A $4\mathrm{.}5-$m$-$long simply supported timber beam carries two concentrated loads as shown. The cross$-$sectional dimensions of the beam are

also shown. Assume $L_1=0\mathrm{.}9m,L_2=1\mathrm{.}8m,P=9kN,Q=37kN,a=165mm,b=140mm,c=70mm,$ and $d=415mm.$

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

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

$($c$)$ Determine the maximum horizontal shear stress that occurs in the beam at any location within the $4\mathrm{.}5-m$ span length.

$($d$)$ Determine the maximum compression bending stress that occurs in the beam at any location within the $4\mathrm{.}5-$m span length.

Answers:

$($a$){}_H=$

kPa

$($b$){}_K=$

kPa

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

kPa

$($d$){}_x=$

kPa