Đang chuẩn bị liên kết để tải về tài liệu:
Standard Handbook of Machine Design P57

CHAPTER 49 STRESS Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor, Michigan 49.1 DEFINITIONS AND NOTATION / 49.1 49.2 TRIAXIAL STRESS / 49.3 49.3 STRESS-STRAIN RELATIONS / 49.4 49.4 FLEXURE/49.10 49.5 STRESSES DUE TO TEMPERATURE /49.14 49.6 CONTACT STRESSES/49.17 REFERENCES / 49.22 49.1 DEFINITIONS AND NOTATION The general two-dimensional stress element in Fig. 49.1« shows two normal stresses Cx and Gy, both positive, and two shear stresses ixy and iyx, positive also. The element is in static equilibrium, and hence ixy = iyx. The stress state depicted by the figure is called plane or biaxial stress. FIGURE 49.1 Notation for two-dimensional stress. (From Applied. | CHAPTER 49 STRESS Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor Michigan 49.1 DEFINITIONS AND NOTATION 49.1 49.2 TRIAXIAL STRESS 49.3 49.3 STRESS-STRAIN RELATIONS 49.4 49.4 FLEXURE 49.10 49.5 STRESSES DUE TO TEMPERATURE 149.14 49.6 CONTACT STRESSES 49.17 REFERENCES 49.22 49.1 DEFINITIONS AND NOTATION The general two-dimensional stress element in Fig. 49. In shows two normal stresses and sy both positive and two shear stresses r and t positive also. The element is in static equilibrium and hence tx xyx. The stress state depicted by the figure is called plane or biaxial stress. a FIGURE 49.1 Notation for two-dimensional stress. From Applied Mechanics of Materials by Joseph E. Shigley. Copyright 1976 by McGraw-Hill Inc. Used with permission of the McGraw-Hill Book Company. 49.1 49.2 STANDARD HANDBOOK OF MACHINE DESIGN Figure 49.1b shows an element face whose normal makes an angle 0 to the x axis. It can be shown that the stress components a and r acting on this face are given by the equations G Vi Vy _ Gy 2 cos 20 T sin 20 sin 20 rXy cos 20 49.1 49.2 2 It can be shown that when the angle 0 is varied in Eq. 49.1 the normal stress 7 has two extreme values. These are called the principal stresses and they are given by the equation 71 7 2 - 49.3 The corresponding values of 0 are called the principal directions. These directions can be obtained from 2t 20 tan-1------ - 7 49.4 The shear stresses are always zero when the element is aligned in the principal directions. It also turns out that the shear stress r in Eq. 49.2 has two extreme values. These and the angles at which they occur may be found from Tl T2 49.5 20 tan-1-0 2t xy 49.6 The two normal stresses are equal when the element is aligned in the directions given by Eq. 49.6 . The act of referring stress components to another reference system is called transformation of stress. Such transformations are easier to visualize and to solve using a Mohr s circle diagram. In Fig. 49.2 we create a .