The nominal loading applied on a cantilever beam is shown in the figure below. You are

required to design a cross$-$section for this beam.

The following are the design requirements of your cantilever beam structure:

To keep it simple, you are required to design the beam for bending stresses only. Shear

stresses are to be ignored for now.

The structure must be able to carry $4$xx the nominal load without yielding.

You are required to determine the cross$-$section of this cantilever beam. The cross$-$

section of your beam can be of any shape, geometry or dimension except the height and

width must not exceed $0\mathrm{.}6$ meters and $3$ meters, respectively, due to manufacturing and

logistics reasons.

The cross$-$section must also be symmetrical about the vertical axis.

The maximum allowable deflection on the cantilever beam is $2\mathrm{.}2$ m $.$

The structure may only be manufactured from a single type of metallic material, e$.$g$.$

steel, aluminium alloy, titanium alloy, Nickel alloy etc.

The structure must be lightweight and cost effective while meeting all the above design

requirements.