A $12\mathrm{.}2-$ft$-$long simply supported timber beam carries a $4\mathrm{.}4-$kip concentrated load at midspan. The cross$-$sectional dimensions of the timber are shown in the second figure. Assume $L=6\mathrm{.}1ft,x=3\mathrm{.}5ft,a=2\mathrm{.}7in.,b=6\mathrm{.}8in.,c=1\mathrm{.}7in,$ and $d=18in.$

$($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 $12\mathrm{.}2-$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 $12\mathrm{.}2-$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.

A $12\mathrm{.}2-$ft$-$long simply supported timber beam carries a $4\mathrm{.}4-$kip concentrated load at midspan. The cross$-$sectional dimensions of the timber are shown in the second figure. Assume $L=6\mathrm{.}1ft,x=3\mathrm{.}5ft,a=2\mathrm{.}7in.,b=6\mathrm{.}8in.,c=1\mathrm{.}7in,$ and $d=18in.$

$($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 $12\mathrm{.}2-$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 $12\mathrm{.}2-$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.