$1\mathrm{.}3$ The beam shown in figure $1$ below has a length of $8m$ and supports a uniform load of $50KNm$ over the full length of the beam, which includes the weight of the beam. The beam is simply supported at its ends with support at mid$-$span.

$EI=32MN{m}^2$

Calculate the following:

Figure $1$: A simply supported beam with a UDL

$1\mathrm{.}3\mathrm{.}1$ The reaction at support $B$ if the deflection at support $B$ is zero.

$1\mathrm{.}3\mathrm{.}2$ The reaction at support $B$ if support $B$ subsides by $30mm($that is support $B$ is $30mm$ lower than supports A and $C.$

$(7)$