A steel hollow structural section $($HSS$)$ flexural member is subjected to a load of $P=23$ kips as shown. The cross$-$sectional dimensions of the shape as also shown are $d=12\mathrm{.}25in.,b=9\mathrm{.}75in.,t=0\mathrm{.}30in.,x_H=3\mathrm{.}75in.,$ and $x_K=3\mathrm{.}25in.$ Using $a=19\mathrm{.}25in.,$ determine the principal stresses and the maximum shear stress acting at points $H$ and $K,$ as shown. Show these stresses on an appropriate sketch for each point.

Calculate the moment of inertia for the entire cross$-$section about its $z$ centroidal axis

Answer: $I_z=$ in$.{?}^4$