On the theoretical background of the generalization of Ayrton–Perry type resistance formulas

The Ayrton–Perry type formulae are very popular models for the standard definition of the buckling resistance of steel members. These standards benefit from the simplicity and flexibility, but most of all from the clear mechanical background of this model, which apparently defines the appropriate meaning of the model parameters. While this mechanical background has been properly clarified for column buckling, however, for the case of the lateral–torsional buckling problem–despite the various numerical verifications of the standard models–the exact derivation is still an unresolved question. This paper introduces a possible way for the rigorous generalization of the Ayrton–Perry formula, so it can be applied to the description of lateral–torsional buckling problems. It is demonstrated that the shape of the initial geometric imperfection has a key role in the solution; an appropriate choice can simplify the problems considerably through a convenient form of the amplification relationship. The equations obtained have various consequences regarding the form of the generalized and equivalent imperfection factors and the multiple curves for lateral–torsional buckling resistance.