고체역학 (Beer) — Transformations of Stress and Strain: Problem 7.164

7.164 The state of plane stress shown occurs in a machine component made of a steel with \(\sigma_Y = 45\text{ ksi}\). Using the maximum-distortion-energy criterion, determine whether yield will occur when (a) \(\tau_{xy} = 9\text{ ksi}\), (b) \(\tau_{xy} = 18\text{ ksi}\), (c) \(\tau_{xy} = 20\text{ ksi}\). If yield does not occur, determine the corresponding factor of safety.