外文翻译--应力应变

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1、五、外文资料翻译 Stress and Strain1. Introduction to Mechanics of MaterialsMechanics of materials is a branch of applied mechanics that deals with the behavior of solid bodies subjected to various types of loading. It is a field of study that is known by a variety of names, including “strength of materials”

2、 and “mechanics of deformable bodies”. The solid bodies considered in this book include axially-loaded bars, shafts, beams, and columns, as well as structures that are assemblies of these components. Usually the objective of our analysis will be the determination of the stresses, strains, and deform

3、ations produced by the loads; if these quantities can be found for all values of load up to the failure load, then we will have obtained a complete picture of the mechanics behavior of the body.Theoretical analyses and experimental results have equally important roles in the study of mechanics of ma

4、terials . On many occasion we will make logical derivations to obtain formulas and equations for predicting mechanics behavior, but at the same time we must recognize that these formulas cannot be used in a realistic way unless certain properties of the been made in the laboratory. Also , many probl

5、ems of importance in engineering cannot be handled efficiently by theoretical means, and experimental measurements become a practical necessity. The historical development of mechanics of materials is a fascinating blend of both theory and experiment, with experiments pointing the way to useful resu

6、lts in some instances and with theory doing so in others. Such famous men as Leonardo da Vinci(1452-1519) and Galileo Galilei (1564-1642) made experiments to adequate to determine the strength of wires , bars , and beams , although they did not develop any adequate theories (by todays standards ) to

7、 explain their test results . By contrast , the famous mathematician Leonhard Euler(1707-1783) developed the mathematical theory any of columns and calculated the critical load of a column in 1744 , long before any experimental evidence existed to show the significance of his results . Thus , Eulers

8、 theoretical results remained unused for many years, although today they form the basis of column theory. The importance of combining theoretical derivations with experimentally determined properties of materials will be evident theoretical derivations with experimentally determined properties of ma

9、terials will be evident as we proceed with our study of the subject. In this section we will begin by discussing some fundamental concepts , such as stress and strain , and then we will investigate bathe behaving of simple structural elements subjected to tension , compression , and shear.2. StressT

10、he concepts of stress and strain can be illustrated in elementary way by considering the extension of a prismatic bar see Fig.1.4(a). A prismatic bar is one that has cross section throughout its length and a straight axis. In this illustration the bar is assumed to be loaded at its ends by axis forc

11、es P that produce a uniform stretching , or tension , of the bar . By making an artificial cut (section mm) through the bar at right angles to its axis , we can isolate part of the bar as a free bodyFig.1.4(b). At the right-hand end the force P is applied , and at the other end there are forces repr

12、esenting the action of the removed portion of the bar upon the part that remain . These forces will be continuously distributed over the cross section , analogous to the continuous distribution of hydrostatic pressure over a submerged surface . The intensity of force , that is , the per unit area, i

13、s called the stress and is commonly denoted by the Greek letter . Assuming that the stress has a uniform distribution over the cross sectionsee Fig.1.4(b), we can readily see that its resultant is equal to the intensity times the cross-sectional area A of the bar. Furthermore , from the equilibrium

14、of the body show in Fig.1.4(b), Fig.1.4 Prismatic bar in tension we can also see that this resultant must be equal in magnitude and opposite in direction to the force P. Hence, we obtain =P/A ( 1.3 ) as the equation for the uniform stress in a prismatic bar . This equation shows that stress has unit

15、s of force divided by area -for example , Newtons per square millimeter(N/mm) or pounds of per square inch (psi). When the bar is being stretched by the forces P ,as shown in the figure , the resulting stress is a tensile stress; if the force are reversed in direction, causing the bat to be compress

16、ed , they are called compressive stress. A necessary condition for Eq.(1.3) to be valid is that the stress must be uniform over the cross section of the bat . This condition will be realized if the axial force p acts through the centroid of the cross section , as can be demonstrated by statics. When

17、 the load P doses not act at thus centroid , bending of the bar will result, and a more complicated analysis is necessary . Throughout this book , however , it is assumed that all axial forces are applied at the centroid of the cross section unless specifically stated to the contrary . Also, unless

18、stated otherwise, it is generally assumed that the weight of the object itself is neglected, as was done when discussing this bar in Fig.1.4.3. Strain The total elongation of a bar carrying force will be denoted by the Greek lettersee Fig .1.4(a), and the elongation per unit length , or strain , is

