$1.$ A simply supported beam on grid $\backslash ($ D $\backslash )$ is shown in the figure below. The beam width is restricted to $450$ mm $,$ and the corner columns are $\backslash (500\backslash$times $500\backslash$mathrm$\{$~mm$\}\backslash ).$ Design the beam shear reinforcing, using $10$M stirrups. The maximum aggregate size is $20$ mm $.$ Concrete strength is $30$ MPa with exposure class N $.($Hint: remember that $\backslash (\backslash$mathrm$\{$I$\}\_\{\backslash$mathrm$\{$n$\}\}=\backslash )$ the clear span, and you need to include self$-$weight of beam in your load calculations$).[8$ marks$]$

$-$ Superimposed dead load $($mechanical$,$ floor finishing, and ceiling$)$ is $2\mathrm{.}4$ kPa $.$

$-$ The slab supports a garage for vehicles less than $4000$ kg $.$

$-$ Beam is $600$ deep reinforced with $5-35$M flexural bars in a single layer.