a$)$ Manually approximate the torsional constant $($J$)$ for a W$21\backslash$times $83$ and an HSS $1010\frac{3}{4}($Table $3\mathrm{.}1$ of Torsional Design Guide $9)$ and compare with the values provided in the AISC Steel Manual. $(10$ pts$)$

b$)$ Determine the torsional capacity $(T_n)$ for each shape using their preferred material $($Table $2-4$ in AISC Steel Manual$).$ Can this be done for all the shapes listed? If not, explain why. $(10$ pts$)$