Fig. $1($a$)$

Fig. $1($b$)$

The frame shown in Fig. $1($a$)$ is subjected to a triangular load due to snow. The beam ABDF can be considered $$rigid$.$ Each of the columns BC$,$ DE$,$ and FG has the cross$-$section shown in Fig. $1($b$),$ and is made of a material with E $=10$ GPa.

$($a$)$ Draw a free$-$body diagram of the beam, and determine all the forces in the columns. Clearly indicate if they are in tension or compression.

$($b$)$ Use the Principle of Virtual Work to determine the vertical deflection at A$.$

$($c$)$ Determine whether you believe any of the columns are susceptible to buckling. If they are not, what is the factor of safety against buckling?