Key member in a windmill truss $(38$ points$)$

The mid$-$sized wind turbine shown below left is supported by a simple truss which can

be considered two$-$dimensional as shown below left.

It is $30$ m tall, $4$ m wide at its base, $2$ m wide at $DE$ and $FG,$ and mostly symmetric.

The wind and weight of the turbine exert a force on point $H$ with total magnitude $650$

N at a slope of $\frac{5}{12}.$

$($Aspect ratio is not to scale, with these dimensions it would be more slender.$)$

$($a$)$ Identify the zero$-$force mmebers in the truss, if any. $(7)$

$($b$)$ Calculate the reactions at rocker A and pin $C.(10)$

$($c$)$ Calculate the force in member $DG$ in the tower shown on the left. Is it in com$-$

pression or tension? $(12)$

$($d$)$ Suppose the mid$-$level diagonal brace is switched as shown on the right. How

does the force in member $EF$ on the right compare to the force in $DG$ in the left

tower? $(9)$