Question $3$

In Figure $3,$ the transverse forces are applied to the beam ABC with a wide$-$flange shapes cross section, given that $d=600mm,b_f=240mm,t_f=15mm,$ and $t_w=10mm$ :

$($a$)$ Draw the free body diagrams of part $AB$ and $BC,$ respectively $3\%,$

$($b$)$ Express the reaction forces at support A and $C$ by distance $a[3\%],$

$($c$)$ Draw and express the bending$-$moment diagram of the beam ABC by distance $a[4\%],$

$($d$)$ Determine the distance a for which the absolute value of the bending$-$moment in the beam is as small as possible $[2\%],$

$($e$)$ Determine the moment of inertia of the wide$-$flange shapes cross section shown $[4\%],$

$($f$)$ Determine the corresponding maximum normal stress due to bending in Prob. $($d$)[4\%].$