A $13\mathrm{.}6-$ft$-$long simply supported timber beam carries a $10\mathrm{.}6-$kip concentrated load at midspan. The cross$-$sectional dimensions of the

timber are shown in the second figure. Assume $L=6\mathrm{.}8ft,x=3\mathrm{.}9ft,a=3\mathrm{.}9in.,b=7\mathrm{.}5in.,c=1\mathrm{.}1in,$ and $d=16in.$

$($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 $13\mathrm{.}6-ft$ 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 $13\mathrm{.}6ft$ span length.

Answers:

$($a$){}_H=$

$($b$){}_K=$

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

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

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