$(35$ points total$)$ For the figure shown below, based on static loading, find

a$)(5$ points$)$ the location of the worst stressed element in the round bar

b$)(5$ points$)$ the shear stress due to torsion at this location

c$)(5$ points$)$ the bending stress at this location

c$)(10$ points$)$ the three principal stresses

d$)(5$ points$)$ the factor of safety based on the distortion energy theory

e$)(5$ points$)$ factor of safety based on the maximum shear stress theory

Given: $S_y=94k$