A $14\mathrm{.}2-$ft$-$long simply supported timber beam carries a $8\mathrm{.}9-$kip concentrated load at midspan. The cross$-$sectional dimensions of the

timber are shown in the second figure. Assume $L=7\mathrm{.}1ft,x=2\mathrm{.}3ft,a=3\mathrm{.}9$ in$.,b=4\mathrm{.}1in.,c=1\mathrm{.}6in,$ and $d=12in.$

$($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 $14\mathrm{.}2-$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 $14\mathrm{.}2-$ft span length.

Answers:

$($a$){}_H=$

psi.

$($b$){}_K=$

psi.

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

psi.

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

psi.