Approximate Methods for Beam Buckling

For a number of quite simple buckling problems, it is possible to derive exact analytical solutions. However, buckling analyses of beams very often lead to transcendental nonlinear buckling conditions that cannot be solved exactly for the buckling load and therefore require a numerical-iterative treatment. In such cases, approximation methods can be employed with the help of which (mostly based on energy methods) approximate solutions for the buckling loads can be determined. A selection of approximation methods is treated in this chapter.