Localized web buckling analysis of beams subjected to concentrated loads using GBT

This paper presents and illustrates a GBT formulation to analyse the elastic localized web buckling of thin-walled steel beams under concentrated loads. The theme of localised web buckling is first introduced by describing the parameters that most influence the buckling behaviour of slender plates subjected to edge loads. After that, a GBT formulation to analyse the elastic localized web buckling of thin-walled steel beams under concentrated loads is presented: the GBT equations are derived and the determination of deformation modes is briefly addressed. Then, two illustrative examples are shown and validated by comparison with shell finite element results: (i) cold-formed steel plain channel beams with web crippling configurations and (ii) welded steel I-section beams with patch loading configurations. It is found that both pre-buckling longitudinal normal ( σ x x 0 ) and shear ( τ x s 0 ) stresses have to be included in the buckling analyses of cold-formed steel beams with External One Flange (EOF) and Internal One Flange (IOF) configurations as well as welded steel beams with Patch Loading Test (PLT) configuration. Furthermore, the pre-buckling transverse normal ( σ s s 0 ) stresses have to be included in the buckling analysis of cold-formed steel beams with External Two Flange (ETF) and Internal Two Flange (ITF) configurations as well as welded steel beams with Opposite Patch Loading Test (OPLT) configuration. In beams with EOF, IOF, PLT configurations, the GBT pre-buckling analysis should consider global and shear modes while the GBT buckling analysis may only consider local modes. In beams with ETF, ITF, OPLT configurations, the GBT pre-buckling analysis should consider transverse extension modes while the GBT buckling analysis may only consider local modes.