Unit 3 Normal stress and shear__ stress.doc

Unit3 Normal Stress and Shear Stress正应力和切应力1. Normal stress正应力Previously we found the internal loads in members of trusses. Unknowingly, the first step was taken in determining the stress in the member. The force found in the member was the load necessary to maintain equilibrium. The force was found by passing a cutting plane through the member and is, therefore, an internal force or internal load. This is the first step in any stress analysis problem- to find that is the principal subject of this part of this part of book, but the first and necessary step is always to find the load causing the stress.在这之前，我们已经知道组成构件的杆件存在内载。不知不觉地，人们把测定杆件的压力作为研究的第一步。而这个力是保持系统平衡的必要载荷。该力是利用穿过杆件的横截面求得的，因此叫做内力或内载荷。这就是压力分析问题的第一步求取内载。第二步则是求由这个载荷产生的应力，这是这部分主要研究的问题，但是求产生这个应力的内载仍然是第一步，也是必不可少的一步。Consider a 2-in. square member that is found to carry say a 1170-lb tensile load as shown in Fig.1.8 (a). Now, given the load in the member, the question is raised. How is that load carried? For the moment it is assumed that it is assumed that it is uniformly carried, as shown in Fig.1.8 (b). If the load is equally shared by all the 2.0 .of cross-sectional area, then the stress in the member is the load divided by the area, or:, or 如图1.8（a）所示的横截面积为2平方英寸的杆件，假设它受到1170磅的拉伸载荷。现在假设载荷已经作用于杆件上，问题随即出现了。这个载荷是如何分布的？对于杆件来说它是均匀分布的，如图1.8（b）所示。如果载荷均匀的分布在这2平方英寸的横截面上，杆件的应力大小就等于载荷除以面积，即, or There are several things to be observed regarding this exercise. The first is the symbol for stress, . This is the lowercase Greek letter sigma, the equivalent to the English s. Some texts use the English s, but is much more common, and so we will use it. Becoming used to it now will make later work more convenient. In structural design it is common to use f for stress.从这个案例中我们注意到：第一是应力的符号，。它是希腊语中的小写字母，类似于英语中的s。有些教材中使用s，但是比较常用，因此我们使用。现在习惯于用将使后面的工作更方便。在结构设计中，通常使用f表示压力。The second point is the equation we now label:第二点是以下的方程： (1.5)This equation, fundamental to the subject at hand, should be learned, and normally it will be, from repeated use. In obtaining the equation it was assumed the stress is uniform, that is, equally distributed. That turns out to have been a very good assumption, which is approximately true in a very large number of cases. Even when it is patently untrue, the design stress is frequently based on average stress, so Eq. (1.5) has very wide application.这个方程对于我们即将研究的问题来说非常重要，应该掌握，它将被重复使用。在获得方程的过程中，假定应力是均匀分布的，也就是平等分布。这是个非常好的假设，在大量的案例中都适用。即使在这个假设不成立的情况下，设计压力通常取平均压力，因此，公式（1.5）有广泛的应用。The direction of this stress should also be noted. It is perpendicular or normal to the surface over which it acts and is, therefore, called a normal stress. “Normal” means perpendicular to the surface. In addition to these two properties (direction and magnitude), a third characteristic of stress is its distribution-uniform in this case. It is often convenient to sketch the stress distribution. When it is not sketched, the student should always visualize a mental picture. A three-dimensional representation is shown in Fig.1.8 (b). The more common two-dimensional representation is shown in Fig.1.8(c).应力的方向也应当注意。它垂直于力作用的表面，因此叫做正应力。“Normal”表示垂直于表面的意思。除了大小和方向这两个性质，应力的第三个特性就是它分布的均匀性。这样，画出应力分布草图就很容易了。当不画草图时，我们学生应当能想象出分布情况。图1.8（b）所示的是三维图。但我们使用更多的是图1.8（c）中的二维图。The sense of the stress is also important. It cannot be determined from the sign of the force vector. It depends instead on the action of the stress on the body. If the stress is tending to stretch the body or pull it apart, it is called tension. Normally, stress-producing tension is considered positive. If the stress is compressing or squashing the body, it is called compression and carries a negative sign.应力产生的效果也是重要的。它不能从矢量力的符号中测得。它不依赖物体的运动而是依赖无物体上的压力。如果压力的趋势是拉伸物体或是使它分开，就叫做张力。通常，把拉伸张力规定为正的。如果应力是压缩或挤压物体，则把它叫做压缩，取负的。The last aspect considered here is that of the units for stress. These follow from Eq. (1.5):最后研究的是应力的单位。In the SI the unit of force is the Newton and the unit of area is the meter squared. Thus the unit of stress is the Newton per meter squared. This is a derived unit in the SI and carries the name Pascal, abbreviated Pa,在国际单位制中，压力的单位是牛顿，面积的单位是平方米。因此，应力的单位是牛每平方米。它是一个导出单位，称为帕斯卡，简称Pa。2. Shear Stress切应力In Fig.1.8 the applied force was normal, that is perpendicular to the cross section.Fig.1.9 (a) represents a section in which the internal load is not normal. In Fig.1.9(b) this force P, a vector, has been resolved into a normal component can be related to a normal component and a tangential component . The normal component can be related to a normal stress. Thus gives the average normal stress, which approximates the true situation very closely. The effect of tangential component is to shear the number, as indicated in Fig.1.10. An average shear stress may be calculated: (1.6) 图1.8中物体所受的力是标准的，也就是垂直于横截面。而图1.9（a）中的力则不是标准的。如图1.9（b），矢量力P分解成竖直分量和切向分量。竖直分量产生正应力。于是根据求得平均正应力，它与真实情况非常相近。切向分量将产生剪应力，如图1.10所示。平均剪应力有以下公式计算得到：。This equation, however, differs considerably from the true stress situation. Nonetheless, for many practical reasons Eq. (1.6) is widely used in many engineering applications. The subscript av indicates that an average stress, not the true stress, is being calculated. 但是，这个方程与真实压力有很大的不同。尽管如此，根据实际需要，方程（1.6）也广泛的应用在许多工程应用中。下脚表av表示计算得到的是平均应力而不是真实应力。The Greek letter tau () is most frequently used for shear stress, although is not uncommon. Since this is also a load divided by an area, it also has units of psi, ksi, Pa, MPa and so on.最常用的表示剪应力的符号是是希腊字母tau ()，而不常用。由于它也是由载荷除以面积得到的，因此它的单位也是psi, ksi, Pa, MPa等等。The preceding section noted the importance of the magnitude, direction, and distribution of the stress represented by Eq. (1.5). This is important for the shear stress as well. The magnitude is, of course, given by Ep.(1.6). The direction is parallel to the surface, tending to shear, and thus is called shear stress. The direction is assumed to be uniform, as shown in Fig.1.10.在前面部分中，公式（1.5）表明了应力大小，方向，分布状态的重要