19、then determined by the equation =/L (1.4)Where L is the total length of the bar . Now that the strain is a nondimensional quantity . It can be obtained accurately form Eq.(1.4) as long as the strain is uniform throughout the length of the bar . If the bar is in tension , the strain is a tensile stra

20、in , representing an elongation or a stretching of the material; if the bar is in compression , the strain is a compressive strain , which means that adjacent cross section of the bar move closer to one another. ( Selected from Stephen P.Timoshenko and James M. Gere, Mechanics of Materials,Van Nostr

21、andReinhold Company Ltd.,1978.)应力应变1、 材料力学的介绍 材料力学是应用力学的分支，它是研究受到各种类型载荷作用的固体物。材料力学所用的方面就我们所知道的类型名称包括：材料强度和可变形物体的力学。在本书中考虑的固体物有受轴向载荷的杆、轴、梁和柱以及用这些构件所组成的结构。通常我们分析物体由于载荷所引起的应力集中、应变和变形作为目的。如果这些是能够获得增长直到超载的重要性。我们就能够获得这种物体的完整的机械行为图。 理论分析和实验结论是研究材料力学的相当重要的角色。在许多场合，我们要做出逻辑推理获得机械行为的公式和方程。但是同时我们必须认识到这些公式除非已知这些

22、材料的性质，否则不能用于实际方法中，这些性质只有通过一些合适的实验之后才能用。同样的，许多重要的问题也不能用理论的方法有效的处理，只有通过实验测量才能实际应用。材料力学的发展历史是理论与实验极有趣的结合。在一些情况下是指明了得以有用结果的道路，在另一些情况下则是理论来做这些事。例如著名人物莱昂纳多达芬奇（1452-1519）和 伽利略加能（1564-1642）做实验以确定铁丝、杆、梁的强度。尽管他们没有得出足够的理论（以今天的标准）来解释他们的那些实验结果。相反的，著名的数学家利昴哈德尤勒（1707-1783）在1744年就提出了柱体的数学理论计算出其极限载荷，而过了很久才有实验证明其结果的重

23、要性。虽然其理论结果并没有留存多少年，但是在今天他仍是柱体理论的基本形式。 随着研究的不断深入，把理论推导和在实验上已确定的材料性质结合起来形容的重要性是很显然的。然后，调查研究简单结构元件承受拉力、压力和剪切的性质。2、 应力 应力和应变的概念可以用图解这种方法。考虑等截面杆发生的延伸。如图1.4(a).等截面杆沿长度方向和轴线方向延伸。在这个图中的杆假设在它的两端承受轴向载荷P致使产生一致的延伸，即杆的拉力。通过杆的假想（mm）截面是垂直于轴的直角面。 我们可以分离出杆的一个自由体作为研究对象图1.4(b). 在右边的端点上是拉力P的作用，而在另一端是被移走的杆上的一部分作用在这部分上的力

24、。这些力分布在水的表面上。强度就是单位面积上的载荷叫应力，用希腊字母表示。假设应力均匀连续分布在横截面上看图1.4(b)。而且在图1.4(b)中看到物体的平衡，我们能够得出这样的合力在大小上必须等于相反方向的载荷P。我们得到等截面杆的应力均匀分布的方程式： =P/A这个方程式表明应力是在面积上分成微分载荷。例如 N/mm或psi。当杆被载荷P拉伸，可以用数值来表示。因此产生的应力为拉应力。如果载荷是相反的方向，造成杆的压缩，这就叫压应力。 方程（1.3）所必须具备的条件就是应力均匀分布在杆的面上。轴向载荷P通过截面的形心，这个条件必须实现。可以用静力学来说明：当加载P不能经过形心，将会导致杆的

25、弯曲，而且有一个更复杂的分析。在本书过程中，如果没有特别说明，我们假定的所有轴向力都作用在横截面的形心上。同样的，除另外的状态，当我们对图1.4讨论时同，对于一般地物体本身是重可忽略。3、 应变由于轴向载荷使杆伸长的总量是用希腊字母表示看图1.4(a)。单位长度的伸长即应变。得到方程式 =/L L为杆的长度。 注意到应变是非空间的量，从方程(1.4)可以获得准确的应变。应变在整个杆的长度上是一致的。如果拉伸，应变庄稼汉叫拉应变，它使材料伸长或延长；如果杆是缩短的，应变就叫压应变，将会使杆的两端距离缩小。 （从选出：史蒂芬.Timoshenko 和詹姆士M.盖尔，材料力学，NostrandReinhold厢式客货两用车有限公司，1978）