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Abstract
This chapter presents an analysis of stress and strain. The analytical processes discussed in the chapter show that when the entire stresses act in directions parallel to one plane, the most complicated stress system is equivalent to a combination of two mutually perpendicular direct stresses. When the stresses at any point in a body all act parallel to one plane, the most general stress system will consist of two mutually perpendicular direct stresses, and two equal complementary shearing stresses. It can be shown that in a general three-dimensional stress system, there are always three mutually perpendicular principal planes on which the shearing stress is zero, that is, there are three principal planes. The corresponding direct stresses on these planes are the principal stresses. For a proof of this statement, and the equations for finding the principal stresses, the reader is referred to works on the Theory of Elasticity.
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