Question $4(34$ Marks$)$

Figure $3$ below shows the plan view of a floor structure in an office building, formed using timber floor joists $($solid lines$)$ and timber beams $($bold dashed lines$)$ supported by timber walls and columns. The flooring includes plywood sheeting screwed to the floor joists $($spaced $500$ mm apart$)$ and main beams. It can be assumed that the self$-$weight of the floor system $($including the joists and beams$)$ generates a $G=1\mathrm{.}2$kPa. The imposed load for the floor can be assumed equal to $Q=3\mathrm{.}0$kPa. The following questions relate to the design of the edge beam identified in Figure $3,$ with a span length of $L=4\mathrm{.}2m.$

Figure $3$: Plan view $($not to scale$)$ of a floor structure for an office building.

$($a$)$ What is the maximum design bending moment demand, M$*,$ for the edge beam associated with the

two ULS load combinations $1\mathrm{.}2$G $+1\mathrm{.}5$Q and $1\mathrm{.}35$G$?$ Present calculations to support your answer.

$[6$ marks$]$

$($b$)$ What is the maximum axial force demand, N$*,$ for the corner column supporting the edge beam, for

the two ULS load combinations $1\mathrm{.}2$G $+1\mathrm{.}5$Q and $1\mathrm{.}35$G$?$ Present calculations to support your answer

$[6$ marks$]$

$($c$)$ If the edge beam in Figure $3$ is to be realised with pairs of grade SG$12$ solid timber beams, each

having sections of $300$mm x$50$mm $($dry section dimensions each $280$mm deep x $45$mm wide$),$

present calculations to check whether the edge beam is strong enough to resist a peak moment

demand, due to $1\mathrm{.}2$G $+1\mathrm{.}5$Q$,$ of M$*=23$kNm$.$

$[10$ marks$]$

$($d$)$ If the edge beam in Figure $3$ is to be realised with pairs of grade SG$12$ solid timber beams, each

having sections of $300$mm x$50$mm $($i$.$e$.$ each $280$mm deep x $45$mm wide$),$ present calculations to

check whether the beam is strong enough to resist a peak shear force demand, of V$*=20$kN$.$

$[6$ marks$]$

$($e$)$ Present checks to show whether the proposed beam section $($described above$)$ is stiff enough to

satisfy a displacement limit of L$/300$ for the SLS load combination: G $+$lQ$.$