TABLE OF CONTENTS We now want to summarize the differences between the stresses applied to an element and the principal stresses that may occur on other planes as a result of the applied stresses. The applied stresses are the nine components of the stress tensor (equation 12.5a, p. 348) that result from whatever loads are applied to the particular geometry of the object as defined in a coordinate system chosen for convenience. The principal stresses are the three principal normal stresses and the three principal shear stresses defined in Section 12-8. Of course, many of the applied-stress terms may be zero in a given case. For example, in a tensile-test specimen the only nonzero applied stress is the ? x term in equation 12.5a (p. 348), which is unidirectional and normal. There are no applied shear stresses on the surfaces normal to the force axis in pure tensile loading. However, the principal stresses are both normal and shear.
In a tensile-test specimen, the applied stress is pure tensile and the maximum principal normal stress is equal to it in magnitude and direction. But a principal shear stress of half the magnitude of the applied tensile stress acts on a plane 45 from the plane of the principal normal stress. Thus, the principal shear stresses will typically be nonzero even in the absence of any applied shear stress. This fact is important to an understanding of why parts fail. The most difficult...
