Problem $2$: $(20$ points$)$

Solve the following continuous beam by the slope deflection method, and draw the shear and bending moment diagrams. Note that support B and C have experienced settlement.

$L_1=30ft$

$L_2=20ft$

$E=29000$ksi $(for$ both spans$)$

$I=2100$ in ${?}^4($for both spans$)$

$P_1=P_2=10$kip

$P_3=5$kip

$D_B=0\mathrm{.}5in$

$D_C=0\mathrm{.}25in$