Looking for a way of calculating the maximum weight (W) to the rod with the given length (L) where the rod did not break and that only bend for (b) mm.

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Need only approximative solution (read: simple as possible :), nothing with finite-elements or integrals or so.

The practical background: What rod i should to use for suspension of 100kg with L=1.5m and max bending approx. b=1cm? For what constants should I looking for in the published "properties" for the different materials and different profiles? E.g. steel rod vs bamboo? :)

Some URL's to helpful practical solutions (read: easy math) is very welcomed - my googling failed.

  • $\begingroup$ While this is a topic in physics, you will find the best practical instructions in the second half of any engineering "Statics" textbook you care to look in. Further search terms that might help include "stress", "strain", "point-load", and "deflection" in various combinations. $\endgroup$ – dmckee --- ex-moderator kitten Jan 30 '12 at 18:26
  • $\begingroup$ Related: physics.stackexchange.com/q/12867/2451 $\endgroup$ – Qmechanic Apr 22 '12 at 11:38

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.).


You need to Google for "beam bending". That will find you lots of relevant pages. Wikipedia has a very thorough article on the subject but it's not "easy maths".

You might want to look at http://www.engineeringcalculator.net/beam_calculator.html. This gives some interactive toys to play with and it also gives the equations (but no derivations).


  • $\begingroup$ Exactly for what i looking. Thanx a lot! :) $\endgroup$ – jm666 Jan 31 '12 at 9:26

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