Design a Roof Beam $($using a UK UB section in S$275$ steel$)$ that has sufficient capacity, and meets the total

deflection limit specified by the client $($span$/250).$ Use Plastic design where possible, and ensure that

your design calculations consider all appropriate modes of failure. The client wishes to minimise the

environmental impact of the Assembly Hall, and requires the Roof Beam chosen to be the Beam $($UB$)$

which uses the lowest amount of steel $($hence the lightest possible beam$)$ whilst meeting the capacity

checks and deflection limit$.$

Note: for the deflection calculations, characteristic loads $($rather than design loads$)$ must be used. These

characteristic loads may be obtained by taking the factored design loads shown in Figure $1$ and Table $1$

and dividing each of them by $1\mathrm{.}5$

a

$=$

$7$

m

$,$

$$b

$=$

$2$

m

$,$

$$c

$=$

$3$

m

$,$

$$P

$=$

$4$

$0$

KN