The beam shown below has fixed supports at A and $C.$ There is a concentrated load at $B$ and a uniformly distributed load from $B$ to $C.$ The flexural stiffness of the beam is $EI=200000$ kip$-f{t}^2.$ Neglect axial deformations of the beam.

Using the two unknown joint displacements shown above, the vertical deflection and rotation of joint $B,$ form the following objects by Displacement Method and solve for $D_1$ and $D_2.$

The joint load vector, hat$(P).$

The fixed$-$end force vector, $P^0.$

The stiffness matrix, $K.$

Solve $D=K^{-1}((hat(P))-P^0)$

$D=\left[\begin{array}{c}-0\mathrm{.}0023132\\ -0\mathrm{.}00036476\end{array}\right]$