$3.$ The plane frame shown in Figure $3$ has rigid joints at $\backslash ($ C $\backslash )$ and $\backslash ($ F $\backslash ),$ is pinned to a wall at $\backslash ($ A $\backslash )$ and is connected to the foundations with a roller at I. All the horizontal members of the frame have the same flexural rigidity $(\backslash (\backslash$mathrm$\{$EI$\}=64\backslash$times $10^\{3\}\backslash$mathrm$\{$kNm$\}^\{2\}\backslash ))$ and this is half the flexural rigidity of the vertical members $($same for all vertical members$).$

$($a$)$ Calculate the bending moments at all the joints in the frame and sketch the full bending moment diagram.

$($b$)$ Sketch the deflected shape, and calculate the vertical reactions at A and I. State also how the bending moment diagram and deflected shape would change if A was fixed.

Module code: CIVE$236001$

Figure $3$