1. A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa (= 50.8 ksi).
Using the maximum-shear-stress theory, determine the factors of safety for the following plane stress states:
(a) $\sigma_x$ = 100, $\sigma_y$ = 30, $\tau_{xy}$ = -50 MPa
(b) $\sigma_x$ = -6, $\sigma_y$ = 18, $\sigma_z$ = -12, $\tau_{xy}$ = 9, $\tau_{yz}$ = 6, $\tau_{zx}$ = -15 kpsi