Question $3$

The figure shows a main beam ABCD supporting two secondary beams at $B$ and $C.$ Given that $L_{AB}=3m$;$L_{BC}=4m$; and $L_{CD}=5m.$ The point loads:

At B: dead load $=150kN$; imposed load $=200kN$

At C: dead load $=100kN$; imposed load $=150kN$

Neglect the self$-$weight of the main beam, and do the following use Eurocode $3($S$275)$:

$($a$)$ Assuming that continuous lateral restraint is provided, design the main beam with particular concern on the cost$-$effectiveness. Ensure the selected section satisfies both ULS and SLS$.V_{ed},$ med $\frac{\text{D}\text{e}\text{f}\text{l}\text{e}\text{c}\text{t}\text{i}\text{o}\text{n}}{?}$

$($b$)$ Assuming that full lateral restraints can be provided only at $A,B,C$ and $D,$ design the main beam under ULS with particular concern on the cost$-$effectiveness. At the locations of lateral restraints, nominal torsional restraints are provided, and the main beam is free to rotate on plan at the location of lateral restraints.