Understanding Buckling

Thanks to CuriosityStream for sponsoring this video. When a bar is loaded in uniaxial tension, it will fail when the normal stress in the bar exceeds the yield or tensile strength of the material. And if it's loaded in compression it will fail by crushing when the compressive strength of the material is exceeded. But there's an additional way the bar can fail when in compression, which is by buckling.

Buckling is a loss of stability that occurs when the applied compressive load reaches a certain critical value, causing a change in the shape of the bar. An initially straight member will buckle suddenly, producing large displacements. This doesn't always result in yielding or fracture of the material, but buckling is still considered to be a failure mode since the buckled structure can no longer support

a load in the way it was designed to. The most simple example of a structure at risk of buckling is a column. But individual members in trusses and frames can also be loaded in compression, and so are at risk of buckling. There are other less obvious examples too. When railway tracks heat up on a hot day, the steel the tracks are made of tends to

expand. But expansion in the axial direction is prevented, and so a compressive axial force builds up, which can lead to buckling. A very similar issue can occur in subsea pipelines that carry hot product. The compression that builds up due to the thermal expansion of the pipe steel can cause the pipeline to buckle on the seabed.

Buckling can clearly lead to catastrophic failure, so how do we take it into account in engineering design and analysis? To answer this question we need to travel back to the mid 18th Century. In 1744, the mathematician Leonhard Euler published a book in which he laid out a new method for analysing functions, called the calculus of variations.