$7.$ A compression strut is designed as a $50$ mm square tube with wall thickness $9$ mm as illustrated below. Assume it is to be made from aluminum and the elastic modulus is $\backslash (\backslash$mathrm$\{$E$\}=70\mathrm{.}7\backslash$mathrm$\{$GPa$\}\backslash ).$ The length of the strut is $2\mathrm{.}3$ m $.$ The ultimate strength of the aluminum is $430$ MPa and the yield strength is $280$ MPa $.$ Assume the end conditions are ball joints so that $\backslash (\backslash$mathrm$\{$C$\}=1\mathrm{.}0\backslash ).$

a$.$ Calculate the cross$-$sectional area, moment of inertia and radius of gyration for the cross$-$section. Express your answers in mm$.$

b$.$ Calculate the critical length where the Euler and Johnson curves intersect. Does the strut fall under the Euler or Johnson curve?

c$.$ Calculate the K factor for Johnson buckling. $($Make this calculation even if the strut falls under the Euler curve and you do not need the K factor.$)$

d$.$ Using a safety factor of $2\mathrm{.}0,$ calculate the buckling capacity of the strut. Express your answer in N force.