Note to Expert : Solve this problem using FEM Method.

The truss shown is composed of members with $E=200$GPa. The cross$-$sectional areas

for members $AB,AC,$ and $AD$ are $15{10}^{3}m{m}^2,2\mathrm{.}0{10}^{4}m{m}^2,$ and $3\mathrm{.}0{10}^{4}m{m}^2.$

$($a$)$ Calculate the vertical and horizontal displacements at $A.$

$($b$)$ Calculate the reactions at $B,C,$ and $D.$

$($c$)$ Determine the internal forces in members $AB,AC,$ and $AD.$