TABLE OF CONTENTS The axis systems taken in Figures 12-7 and 12-8 are arbitrary and are usually chosen for convenience in computing the applied stresses. For any particular combination of applied stresses, there will be a continuous distribution of the stress field around any point analyzed. The normal and shear stresses at the point will vary with direction in any coordinate system chosen. There will always be planes on which the shear-stress components are zero. The normal stresses acting on these planes are called the principal stresses. The planes on which these principal stresses act are called the principal planes. The directions of the surface normals to the principal planes are called the principal axes, and the normal stresses acting in those directions are the principal normal stresses. There will also be another set of mutually perpendicular axes along which the shear stresses will be maximal. The principal shear stresses act on a set of planes that are at 45 angles to the planes of the principal normal stresses. The principal planes and principal stresses for the 2-D case of Figure 12-8 are shown in Figure 12-9.
Since, from an engineering standpoint, we are most concerned with designing our machine parts so that they will not fail, and since failure will occur if the stress at any point exceeds some safe value, we need to find the largest stresses (both normal and shear) that occur anywhere in...
