Problem $1$

For the beam in the figure below, assume $E=29,000$ksi and $I=600i{n}^4$ for the whole beam.

$($a$)$ Determine the reactions at the supports $A,B,$ and $C$ using the reaction at $C(C_y)$ as the redundant.

$($b$)$ Draw the shear and moment diagram.

$($c$)$ Compute the vertical displacement below the load $P$ in the span $AB.$

$($d$)$ Sketch the deflected shape. Hint: note the beam is symmetric about support $B.$