A uniformly distributed permanent load, $G_{k,1}=15k\frac{N}{m},$ an axial permanent load, $G_{k,2}=300kN,$ a leading uniformly distributed variable load, $Q_{k,1}=25k\frac{N}{m},$ and an accompanying concentrated variable load, $Q_{k,2}=350kN$ are applied on a simply supported beam $AB,$ as shown in the figure below. The beam is located on the $3^{rd}$ floor of an office building and is made of steel S$235.$ Given that the cross$-$section of the beam is the one shown in the figure,:

i$)$ check the capacity of the beam as per EC$3$ based on ultimate limit state design, and

ii$)$ check whether the deflection requirements of the beam are satisfied, as per EC$3$ based on serviceability limit state design.

$($a$)$

Figure $1.$ Simply supported beam $AB,($b$)$ cross$-$section of beam $AB$