A $11\mathrm{.}6-$ft$-$long simply supported timber beam carries a $4\mathrm{.}1-$kip concentrated load at midspan. The cross$-$sectional dimensions of the timber are shown in the second figure. Assume $L=5\mathrm{.}8ft,x=2\mathrm{.}7ft,a=3in.,b=7\mathrm{.}9in.,c=1\mathrm{.}2in,$ and $d=10in.$

$($a$)$ At section $a-a,$ determine the magnitude of the shear stress $T_H$ in the beam at point $H.$

$($b$)$ At section $a-a,$ determine the magnitude of the shear stress $I_k$ in the beam at point $K.$

$($c$)$ Determine the maximum horizontal shear stress $I_{\text{m}\text{a}\text{x}}$ that occurs in the beam at any location within the $11\mathrm{.}6-$ ft span length.

$($d$)$ Determine the maximum tension bending stress ${}_{\text{m}\text{a}\text{x}}$ that occurs in the beam at any location within the $11\mathrm{.}6-$ft span length.