Stress and Strain Transformations

A component may not have the same strength across all planes at a particular location of it. Also, the strengths in tension, compression, and shear may be different at a given location. Since failure in a component occurs when a stress exceeds its limiting value, in the design and failure studies of an object, it is important to know the magnitudes and directions of the stresses at a location of the object and the planes on which these stresses act. Similarly, in deformation studies, it is important to know the strains along different directions and with respect to different corners at a given location of the body. Stress transformation and strain transformation are the main considerations in the present chapter. The contents of the chapter are the following: Stress transformation: finding stresses on different planes at the same location, Use of Mohr’s circle for stress transformation, Determination of principal stresses, maximum in-plane shear stress, and absolute maximum shear stress, Thin-walled pressure vessels, Strain transformation, Use of Mohr’s Circle for strain transformation, Determination of principal strains, maximum in-plane shear strain, and absolute maximum shear strain, Theory of strain measurement, and Theories of failure for ductile and brittle materials.