The steel $($E $=30,000$ ks$)$ I$-$beam shown in Figure $1$ has an S$5$ x $10$ cross section. The section$\text{'}$sdepth $($the total height$)$ is $5$ in$.,$ with $3$ in$.-$wide, $0\mathrm{.}326$ in$.-$thick flanges, and a web thickness of $0\mathrm{.}214$ in$.$ With reference to the figure:$($a$)$ Calculate the external reactions in A and C$.($b$)$ Draw the internal load diagrams across the entire span of the beam.$($c$)$ Taking a cross section at point B$,$ locate the two $($or more$)$ points that are likely to experience the highest combined stresses.$($d$)$ Using the correct Mohr's circle, calculate the principal stresses of the critical point.$($e$)$ Derive the expressions for the vertical deflection of the beam and its slope.