(2) Given a Cartesian coordinate system, a state of stress that corresponds to what is called...

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(2) Given a Cartesian coordinate system, a state of stress that corresponds to what is called plane stress is given by = 11 012 0 022 0 0 0 FIGURE 1. 012 0 It is of interest to express this stress state in a polar coordinate system that shares the same origin as the Cartesian system. Derive the Orr, Tre, and the de components of the stress tensor, according to Figure 1, as a function of the stress components 11, 12 and 22 expressed in the Cartesian coordinate system and the angle . Recall that the traction vector, t, on a surface with unit normal vector n is given by X t 011 012 013 8-6 t2 = 012 022 023 t3 013 023 033 1 0 ni ][B] n3 (2) Given a Cartesian coordinate system, a state of stress that corresponds to what is called plane stress is given by = 11 012 0 022 0 0 0 FIGURE 1. 012 0 It is of interest to express this stress state in a polar coordinate system that shares the same origin as the Cartesian system. Derive the Orr, Tre, and the de components of the stress tensor, according to Figure 1, as a function of the stress components 11, 12 and 22 expressed in the Cartesian coordinate system and the angle . Recall that the traction vector, t, on a surface with unit normal vector n is given by X t 011 012 013 8-6 t2 = 012 022 023 t3 013 023 033 1 0 ni ][B] n3