Q$1$: $(10$ points$)$ The internal loadings at a cross section through the $6$ in diameter drive shaft of a turbine consists of an axial force of $2750$ lb $,$ a bending moment of $800$ lbft and a torsional moment of $1350$ lbft $.$ Determine the principal stresses at point B$.$ Also calculate the maximum in$-$plane shear stress at this point.

Hint: how do the applied torque and bending moment relate to the stress experienced at point B $?$ Draw the stress element, which only contains two$-$dimensional components. Note that moment of inertia for a circle, $I_{x-x}=\frac{1}{4}**{}^{**}{r}^4.$Q$1$: $(10$ points$)$ The internal loadings at a cross section through the $6$ in diameter drive shaft of a turbine consists of an axial force of $2750$ lb $,$ a bending moment of $800$ lbft and a torsional moment of $1350$ lbft $.$ Determine the principal stresses at point B$.$ Also calculate the maximum in$-$plane shear stress at this point.

Hint: how do the applied torque and bending moment relate to the stress experienced at point B $?$ Draw the stress element, which only contains two$-$dimensional components. Note that moment of inertia for a circle, $I_{x-x}=\frac{1}{4}**{}^{**}{r}^4.$