Mohr Circle for Plane Stresses

Consider a plane-strain problem in the x-z plane, as shown in Fig. 8.2. The stress tensor, expressed in Cartesian coordinates, takes the form 

Since a tensor is invariant with respect to the selection of the reference coordinates, the stresses on any plane can be expressed in terms of ox, crz, and rxz. As shown in Fig. 8.3, the force balance of the differential element results in the stress relationships on the BC plane, as given by 

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