a$)$ A composite beam comprises a $130mm$ thick concrete slab with an $f_{ck}$ of $50\frac{N}{m}{m}^2$

formed on a dovetail trough decking, connected via headed stud shear connectors to

the top surface of a $40617867$ UKB in S$275$ steel. The beam is simply supported, is

subject to a uniformly distributed load and has a span of $6\mathrm{.}5$ metres. The decking has a

profile spacing of $152mm,$ and the dovetail troughs are $55mm$ deep. What is the

moment capacity of the composite beam, assuming full shear connection?

$[15$ marks$]$

b$)$ If the decking was running transverse to the beam span, and the shear studs are spaced

down the entire length of the beam with only one stud per trough $($and are positioned

centrally within the trough$),$ what would be the moment capacity of the beam? You

should assume the shear capacity of a single shear stud in this concrete is $107kN.$

$[5$ marks$]$