Problem $2$:

A W$41046$ beam of $350$ W steel is simply supported over a $\backslash (10-\backslash$mathrm$\{$m$\}\backslash )$ span. It supports a reinforced concrete floor slab that provides continuous lateral support of the compression flange. The beam supports a superimposed dead load of $\backslash (7\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash )($in addition to its self$-$weight$)$ and a live load of $8\backslash (\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The beam is unstiffened.

Check the adequacy of the beam $($check the flexural capacity, shear capacity, and deflection$).$ Consider LL deflection limit of L$/300.$