Exercise $2$: Straight beams: Strain Energy methods

A beam defined in figure below, is submitted to a partial distributed load w between $($AB$),$ and a single load $F$ at point $C.$ The characteristics of the problems are:

Simple support at point A $($Vertical and horizontal displacements null$)$

Support at point D $($only vertical displacement null$)$

Lengths between points defined into the figure: $(AB),($BC$),($CD$)$

Young Modulus E and area moment of inertia I

Define:

By applying unit load method $($principle virtual of work$)$ define:

Vertical deflection at point C $($only final integral equation with all details$)$

Vertical deflection at point B $($only final integral equation with all details$)$