Generalisation of the Ayrton-Perry formula for the global-distortional-local buckling of thin-walled members

The paper introduces a generalisation of the Ayrton-Perry formula for thin-walled members, covering uncoupled and coupled instabilities of global, distortional and local type. This semi-analytical solution is based on the Generalised Beam Theory (GBT) and it provides the maximum carrying capacity in elastic domain for simply-supported thin-walled members with initial geometric imperfections, under various loading conditions. Direct generalised Ayrton-Perry formulae are developed for the buckling described by one or a combination of two pure imperfection/deformation modes; for more than two coupled modes, a simple incremental procedure is provided.