I plan to DIY a 6 legged table with the following dimensions:

  • 140 cm long
  • 70 cm wide
  • 100 cm high

I know the breaking strength of the wood, but not sure how to calculate how thickness of the table legs that I need. The loading weight for the table will be around 400~500kg.

I'm planning to use 6cm * 6cm wood for the legs. Is that big enough to be safe?

  • 2
    Are you missing some 0s in your table's measurements? 14cm x 7cm (98cm²) with 6 legs of 6cm x 6cm (216cm²) I would say that will be pretty solid, no matter what type of wood... :) Also, a drawing or picture might help. – Maxime Morin Aug 23 '14 at 11:34
  • Doublecheck the table dimensions. Also, tell us how long the legs are to be - that makes a huge difference. If the legs are only to be 2mm long, it's perfectly safe. If they're to be 2m long, it's definitely not safe. – TDHofstetter Aug 23 '14 at 12:38
  • It's been a while since I took Mechanics of Materials, but if you're mathematically inclined, search for "buckling strength of an eccentrically loaded cantilever column" to find the right literature/formulas for this application. Sorry, I'm feeling lazy today and don't feel like relearning the material for a proper answer. – Doresoom Aug 23 '14 at 15:18
  • @Maxime Morin I should use cm but not mm. Sorry for that. – MaFai Aug 29 '14 at 2:44

The maximum load you can place on a relatively slender column such as a table leg is usually dictated by the buckling strength, rather than the compressive strength. The critical load can be calculated using Euler's formula applied to a fixed-free column:

Pcr= (pi^2*EI)/(f*Le^2)

where E is the modulus of elasticity
      I is the area moment of inertia (w^4/12 in this case)
      Le is the effective length (2L in a fixed-free case)
      f is the safety factor

Naively assuming that the entire load is uniformly distributed, the loadings on each leg are centric (perfectly rigid table top), and the loading on each leg is 1/6th of the total (six-legged tables are statically indeterminate), then each leg is subject to a loading of 654-818 Newtons.

Plugging in a length of 1 m, a safety factor of 10 (lots of assumptions here) and one of the following values of modulus of elasticity:

  • 9 GPa (pine)
  • 11 GPa (oak)

we get a minimum leg width dimension of:

  • 3.9 cm (pine)
  • 3.7 cm (oak)

I'd still stick with your initial plans for 6 cm square legs though. There are a lot of assumptions made for those calculations, including no lateral loading, no deflection of the table top, no knots or imperfections in the wood, and overlooking the fact that wood is anisotropic.

If you're working with a different type of wood, here's a good chart for modulus of elasticity (PDF) (don't forget to convert from MPSI to GPa!)

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  • +1 This is really interesting, I learned a lot! Thanks! :) – Maxime Morin Aug 30 '14 at 1:26

With those dimensions, you should be fine... provided that you provide a lot of bracing (especially diagonal bracing) to prevent the table from "racking" (falling over sideways like a cardboard box with no ends), and also providing that you use a relatively strong (in compression) wood for overall construction. I think you're well within the safe "slenderness ratio" limits for your application.

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