Consider the BF beam $($in steel: E $=200$ GPa $)$ having 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 selfweight and permanent overload$).$ Take into consideration that the floor is of a bathroom gymnasium $($see NBCC Table $4\mathrm{.}1\mathrm{.}5\mathrm{.}3$ to obtain the load of use in kPa$).$

a$)$ Find the maximum weighted moment Mf in kN$.$m that the beam must resist using the load combination:

$\backslash (1\mathrm{.}25\backslash$mathrm$\{$D$\}+1\mathrm{.}5\backslash$mathrm$\{$~L$\}\backslash ).$ Select a beam $($see table on page following$)$ which has a capacity Mr $\backslash (\backslash$geq $\backslash )$ Mf under the effect of this load combination. $(5+2)$ pts

b$)$ Does the beam selected in question a$)$ satisfy the requirement for deflection service limits $($L$/360)$ under the working load $($live load$)?$ Otherwise, choose one beam which would be adequate. Problem $3$: Checking deflections $(14$ pts$)$

Consider the BF beam $($in steel: $\backslash (\backslash$mathrm$\{$E$\}=200\backslash$mathrm$\{$GPa$\}\backslash ))$ having 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 selfweight and permanent overload$).$ Take into consideration that the floor is of a bathroom gymnasium $($see NBCC Table $4\mathrm{.}1\mathrm{.}5\mathrm{.}3$ to obtain the load of use in kPa$).$

a$)$ Find the maximum weighted moment Mf in kN$.$m that the beam must resist using the load combination:

$\backslash (1\mathrm{.}25\backslash$mathrm$\{$D$\}+1\mathrm{.}5\backslash$mathrm$\{$~L$\}\backslash ).$ Select a beam $($see table on page following$)$ which has a capacity Mr $\backslash (\backslash$geq $\backslash$mathrm$\{$Mf$\}\_\{\backslash$text $\{$u $\}\}\backslash )$ under the effect of this load combination. $(5+2)$ pts

b$)$ Does the beam selected in question a$)$ satisfy the requirement for deflection service limits $($L$/360)$ under the working load $($live load$)?$ Otherwise, choose one beam which would be adequate.