Cross sectional analysis

For a proposed hollow square cross section beam

Density of Mild Steel: 7800 kg/m3

If the maximum weight per section is to be 30kg, then the volume available for the beam is:

V = m / ρ = 30 / 7800 = 3.85e-3 m3

If the length of the beam is 9m, that gives an available cross sectional area of:

3.85e-3 / 9 = 4.27e-4 m2 ( = 427mm2)

This is equivalent to 20 x 20mm square. Clearly this is inadequate to support a 1000kg load.

If the beam is constructed of 3 sections each 3m long, then the cross-sectional area will be:

(30 / 7800) / 3 = 1282.05mm2

Which would give us a 35 x 35mm solid square cross section of mild steel. Once constructed as an hollow square, this may give us a second moment of area that can withstand a 1000kg load.

A hollow square cross section would be better suited to the job as it withstands vertical and horizontal forces whereas an I-beam would only withstand vertical forces. If the crane is to be used on uneven ground, which it is in this case, then the force will not be a direct vertical force as the beam would not be completely horizontal and as the load would probably be swinging as it is moved, the load will not be directly vertical.