A timber $E=12$GPa beam is loaded and supported as shown. The cross section of the timber beam is $b=110-mm.$ wide and $h=250-mm$ deep. The beam is supported at $B$ by a $13-$mm$-$diameter steel $=190$GPa rod, which has no load before the distributed load is applied to the beam. After a distributed load of $w=11k\frac{N}{m}$ is applied to the beam, determine:

$($a$)$ the force carried by the steel rod.

$($b$)$ the maximum bending stress in the timber beam.

$($c$)$ the deflection of the beam at $B.$

Assume $L=18\mathrm{.}0m,L_1=6\mathrm{.}0m.$