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1、Translation The concepts of stress and strain can be illustrated in an elementary way by considering the extension of a prismatic bar. As shown in Fig. 1, a prismatic bar is one that has constant cross section throughout its length and a straight axis. In this illustration the bar is assumed to be l
2、oaded at its ends by axial forces P that produce a uniform stretching, or tension, of the bar. 应力和应变的概念可以通过考虑一根矩形梁的拉伸的简单方 法来举例说明。如图1所示，这根矩形梁可以看作是由遍及长度 方向的连续横截面所组成，这些横截面垂直于它的轴向。在这个 例子中，这根矩形梁被假定在它两端施加了一对使它发生均匀拉 伸的轴向力P。 By making an artificial cut (section mm) through the bar at right angles to its axi
3、s, we can isolate part of the bar as a free body see Fig.1(b). At the left-hand end the tensile force P is applied, and at the other end there are forces representing the action of the removed portion of the bar upon the part that remains. These forces will be continuously distributed over the part
4、cross section, analogous to the continuous distribution of hydrostatic pressure over a submerged surface. 假设在梁的轴向上做一个垂直截面（截面mm），可以分离出 一部分自由的梁见图1(b)。在该梁的左端，有拉力P，而在另一 端有相应的力可以替代梁的分离部分对它的作用。这些力连续分 布在横截面上，类似于在水平面下的静水压力的连续分布。 The intensity of force, that is, the force per unit area, is called the stress
5、and is commonly denoted by the Greek letter . Assuming that the stress has a uniform distribution over the cross section see Fig.1(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 of the body shown in F
6、ig.1(b), 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) 力的强度，也就是说单位面积上的力，被称为应力，通常用 希腊字母来表示。假定应力在横截面上均匀分布见图1 ( b )， 那么我们可以很容易的看出它的合力等于强度乘以梁的横截面 积A。而且，从图1上显示的物体的平衡来看，我们可以发现这个 合力是跟拉力P在数值上相等，方向相反的。因此，我们得到方 程（1） = P/A。
7、Eq.(1) can be regarded as the equation for the uniform stress in a prismatic bar. This equation shown that stress has units of force divided by area. When the bar is being stretched by the force P , as shown in the figure, the resulting stress is a tensile stress; if the forces are reversed in direc
8、tion, causing the bar to be compressed, they are called compressive stress. 方程(1) 用于求解在梁中均匀分布的应力问题。它表示了应力 的单位是力除以面积。正如我们在图1中所看到的，当梁被力P拉 伸的时候，生成的应力是拉应力；如果力的方向被颠倒，导致梁 被压缩时，产生的应力被称为压应力。 A necessary condition for Eq.(1) to be valid is that the stress must be uniform over the cross section of the bar. Th
9、is condition will be realized if the axial force P acts through the centroid of the cross section. When the load P does not act at the centroid, bending of the bar will result, and a more complicated analysis is necessary. At present, however, it is assumed that all axial forces are applied at the c
10、entroid of the cross section unless specifically stated to the contrary. Also, unless stated otherwise, it is generally assumed that the weight of the object itself is neglected, as was done when discussing the bar in Fig.1. 方程(1) 成立的必要条件是应力在梁的横截面上是均匀分布 的。如果轴向力P通过横截面的形心，那么这个条件是可以实现 的。如果轴向力P不通过横截面的形心
11、，则会导致梁的弯曲，必 须经过更复杂的分析。然而，目前除非特定说明，都假定所有的 轴向力都通过横截面的形心。同样，除非是另外说明，一般我们 不考虑物体自重，正如我们在图1中讨论的梁一样。 The total elongation of a bar carrying an axial force will be denoted by the Greek letter see Fig.1(a), and the elongation per unit length, or strain, is then determined by the equation =/L (2). Where L is
12、the total length of the bar. Note that the strain is a non -dimensional quantity. It can be obtained accurately from Eq.(2) as long as the strain is uniform throughout the length of the bar. If the bar is in tension, the strain is a tensile strain, representing an elongation or stretching of the mat
13、erial; 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. 在轴向力作用下，梁的总伸长用希腊字母来表示见图1(a) ，单位伸长量或者说应变将由方程(2)决定，这里L是指梁的总长 度。注意，这里应变是一个无量纲量，只要应变在梁的长度上各 处是均匀的，那么它可以通过方程(2)精确获得。如果梁被拉伸， 那么得到拉应变，表现为材料的延长或者拉伸；如果梁被压缩，
14、那么得到压应变，意味着梁的横截面将彼此更加靠近。 When a material exhibits a linear relationship between stress and strain, it is said to be linear elastic. This is an extremely important property of many solid materials, including most metals, plastics, wood, concrete, and ceramics. The linear relationship between stress a
15、nd strain for a bar in tension can be expressed by the simple equation =E (3) in which E is a constant of proportionality known as the modulus of elasticity for the material. 当一种材料的应力与应变表现出线性关系时，我们称这种材 料为线弹性材料。这是许多固体材料的一个极其重要的性质，这 些材料包括大多数金属，塑料，木材，混凝土和陶瓷。对于被拉 伸的梁来说，这种应力与应变之间的线性关系可以用简单方程(3) = E 来表示，这
16、里E是一个已知的比例常数，即该材料的弹性模 量。 Note that E has the same units as stress. The modulus of elasticity is sometimes called Youngs modulus, after the English scientist Thomas Young (1773-1829) who studied the elastic behavior of bars. For most materials the modulus of elasticity in compression is the same as in tension. 注意，弹性模量的单位跟应力的单位相同。在研究梁的弹性 行为的英国科学家Thomas Young (1773-1829)出现之后，弹性模 量有时也被称为杨氏模量。对大多数材料而言，压缩和拉伸时的 弹性模量是一样的。 Translation The relationship bet
