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零。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。

27、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相符。一旦一个节点已经被分析，其上的构件成为构件，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，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 all truss systems are configured装配so that analysis using the method of joints must begin at one end and proceed继续joint by joint toward the other end. If it

28、 is necessary to evaluate the forces carried by a member located位于some distance from the ends, the method of joints requires the calculation of the forces in many members before the desired one is reached. The method of sections provides a means方法for a direct calculation in these cases. After the su

29、pport reactions have been calculated the truss is cut through切开(analytically分析上) so that one part of the truss is completely severed from the rest. When this is done, no more than three unknown members should be cut. If possible如果可能the cut切口should pass through the member or members whose internal fo

30、rces are to be found. A free-body diagram of the part of the truss on one side of在.一边this section is drawn, and the internal forces are found through the equilibrium equations. Since the system of forces力系on the free-body diagram is a plane non-concurrent非共点force system, three equilibrium equations

31、may be written and solved for the three unknowns. 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构件之前计算很多构件中的力。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，从而一局部桁架同其余局部完全别离。当这样切开时，应该切出不超过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的构件。画出在截面一边的桁架局部的隔离体图，并通过平衡方程式求解内力。由于隔离体图

32、上的力系是平面非共点的，因而可以写出三个平衡方程式并求出三个未知力。 Influence lines影响线have important application for应用the design of structures that resist large live loads活荷载. An influence line represents代表the variation of either the reaction, shear, moment, or deflection at a specific 特定的point in a member as concentrated force mov

33、es over the member. Once this line is constructed作图, one can tell at a glance一眼便知where a live load should be placed on the structure so that it creates引起the greatest influence at the specified point. Furthermore, the magnitude大小of the associated 相关的reaction, shear, moment, or deflection at the point

34、 can then be calculated from the ordinates纵坐标of the influence-line diagram. For these reasons因此, influence lines play an important part in the design of bridges, industrial crane rails吊车轨道, conveyors, and other structures where loads move across their span全长. Although the procedure步骤for constructing

35、 an influence line is rather basic根本的, one should clearly be aware of the difference between constructing an influence line and constructing a shear or moment diagram. Influence lines represent the effect of a moving load only at a specified point on a member, whereas shear and moment diagrams repre

36、sent the effect of fixed loads at all points along the axis of 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。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。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。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。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。虽然画出一条影响线的步骤是相当根本的，但任何人应

37、该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。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影响。 Deflections of structures can occur from various sources原因, such as loads, temperature, fabrication errors, or settlement. In design, deflections must be limited in order to prevent cracking of attached附属的 brittle material

38、s such as concrete or plaster (石膏) . Furthermore, a structure must not vibrate or deflect变位severely in order to “appear safe for its occupants居住者. More important, though然而, deflections at specified points in a structure must be computed if one is to analyze statically indeterminate structures. We of

39、ten determine the elastic deflections of a structure using both geometrical and energy methods. Also, the methods of double integration双重积分are used. The geometrical methods include the moment-area theorems弯矩图面积定理and the conjugate-beam method共轭梁法, and the energy methods to be considered are based on

40、virtual work虚功and Castiglianos theorem卡氏最小功定理. Each of these methods has particular advantages or disadvantages. 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，为了向居住者显示平安性，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，必须计算出结构中规定点的挠度。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。几何法包括弯矩图面积定理和共轭梁法，而考虑的能量法是基

41、于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。 We can determine the equation of the elastic curve by integration of equation d2v / dx2 = M / EI. Solution of this equation requires two successive连续的integrations to obtain the deflection v of the elastic curve. For each integration, it is necessary to introduce引入a “con

42、stant of integration积分常数, and then solve for the constants to obtain a unique solution唯一解for a particular特定的problem. It should be realized that the method of double integration is suitable only for elastic deflections变位such that the beams slope is very small. Furthermore, the method considers only d

43、eflections due to bending. 我们可以通过对方程d2v / dx2 = M / EI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分，以获得弹性曲线的挠度v。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。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。而且，该法只考虑了由于弯曲引起的挠度。 The initial ideas最初的概念for the two moment-area theorems were developed提出by Otto Mohr and later stated formally正式确定by Ch

44、arles E. Greene in 1872. These theorems provide a semi-graphical 半图解technique for determining the slope of the elastic curve and its deflection due to bending. They are particularly advantageous有利when used to solve problems involving beams especially those subjected to a series of concentrated loadi

45、ngs or having segments段with different moment of inertia惯性矩. Theorem 1: The change in slope转角变化between any two points on the elastic curve equals the area of the M / EI diagram between these two points. Theorem 2: The deviation偏差of the tangent正切at point B on the elastic curve with respect to相对于the ta

