Wood – How to calculate the minimum allowable cross sectional area of a table leg

wood

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?

Best Answer

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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