$(25\%)$ A steel part is loaded with a combination of bending, axial, and torsion such that the following stresses are created at a particular location:

Bending: Completely reversed, with a maximum stress of $50$ MPa $.$

Axial: Constant stress of $10$ MPa

Torsion: Repeated load, varying from $0$ MPa to $80$MPa,$S_C=160$MPa

Assume the varying stress are in phase with each other. The part contains a notch such that $K_{f,\text{b}\text{e}\text{n}\text{d}\text{i}\text{n}\text{g}}=14,K_{f,\text{a}\text{x}\text{i}\text{a}\text{l}}=1\mathrm{.}1,K_{f,\text{t}\text{o}\text{r}\text{s}\text{i}\text{o}\text{n}}=2\mathrm{.}0.$ The material properties are $S_y=300$Mpa and $S_u=400$MPa. Find the factor of safety for fatigue based on infinite life, using the Goodman criterion. If the life is not infinite, estimate the number of cycles, using the Walker criterion to find the equivalent completely reversed stress. Be sure to check for yielding.