$5\mathrm{.}5-23$ A beam ABC with an overhang from $B$ to

$C$ supports a uniform load of $3k\frac{N}{m}$ throughout its

length $($see figure$).$ The beam is a channel section with

dimensions as shown in the figure. The moment of iner$-$

tia about the $z$ axis $($the neutral axis$)$ equals $210c{m}^4.$

$($a$)$ Calculate the maximum tensile stress ${}_t$ and

maximum compressive stress ${}_c$ due to the

uniform load.

$($b$)$ Find the required span length a that results in

the ratio of larger to smaller compressive stress

being equal to the ratio of larger to smaller ten$-$

sile stress for the beam. Assume that the total

length $L=a+b=6m$ remains unchanged.