A $15\mathrm{.}4-$ft$-$long simply supported timber beam carries a $6\mathrm{.}8-$kip concentrated load at midspan. The cross$-$sectional dimensions of the timber are shown in the second figure. Assume $L=7\mathrm{.}7ft,x=2\mathrm{.}5ft,a=3\mathrm{.}9in.,b=5\mathrm{.}4in.,c=1in,$ and $d=11in.$

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

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

$($c$)$ Determine the maximum horizontal shear stress ${}_{\text{m}\text{a}\text{x}}$ that occurs in the beam at any location within the $15\mathrm{.}4-$ 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 $15\mathrm{.}4-$ft span length.

Answers:

$($a$){}_H=$

i $$ psi.

$($b$){}_K=$ psi.

$($c$){}_{\text{m}\text{a}\text{x}}=$ psi.

$($d$){}_{\text{m}\text{a}\text{x}}=$ psi.