The simply$-$supported beam shown below $($length $L=597\mathrm{.}5mm)$ has a U$-$

channel cross$-$section with the following properties:

$w=60mm,h=12\mathrm{.}5mm,t_f=1\mathrm{.}5mm,t_w=0\mathrm{.}25mm$

$A=51\mathrm{.}8m{m}^2,I_z={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{y}^{2}dA=876m{m}^4,$ and $I_y={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{z}^{2}dA=35949m{m}^4$

Additionally, $x_G=0mm,$ and $y_G=-1\mathrm{.}69mm,$ with respect to the nominal

center of the section.

If the beam is subjected to a uniform distributed load of $q=-0\mathrm{.}20$hat$(j)+0\mathrm{.}10$hat$(k)$

$\frac{N}{m}m,$ what is the largest magnitude principal stress, ${}_1$ or ${}_2,$ in the material

$($in units of MPa$),$ expressed as a positive number?