The general two-dimensional stress element in Fig. « 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. | CHAPTER 49 STRESS Joseph E. Shigley Professor Emeritus The University of Michigan Ann Arbor Michigan DEFINITIONS AND NOTATION TRIAXIAL STRESS STRESS-STRAIN RELATIONS FLEXURE STRESSES DUE TO TEMPERATURE CONTACT STRESSES REFERENCES 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 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. STANDARD HANDBOOK OF MACHINE DESIGN Figure 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 2 It can be shown that when the angle 0 is varied in Eq. the normal stress 7 has two extreme values. These are called the principal stresses and they are given by the equation 71 7 2 - The corresponding values of 0 are called the principal directions. These directions can be obtained from 2t 20 tan-1------ - 7 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. has two extreme values. These and the angles at which they occur may be found from Tl T2 20 tan-1-0 2t xy The two normal stresses are equal when the element is aligned in the directions given by Eq. . 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. we create a .
