Astm Cast Iron Has Minimum Ultimate Strengths Of 30

An ASTM cast iron has minimum ultimate strengths of 30 kpsi in tension and 100 kpsi in compression. Find the factors of safety using the MNS, BCM, and MM theories for each of the following stress states. Plot the failure diagrams in the σA , σB plane to scale and locate the coordinates of each stress state.
(a) σx = 20 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, τx y = 8 kpsi

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