A frame system is shown below. For all members, E $=30$ GPa. For the columns, Ac $=93,000$mm$2$ and Ic $=720\backslash$times $106$mm$4.$ For the girders, Ag $=140,000$mm$2$ and Ig $=2,430\backslash$times $106$mm$4.$ All members are modeled as frame elements.

$($a$)$ Determine the joint displacements, member local end forces, and support reactions.

$($b$)$ Condense the DOFs such that only horizontal degrees of freedom are included $(6$ total DOFs$).$ Determine the horizontal displacements and horizontal support reactions.