A part is made of ASTM 30 cast iron with ultimate strengths of 30 ksi in tension and 100 ksi in compression. Find factors of safety using the Coulomb-Mohr theory of failure (CMIF) and modified Mohr theory of failure (MMTF) for the following critical point states of stress:
a = 20 ksi, σ = -35 ksi, σ₀ = -60 ksi, Txy = -40 ksi, b₀ = -20 ksi, σ₀ = 20 ksi.