3. 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 Columb-Mohr theory of failure (CMTF) and modified Mohr theory of failure (MMTF) for the following critical point states of stress.
(a) $\sigma_1$ = 20 ksi, $\sigma_2$ = -35 ksi
(d) $\sigma_x$ = -60 ksi, $\tau_{xy}$ = -40 ksi
(b) $\sigma_1$ = 20 ksi, $\sigma_2$ = 20 ksi