A steel has the following material properties Syt = 40 kpsi, Syc = 60 kpsi, and εf = 0.06. Determine the factors of safety and state whether or not the part is predicted to fail for the following states of stress. Also plot all four cases on a σ1,σ3 plot showing load lines and failure lines.
(a) σx = -60 kpsi, σy = -30 kpsi, σz = -50 kpsi, τxy = 20 kpsi cw
(b) σx = -40 kpsi, σy = 20 kpsi, σz = 10 kpsi, τxy = 30 kpsi ccw
(c) σx = 10 kpsi, σy = 20 kpsi. σz = 15 kpsi, τxy = 10 kpsi cw
(d) σx = -8 kpsi, σy = 4 kpsi., σz = 0 kpsi, τxy = 12 MPa ccw