Question $(1)$: $(20$ Marks$)$ construction analysis $2$

For the shown loaded frame with variable moment of inertia. Using the consistent deformation method

$($a$)$ Find the reactions at the supports A and $B.$

$($b$)$ Draw the bending moment diagram.

The relative moments of inertia are given between brackets and $E$ is constant.

Note:

Take the main system by removing the hinge support B$.$