A simple beam shown below is subjected to a uniformly distributed load of $w=80k\frac{N}{m}$ and laterally supported at the ends and at the midpoint.

a$.$ Draw the bending moment diagram.

b$.$ Compute the nominal moment strength of the beam and check to see if the section $($HE$450$ A$)$ adopted is satisfactory for the beam configuration and loading shown below. Use ASD. $(40$ points$)$

S $355F_y=355\frac{N}{m}{m}^2,F_u=510\frac{N}{m}{m}^{2}E=200000\frac{N}{m}{m}^2,Lr=9860mm.$

$HE450A$

$A=178cm$

$I_x=63720c{m}^4$

$S_x=2896c{m}^3$

$Z_x=3216c{m}^3$

$r_y=72\mathrm{.}9mm$

$b=300mm$

$tf=21mm$

$t_w=11\mathrm{.}5mm$

$d=440mm$

$h=344mm$