If you are looking to limit deflections in the beam then there are three main properties you need to look out for:
- The second moment of area of the cross section of the beam, I
- The elastic modulus of material that the beam is made from, E
- The yield stress of the material that the beam is made from, p.
The elastic deflection of a simple beam with a point load at mid-span is given by:
W * L^3 / (48 E I)
You need to make sure that the system of units are addressed when you do this calculation because the properties are usually defined using slightly different units.
You will also need to check that the strength of the beam is not exceeded by the load you have applied or the deformation will increase very quickly potentially resulting in failure of the beam.
Do this initially by calculating the mid-span bending moment using:
M = W * L / 4
The stress in the beam can then be calculated from the bending moment using:
stress = M * y / I
Where y is normally half the depth of the beam although does require some more careful calculation where the beam is not symetrical.
You need to check that your calculated stress is less than the yield stress of the material.
This all gives the basics of the calculation, although there are a lot of subtleties that I have not addressed here (shear deflection, shear failure, bearing effects etc.).
