Buckling Under Pressure

Would you try a small experiment for me? Go and find three sheets of printer paper and a roll of sticky tape. I’d like you to start by rolling two of sheets up into cylinders lengthways and just hold each cylinder together with a single strip of lengthways sticky tape: one of them quite thin – say 2-3cm (or about an inch) across, the other quite wide with just a couple of centimetres overlap at the edge.

Now, very carefully put each cylinder on a table top and with the flat of your hand, push down on it without supporting it in the middle at all. Slowly increase the push, and see how hard you can push before the cylinder crushes.

What you should notice is that the wider cylinder, despite having much thinner “walls” took much more load than the thinner cylinder. This isn’t what you might intuitively expect, as perhaps you might have expected the thicker walled cylinder to be stronger?

What you have just experienced in both cylinders is what engineers call a buckling failure, where a structure under compression becomes structurally unstable and collapses. There’s a standard equation for this, designed in 1757 by Swiss mathematician Leonhard Euler (the Euler family interestingly were friends with the Bernoulli family, and Leonhard Euler and  Daniel Bernoulli were contemporaries and collaborators – Swiss mathematicians have a lot to answer for!) It looks like this:- and is known as the Euler Buckling Load formula. Some of these terms should be obvious, some not. The easy ones are F (the force at which our strut buckled), π = 3.14 (circumference divided by the diameter of a circle) and L is the length of the strut.

Three other terms will be much less familiar to non-Engineers.