46、ngent at point A equals the “moment of the M / EI diagram between the two points A and B computed about point A (the point on the elastic curve), where这里the deviation tA/B is to be determined. 最初的关于两个弯矩图面积定理的概念是由Otto Mohr提出，后来由Charles E. Greene在1872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。当用以解决包括梁在内

47、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，它们指弯矩图面积定理是特别得有利。定理1：弹性曲线上任何两点之间转角的变化等于这两点之间的M / EI图的面积。定理2：弹性曲线上B点的正切相对于A点的正切的偏差等于点A与点B之间的M / EI图对A点该点在弹性曲线上的矩，这里偏差tA/B将被确定。 The conjugate-beam method was first presented提出by Otto Mohr in 1860. Essentially本质上, it requires the same amount of computation计算量as the momen

48、t-area theorems to determine a beams slope or deflection; however, this method relies only on the principles of statics and hence its application will be more familiar常见. The basis for the method comes from来自于the similarity相似性between both dV/dx = - and d2M/dx2 = - , which relate a beams internal she

49、ar and moment to its applied loading, and d/dx = M/EI and d2y/dx2 = M/EI, which relate the slope and deflection of its elastic curve to the internal moment. 共轭梁法首先在1860年由Otto Mohr提出。本质上说，它与弯矩图面积定理一样在确定梁的转角或挠度上需要相同的计算量；但是这种方法只依赖于静力学的原理，因此，它的应用更常见。该法的根底来自于dV/dx=-和d2M/dx2=-之间的相似性，它将梁的内部剪力和弯矩与它施加的荷载联系起来

50、，而d/dx = M/EI和d2y/dx2 = M/EI将弹性曲线的转角和挠度与内部弯矩联系起来。 Note that the shear V compares with与.对应the slope , the moment M compares with the displacement y and the intensity of the external load compares with the area under the M/EI diagram. To make use of this comparison we will consider a beam having the s

51、ame length as the real beam, but referred to here as the “conjugate beam. 注意剪力V与转角相对应，弯矩M与位移y相对应，而外力的强度与M/EI图下的面积相对应。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。In general, though然而, remember that if the real support allows a slope, the conjugate support must develop产生a shear; and if the real support allows

52、 a displacement, the conjugate support must develop a moment, note that the conjugate beam is “loaded with the M/EI diagram, in order to conform to与.一致the load on the real beam. We can therefore state陈述two theorems related to the conjugate beam, namely即, Theorem 1: The slope at a point in the real b

53、eam is equal to the shear at the corresponding point相应点in conjugate beam. Theorem 2: The displacement of a point in the real beam is equal to the moment at the corresponding point in the conjugate beam. 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，注意共轭梁用M/EI图来加荷，以便与实际梁上的荷载一致。因此，我们可

54、以陈述与共轭梁相关的两种定理，即，定理1：实际梁上某一点的转角等于共轭梁上相应点的剪力。定理2：实际梁上某一点的位移等于共轭梁上相应点的弯矩。 For more complicated loadings or for structures such as trusses and frame, it is suggested建议that energy methods be used for the computation. All energy methods are based on the conservation of energy principle能量守恒原那么, which stat

55、es规定that the work功done by all the external forces acting on a structure, Ue, is transformed into转化为internal work or strain energy应变能UI, which is developed形成when the structure deforms变形. 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原那么，它规定了作用在结构上的所有外力作的功Ue转化成内部功或结构变形时形成的应变能UI 。 The principle of virtua

56、l work was developed by John Bernoulli in 1717 and is sometimes referred to as the unit-load method单位荷载法. It provides a general means一般方法of obtaining the displacement and slope at a point on a structure, be it无论是a beam, frame, or truss. Before developing the principle of virtual work, it is necessar

57、y to make some general statements一般规定regarding the principle of work and energy. 虚功原理在1717年由John Bernoulli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。If we take取a deformable可变形structure of any shape or size and apply a series of external loads P to it, it will c

58、ause internal loads u at points throughout the structure. It is necessary that the external and internal loads be related by the equation of equilibrium. As a consequence of通过these loadings, external displacement will occur at the P loads and internal displacement will occur at each point of interna

59、l load u. 如果我们取一个任何形状或尺寸的可变形结构，并对它施加一组外力P，它将导致整个结构上的点产生内力u。有必要通过平衡方程将内外力联系起来。通过这些荷载，外部的位移发生在荷载P作用处，而内部位移发生在内力u所处的每个点。 In general, these displacements do not have to be elastic, and they may not be related to与.有关the loads; however, the external and internal displacements must be related by the compat

60、ibility of the displacements. In other words, if the external displacements are known, the corresponding internal displacements are uniquely defined唯一确定. In general, then, the principle of work and energy states表述: P= u 5-1 Work of External Loads = Work of Internal Loads一般来说，这些位移不必是弹性的，它们可能与荷载无关。但是外