QUESTION $1[30$ MARKS$]$

A simply supported $40617860k\frac{g}{m}$ I beam shown in Figure $1$ supports a uniformly distributed characteristic dead load of $40k\frac{N}{m}$ and a uniformly distributed live load of $20k\frac{N}{m}.$ The beam is fully laterally restrained.

Do the following:

i$.$ Calculate the design load on the beam. Ignore self$-$weight of the beam for all calculations.

ii$.$ Draw the shear and bending moment diagrams.

iii. Classify the section.

iv$.$ Check the shear and moment resistance of the beam.

v$.$ Check the deflection of the beam. Comment on your final answer.