For a simple supported beam with a cross section shown in Figure is subjected to uniformly distributed loads and eouple forces. Determine;

$($a$)$ Flexural stresses at top and neutral axis of the beam cross section due to the moment produced at $6m$ and also discuss their variation.

$($b$)$ Shear stresses at bottom and neutral axis of the beam cross section due to the shear force produced at $2m$ and also discuss their variation.

$($c$)$ A steel beam $120mm$ wide and having width to depth ratic of $0\mathrm{.}4$ is reinforced on top and bottom by $20mm-$thick carbon fiber plates. Find out the maximum bending stresses in the steel and the carbon fiber produced due to the maximum bending moment in a simple supported beam shown above, assuming, that the ratio of the moduli of elasticity of carbon fiber and steel is $20.$