Q$2.[40$ pts$]$ The given beam is subjected to factored dead and live loads. The moment diagram under factored loads is given below. The beam is laterally supported at its full length. Check whether the given beam have sufficient flexural capacity to carry the given loads safely. Assume deflections are at acceptable levels.

$($Steel: S$355-F_y=3600kg\frac{f}{c}{m}^2,E_s=2{10}^{6}kg\frac{f}{c}{m}^2)$

$S_y=2352c{m}^3$

$Z_y=2585c{m}^3$