$9-42.$ The drill pipe has an outer diameter of $3$ in $.,$ a wall thickness of $0\mathrm{.}25$ in $.,$ and a weight of $50l\frac{b}{f}t.$ If it is subjected to a torque and axial load as shown, determine $($a$)$ the principal stresses and $($b$)$ the maximum in$-$plane shear stress at a point on its surface at section $a.$

Prob. $9-42$