QUESTION $1$: $(60$ marks$)$ PLEASE DONT USE CHATGPT OR I WILL SIGNAL $!$

A simply supported beam $($L$=8$ m$)$ has been designed as a composite steel$-$concrete

member using a structural steel section of W$410$ x $54.$ The effective concrete slab width has been

established as $1750$ mm$,$ the slab thickness is $100$ mm$,$ the $28-$day strength of the concrete is $30$

MPa and the steel is $350$W$.$ The beam has been provided with $60$ end welded studs evenly

distributed over the whole span length. Assume the following stud properties: stud diameter of $19$

mm and the ultimate tensile strength of $415$ MPa.

a$)$ Determine the maximum flexural capacity of the composite beam.

b$)$ Based on the results of Part a$),$ what do you recommend to reduce the cost without any

reduction in the flexural capacity.