For the loading and material information shown below, according to EC$3,$ design and check the

bending and shear capacities of steel beam which is $10$ m long for carrying the listed loading.

Information: Beam span length $=10m,$ Bay width $=5m,$ Slab depth $=18cm,$

Partitions $=0\mathrm{.}75k\frac{N}{m^2},$ Imposed load $=2\mathrm{.}5k\frac{N}{m^2},$

Concrete density $=24k\frac{N}{m^3},$ Steel grade $=S355$

Design the beam as a restrained beam as lateral restraint is provided by the concrete slab $($as shown$).$

Simple support condition of beam ends can be assumed.

Check also the deflection of the beam and see if it can satisfy the serviceability limit states or not.