Among the decisions a designer must make is selection of the failure criteria that is applicable to the material and its static loading. A 1020 hot-rolled steel has the following properties: Sy = 42 kpsi, Sut = 66.2 kpsi, and true strain at fracture εf = 0.90. Plot the failure locus and, for the static stress states at the critical locations listed below, plot the load line and estimate the factor of safety analytically and graphically.
(a) σx = 9 kpsi, σy = −5 kpsi.
(b) σx = 12 kpsi, τx y = 3 kpsi ccw.
(c) σx = −4 kpsi, σy = −9 kpsi, τx y = 5 kpsi cw.
(d) σx = 11 kpsi, σy = 4 kpsi, τx y = 1 kpsi cw.