$14\mathrm{.}21$ A solid rectangular simply supported timber beam $6$ in$.$ wide, $20$ in$.$ deep, and $10$ ft long carries a concentrated load of $16,000$ lb at midspan. Use nominal dimensions.

$($a$)$ Compute the maximum horizontal shear stress at the neutral axis.

$($b$)$ Compute the shear stress $4$ in$.$ and $8$ in$.$ above and below the neutral axis. Neglect the weight of the beam.