$(25$ points$)$: A rectangular beam of varying height is loaded downward by a $50$ lbf

force applied at the pin $($roller$)$ at location $C$ and is supported by identical pins at points

A and $B$ as shown. The bar is $30$ in long overall, with the distance from $A$ to $B$ of $12$ in

and the total distance from $A$ to $C$ of $28$ in $.$ From the left end until $9$ in from point $A,$

the bar has a rectangular cross section, $0\mathrm{.}5$ in thick $($into the page$)$ and $1\mathrm{.}5$ in high. After

that, the section maintains the full thickness and its height increases to $2$ in $,$ with a corner

radius of $\frac{1}{16}in(0\mathrm{.}0625in)$ at the transition. The beam is manufactured from $2024-$T$351$

aluminum