Using the Moment$-$Area Method $($Mohr$\text{'}$s Theorems$)$:

$($a$)$ Determine the bending moments in the frame shown in Fig. Q$3$

when a load of $90$ kN is applied at B as shown.

Hence sketch the bending moment diagram.

$(15$ marks$)$

$($b$)$ Calculate the horizontal deflection of joint C $.$

$(10$ marks$)$

Assume $E=200k\frac{N}{m}{m}^2.$

Assume $I=8{10}^{7}m{m}^4.$

FIG. Q$3$