Problem $4\mathrm{.}5$ A simply supported beam with a cantilever has a span of $6$ m and a cantilever of $2$ m $.$ It carries a uniform dead load including self$-$weight of $\backslash (30\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )$ and a uniform live load of $20\backslash (\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ).$ Assume concrete strength $\backslash (\backslash$mathrm$\{$fc$\}^\{\backslash$prime$\}=40\backslash$mathrm$\{$MPa$\}\backslash )$ and the yield stress of steel is fy$=350$ MPa with an E$-$value of steel as $200$ GPa and the unit weight of concrete is $\backslash (24\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}3\backslash ).$

$($a$)$ Plot the factored bending moment diagram for the beam

$($b$)$ Suggest at least five possible sections for the beam and select one for detailed design

$($c$)$ Determine the required tension steel at the location of the maximum positive bending moment.

$($d$)$ Design the required tension reinforcement at the cantilevering support.

$($e$)$ Show the reinforcement in elevation and at the locations of the maximum moments.