The T$-$section beam in Fig. $2$ is loaded as shown. Using singularity functions, calculate the

deflection and slope of the beam at $A($i$.$e$.,y_A$ and $d\frac{y}{d}x{|}_A|),$ and the maximum tensile and compressive

normal stresses in the beam at the midpoint of section $BC.$ The beam is made of hot$-$rolled steel

$200$GPa

Cross section $($enlarged$)$