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Tham khảo tài liệu 'sổ tay tiêu chuẩn thiết kế máy p57', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 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 .
