$(9$ points$)$ Difficulty $(3/5)$

A structural steel W$406$x$100$ beam has dimensions $a=5\mathrm{.}2m$ and $b=2\mathrm{.}9m$ and is loaded with a force of $F=50kN.$ Neglecting the effect of self$-$weight, determine the following:

$($a$)$ The slope of the beam at support $B.$

$($b$)$ The deflection of the beam midway between the supports.

$($c$)$ The deflection of the beam at point $C.$

Answers:

$($Denote upward deflections, with positive values, and downward deflections with negative values. Denote positive slopes with positive values and negative slopes with negative values.$)$

$($a$){}_B=$

$($b$)y_{AB-\text{m}\text{i}\text{d}\text{p}\text{o}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}}=$

$($c$)y_C=$ be sure to include units with your answers