Beams $AB$ and CDE are connected using rigid link $DB$ with hinges $($or moment releases$)$ at ends $D$ and $B($see figure a$).$ Beam $AB$ is fixed at joint A and beam CDE is pin$-$supported at joint $E.$ Load $P=150lb$ is applied at $C.$

$($a$)$ Calculate the deflections of joints $B$ and joint $C.$ Assume $L=9ft$ and $EI=127,000$ kip$-$in ${?}^2.$

$($b$)$ Repeat part $($a$)$ if rigid link $DB$ is replaced by a linear spring with $k=20$kip$\frac{s}{i}n($see figure b$).$