$1-(15\%)$ A solid round machine component is subjected to a maximum bending moment of M $=4000$ in$-$Ib

and a maximum axial force of P $=1000$ lb$.$ The part has a $1\mathrm{.}0$ inch in diameter and is made of steel with the

yield strength of $97000$ psi.

a$)$ Use the maximum shear stress theory to determine the safety factor guarding against yielding.

b$)$ Use the energy distortion theory $($von Mises stress$)$ to determine the safety factor guarding against yielding.