A $6\mathrm{.}3-$m$-$long simply supported timber beam carries a uniformly distributed load of $10\mathrm{.}5k\frac{N}{m}.$ The cross$-$sectional dimensions of the

beam are shown in the second figure. Assume $x=0\mathrm{.}9m,b=90mm,d=330mm,y_H=73mm$ and $y_K=82mm.$

$($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 $6\mathrm{.}3-$m span length.

$($d$)$ Determine the maximum compression bending stress ${}_{\text{m}\text{a}\text{x}\text{C}}$ that occurs in the beam at any location within the $6\mathrm{.}3-$m span length.

Answers:

$($a$){}_H=$

MPa.

$($b$){}_K=$

MPa.

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

MPa.

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

MPa.