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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
50 kpsi
0 kpsi
100 kpsi
150 kpsi
200 kpsi
Set 3
Set 4
-50 kpsi
-25 kpsi
-100 kpsi
110 kpsi
-110 kpsi
130 kpsi
-65 kpsi
-150 kpsi
-75 kpsi
-200 kpsi
Set 5
25 kpsi
65 kpsi
-130 kpm
75 kpsi
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