An efficient and direct method for buckling analysis of steel frame structures

Abstract The buckling analysis of steel frame structures is customarily carried out in a two step approach. Firstly, an analysis of the structure, generally linear–elastic, is performed to obtain the internal forces and moments; and secondly, the buckling analysis and design is done for each individual element taking into account an initial imperfection. Steel design codes, and in particular Eurocode-3 (EC3), base the buckling analysis upon the element effective length factor K. This factor depends on the buckling shape of that particular element within the structure, and in practical cases it is obtained by means of approximations or even by mere estimation. This paper presents a direct one-step method for the buckling analysis of steel frame structures. The method avoids the use of the effective length factor of each individual element. The key point is to perform a non-linear analysis of the structure starting from an initial deformation state that includes the initial imperfections of the elements. Such initial deformation state is obtained from the first buckling mode of the structure by a suitable scaling procedure based on an energy approach. The resulting initial deformed shape is introduced along with the external loads in a fully non-linear structural analysis that yields the resulting element stresses including the buckling effects. The performance of the method is checked against the procedures established in EC3 by means of a series of numerical examples.