Plot the following sets of stress states on a set of

Question

Plot the following sets of stress states on a set of principal axes (an example is provided in Figure 2A of the Appendix). Calculate the factor of safety for each stress state using both the Brittle Coulomb Mohr and Modified Mohr failure theories. Assume cast iron is used that has an ultimate tensile strength of 150 kpsi and an ultimate compressive strength of 400 kpsi.

	Set I			Set 2
σ1	σ2	σ3	σ1	σ2	σ3
50 kpsi	50 kpsi	0 kpsi	50 kpsi	0 kpsi	0 kpsi
100 kpsi	100 kpsi	0 kpsi	100 kpsi	0 kpsi	0 kpsi
150 kpsi	150 kpsi	0 kpsi	150 kpsi	0 kpsi	0 kpsi
200 kpsi	200 kpsi	0 kpsi	200 kpsi	0 kpsi	0 kpsi
	Set 3			Set 4
σ1	σ2	σ3	σ1	σ2	σ3
50 kpsi	0 kpsi	-50 kpsi	50 kpsi	0 kpsi	-25 kpsi
100 kpsi	0 kpsi	-100 kpsi	100 kpsi	0 kpsi	-50 kpsi
110 kpsi	0 kpsi	-110 kpsi	130 kpsi	0 kpsi	-65 kpsi
150 kpsi	0 kpsi	-150 kpsi	150 kpsi	0 kpsi	-75 kpsi
200 kpsi	0 kpsi	-200 kpsi	200 kpsi	0 kpsi	-100 kpsi
	Set 5
σ1	σ2	σ3
25 kpsi	0 kpsi	-50 kpsi
50 kpsi	0 kpsi	-100 kpsi
65 kpsi	0 kpsi	-130 kpm
75 kpsi	0 kpsi	-150 kpsi
100 kpsi	0 kpsi	-200 kpsi