Problem $2$:

A simply supported beam $AC$ is subjected a concentrated bending moment $(M_B)$ at its middle span

$($point $B).$ The $EI$ and $L$ are given.

$(1)$ Use the beam equation to solve the beam rotation at point $B.$

$(2)$ Use the Castigliano's theorem to solve the beam rotation at point $B.$ Neglect the shear effect in strain

energy.