Problem # $5(20$ points$)$

If the beam is made of a material having a fail tensile and compressive stress of $({}_{\text{F}\text{a}\text{i}\text{l}})t=225$MPa and $({}_{\text{F}\text{a}\text{i}\text{l}})c=300$MPa, respectively, and S$.$F$.$ is $1\mathrm{.}5,$ determine:

$($a$)$ The maximum allowable internal moment $M$ that can be applied to the beam in kN$.$m$.$

$($b$)$ Normal force resisted by the upper flange of the beam in kN $.$

Take: $\frac{?}{\text{b}\text{a}\text{r}}(y)=174\mathrm{.}69mm$ from the base of the beam and

$I_{N.A}=2\mathrm{.}1818{10}^{8}m{m}^4$