Buckling
Buckling can occur even when the stress in the column is less than the yield strength.
Euler’s formula for critical buckling load is widely used and calculates the maximum compressive load in a slender column that will cause it to suddenly bend or buckle.
The critical buckling load is also called the load factor or eigenvalue for the first mode.
Euler’s formula is based on linear buckling whereby the material is isotropic, the load is only applied in the axial direction, the column is straight and slender and there is no other loading from the joints.
FEA models built with beam elements should be a very good match with the calculated Euler’s critical buckling load. The example shown in the picture was built with solid elements and was quite close.
The way the column is held at each end has a big influence on the critical buckling load.
In the example shown in the picture, if both ends were pinned, this would approximately halve the critical buckling load.
If the base of the column is fixed and the top of the column is free, like a mast, the critical buckling load would be about 8 times less.
There are other types of buckling such as torsional buckling, lateral torsional buckling and local buckling of individual plates (stiffeners & web)
