A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 50 kpsi. Using the distortion-energy and maximum-shear-stress theories determine the factors of safety for the following plane stress states:
(a) σx = 12 kpsi, σy = 6 kpsi
(b) σx = 12 kpsi, τx y = −8 kpsi
(c) σx = −6 kpsi, σy = −10 kpsi, τx y = −5 kpsi
(d) σx = 12 kpsi, σy = 4 kpsi, τx y = 1 kpsi