Exercise $3$: Beam under simple supports $($Points A & B$)$ and single load

A beam $($below figure$)$ of length $L$ between support $A$&$B$ and length a between point $B$ to $C$ is submitted to a single load $F$ at his extremity $C$

E: Young Modulus and I: Area moment of Inertia

Define the following:

Reaction Ra and Rb

Bending moment equation on portion $($AB$)$ and portion $($BC$)$

Vertical Deflection at point C using Castigliano Theorem

Vertical Deflection at point C using Unit Load Method

Vertical Deflection at point