$($a$)$ For the frame shown in Fig. Q$4($a$),$ using Mohr's Theorems:

$($i$)$ Determine the vertical reaction at joint $C$;

$($ii$)$ Draw the bending moment diagram;

$($iii$)$ Determine the horizontal deflection of joint $C.$

Note:

You may neglect axial effects in the members.

Take $EI=36{10}^{3}kN{m}^2$ for all members.

$(15$ marks$)$