$5\mathrm{.}6-11$ A beam ABC with an overhang from $B$ to

$C$ is constructed of a UPN $260$ channel section with

flanges facing upward $($see figure$).$ The beam sup$-$

ports its own weight $(372\frac{N}{m})$ plus a triangular load

of maximum intensity $q_0$ acting on the overhang. The

allowable stresses in tension and compression are

$138$MPa and $75$MPa, respectively.

$($a$)$ Determine the allowable triangular load inten$-$

sity $q_{0,\text{a}\text{l}\text{l}\text{o}\text{w}}$ if the distance $L$ equals $1\mathrm{.}2m.$

$($b$)$ What is the allowable triangular load intensity

$q_{0,\text{a}\text{l}\text{l}\text{o}\text{w}}$ if the beam is rotated $180$ about its lon$-$

gitudinal centroidal axis so that the flanges are

downward?