Beam ABC carries a concentrated load $P=50$kips at the end $C$ and a distributed loading

$w=2$kip$\frac{s}{f}t$ within $AB$ segment. $EI=2{10}^{10}*i{n}^4.$ Node $A$ is fixed on a wall and node $B$

is simply supported. Use superposition method to solve:

$($a$)$ Divide the problem into three cases.

$($b$)$ For each case, write out the analytical solution for the deflections at node $B$ and node

C$,$ respectively.

$($c$)$ Impose the boundary condition at node $B$ to determine the reaction $Rb$ at point $B.$

$($d$)$ Write out the deflection at node $C.$

$($e$)$ Find the force and moment reactions at node $A.$