Problem $2$: Slope Deflection$-$Support Settlement

For the beam shown below, determine the reactions and draw the shear and bending moment diagrams. In this beam, supports B and C exhibited downward settlement of $60$ mm and $40$ mm $,$ respectively. Take $E=200$GPa and $I=240({10}^6)m{m}^4.$

$20$ kN$/$m

A