w$=7$kN$/$m$,$ d$=318$mm$,$ bf$=167$mm$,$ tf$=13\mathrm{.}2$mm$,$ tw$=7\mathrm{.}62$mm

STEP $1$: Draw the shear and bending moment diagrams of your beam neatly.

STEP $2$: Check with respect to Bending stress and shear stress if the cross$-$section is adequate to carry your load. You are provided with allowable bending stress and shear. Therefore, you need to check if you are under these values. $($The modulus of elasticity E$=200$GPa. The allowable bending stress is $180$MPa. The allowable shear stress is $100$MPa$)$

Check your deflection with respect to L$/180.$ You need to check this for both the maximum deflection between the supports and the portion for the section beyond the supports. Use L according to what portion you are investigating $($i$.$e$.$ between the supports it is equal to L$=15$m$)$

STEP $3$: Check your final design for deflection requirements for both the part of the beam between the supports and the overhung portion. You will need show your deflection equation calculations including how you get the integral constants.