For the below given system, use virtual work principle to answer the followings.

$($a$)$ Calculate the values of translational displacements ${}_x,{}_y$ and relative rotation of ${}_G$ in terms of $EI.$

$($b$)$ Consider the case when the system is only under effect of a $t=+20C$ uniform temperature change to determine ${}_G.$ In your calculations take $={10}^{-5}\frac{1}{}C,$ neglect any axial and shear deformations.

$($c$)$ Repeat the above part $($b$)$ for a $t=+15C$ non$-$uniform temperature change.