1、本书中研究的固体包括受轴向载荷的杆，轴，梁，圆柱及由这些构件组成的结构。一般情况下，研究的目的是测定由荷载引起的应力、应变和变形物理量；当所承受的荷载达到破坏载荷时，可测得这些物理量，画出完整的固体力学性能图。Theoretical analyses and experimental results have equally important roles in the study of mechanics of materials. On many occasions we will make logical derivations to obtain formulas and equati
2、ons for predicting mechanical behavior, but at the same time we must recognize that these formulas cannot be used in a realistic way unless certain properties of the material are known. These properties are available to us only after suitable experiments have been made in the laboratory. Also, many
3、problems 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
4、 results 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 determine the strength of wires, bars, and beams, although they did not develop any adequate theories （by todays standards） to their test
5、results. By contrast, the famous mathematician Leonhard Euler（1707-1783） developed the mathematical theory 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 theoretical results remained
6、 unused for many years, although today they form the basis of column theory.在材料力学的研究中，理论分析和实验研究是同等重要的。必须认识到在很多情况下，通过逻辑推导的力学公式和力学方程在实际情况中不一定适用，除非材料的某些性能是确定的。而这些性能是要经过相关实验的测定来得到的。同样，当工程中的重要的问题用逻辑推导方式不能有效的解决时，实验测定就发挥实用性作用了。材料力学的发展历史是一个理论与实验极有趣的结合，在一些情况下，是实验的指引得出正确结果而产生理论，在另一些情况下却是理论来指导实验。例如，著名的达芬奇（1452
7、-1519）和伽利略（1564-1642）通过做实验测定钢丝，杆，梁的强度，而当时对于他们的测试结果并没有充足的理论支持（以现代的标准）。相反的，著名的数学家欧拉（1707-1783） ，在1744年就提出了柱体的数学理论并计算其极限载荷，而过了很久才有实验证明其结果的正确性。 因此，欧拉的理论结果在很多年里都未被采用，而今天，它们却是圆柱理论的奠定基础。 The concepts of stress and strain can be illustrated in an elementary way by considering the extension of prismatic bar
8、see Fig.1.4（a）. 通过对等截面杆拉伸的研究初步解释应力和应变的概念如图1.4（a）。A prismatic bar is one that has constant cross section throughout its length and a straight axis. 等截面杆是一个具有恒定截面的直线轴。In this illustration the bar is assumed to be loaded at its ends by axial forces P that produce a uniform stretching, or tension, of th
9、e bar. 这里，假设在杆的末端施加轴向力P，产生均匀的伸展或拉伸。By making an artificial cut （section mm） though the bar at right angels to its axis, we can isolate part of the bar as a free body Fig.1.4 （b）. 假设沿垂直于轴线的方向切割杆，我们就能把杆的一部分当作自由体隔离出来图1.4（b）。At the right-hand end the tensile force P is applied, and at the other end ther
10、e are forces representing the removed portion of the bar upon the part that remains. 张力P作用于杆的右端，在另一端就会出现一些力来代替杆被切除的那一部分。These forces will be continuously distributed over the cross section, analogous to the continuous distribution of hydrostatic pressure over a submerged surface. 这些力连续地分布在横截面上，类似于作用
11、在被淹没物体表面的连续的静水压力。The intensity of force, that is, the per unit area, is called the stress and is commonly denoted by the Greek letter .力的密度，也就是单位面积上的力的大小，称为应力，一般用表示。Assuming that the stress has a uniform distribution over the cross section see Fig.1.4（b）, we can readily see that its resultant is equ
12、al to the intensity times the cross-sectional area A of the bar. 假设应力是均匀分布在横截面上如图1.4（b），易得出它的大小等于密度乘以杆的横截面积A。Furthermore, from the equilibrium of the body shown in Fig.1.4 （b）, we can also that this resultant must be equal in magnitude and opposite in direction to the force P. 另外，通过图1.4（b）中所示物体，也由力的
13、平衡可得到它与力P等大反向。Hence, we obtain 因此得到 （1.3）as the equation for the uniform stress in a prismatic bar.为等截面杆中平均应力的计算公式。This equation shows that stress has units of force divided by area-for example, Newtons per square millimeter （） or pounds per square inch （psi）. 从这个公式可以看出，应力的单位是力除以面积例如：牛每平方毫米（）或磅每平方英寸
14、（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 forces are reversed in direction, causing the bar to be compressed, they are called compressive stresses. 当杆在力的作用下被拉伸时，如图所示，所产生的应力称为拉应力；当施加相反方向的力时，杆被压缩，这时所产生的应力称为压应力。A nece
15、ssary condition for Eq. （1.3） to be valid is that the stress must be uniform over the cross section of the bar. 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 the load P does not act at the centroid, bendin
16、g 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 stated otherwise, it is generally assumed that the weig
17、ht of the object itself is neglected, as was done when discussing the bar in Fig.1.4.方程（1.3）的必要条件是应力必须均匀分布在杆的横截面上。如果轴向力P通过截面的形心时，这个条件可以满足，同时也可以通过静力学验证。当载荷P不是作用在形心时，将会产生挠度，就需要更加复杂的分析了。如果没有特殊说明，本书中假定所有的轴向力都作用在横截面的形心。除非另有说明，否则物体本身的质量一般忽略不计，如讨论图1.4中的杆情况一样。 The total elongation of a bar carrying an axial
18、 force will be denoted the Greek letter see Fig. 1.4（a）, and the elongation per unit length, or strain, is then determined by the equation （1.4）where L is the total length of the bar. Note that the strain is nondimensional quantity. It can be obtained accurately from Eq. （1.4） as long as the strain
19、is uniform throughout the length of the bar. If the bar is in tension, the strain is a tensile strain, 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 sections of the bar move closer to one
20、another.受轴向力时，杆的总伸长量用希腊字母表示，如图1.4（a）所示。单位长度的伸长即应变，可以用计算得到。这里L是杆的总长度。注意应变是无量纲量，只要应变在杆上是均匀的，就可以通过方程（1.4）得到精确的结果。如果杆被拉伸，此时的应变称为拉应变，即材料伸长或被拉伸；如果杆被压缩，即为压应变，这就意味着杆的相邻截面间的距离变小。 （Selected from Stephen P.Timoshenko and James M.Gere,mechanics of materials,Van Nostrand Reinhold Company Ltd.,1978 ）材料力学是应用力学的一个分
21、支，用来处理固体在不同荷载作用下所产生的反应。通过对等截面杆拉伸的研究初步解释应力和应变的概念如图1.4（a）。等截面杆是一个具有恒定截面的直线轴。这里，假设在杆的末端施加轴向力P，产生均匀的伸展或拉伸。假设沿垂直于轴线的方向切割杆，我们就能把杆的一部分当作自由体隔离出来图1.4（b）。张力P作用于杆的右端，在另一端就会出现一些力来代替杆被切除的那一部分。这些力连续地分布在横截面上，类似于作用在被淹没物体表面的连续的静水压力。力的密度，也就是单位面积上的力的大小，称为应力，一般用表示。假设应力是均匀分布在横截面上如图1.4（b），易得出它的大小等于密度乘以杆的横截面积A。另外，通过图1.4（b）中所示物体，也由力的平衡可得到它与力P等大反向。因此得到为等截面杆中平均应力的计算公式。从这个公式可以看出，应力的单位是力除以面积例如：当杆在力的作用下被拉伸时，如图所示，所产生的应力称为拉应力；方程（1.3）的必要条件是应力必须均匀分布在杆的横截面上。受轴向力时，杆的总伸长量用希腊字母表示，如图1.4（a）所示。Rochiny
