$3.$ A box beam is subjected to a $\backslash (26-\backslash$mathrm$\{$kN$\}\backslash )$ force that is applied at the centre of its width, $75$ mm from each side $($see Fig. $3.)$

a$.$ Determine the principal stresses and their directions at points $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash ),$ and show the results on elements located at each of these points;

b$.$ Determine the absolute maximum shear stress at points $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$; and,

c$.$ Calculate the bending moment necessary to yield the flanges of the box while the webs remain linearly elastic. What percent of that moment is resisted by the elastic core?