Problem $3$: Deflection Check

Consider the BF beam $($steel: $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ))$ with a span of $7$ m and a tributary width of $3$ m $($Figure $3).$ The total permanent load acting on the BF beam is $4\mathrm{.}2$ kPa $($this includes self$-$weight and permanent load$).$ Assume the floor is part of a gymnasium $($refer to NBCC Table $4\mathrm{.}1\mathrm{.}5\mathrm{.}3$ for live load in kPa $).$

a$)$ Find the maximum factored moment Mf in $\backslash (\backslash$mathrm$\{$kN$\}\backslash$cdot $\backslash$mathrm$\{$m$\}\backslash )$ that the beam must resist using the load combination: $1\mathrm{.}25$D $+1\mathrm{.}5$ L $.$ Select a beam $($from the table on the next page$)$ with a capacity Mr $\backslash (\backslash$geqq $\backslash )$ Mf under this load combination.$|$

b$)$ Does the beam selected in part a$)$ meet the serviceability deflection limit $($L$/360)$ under the live load? If not, choose a beam that would be suitable.

BEAM SELECTIO T TABLE

WWF and W Sha, is