Formulae for Calculating Elastic Local Buckling Stresses of Full Structural Cross-sections

Abstract

Formulae for determining the full cross-section elastic local buckling stress of structural steel profiles under a comprehensive range of loading conditions, accounting for the interaction between the individual plate elements, are presented. Element interaction, characterised by the development of rotational restraint along the longitudinal edges of adjoined plates, is shown to occur in cross-sections comprising individual plates with different local buckling stresses, but also in cross-sections where the isolated plates have the same local buckling stress but different local buckling half-wavelengths. The developed expressions account for element interaction through an interaction coefficient ζ that ranges between 0 and 1 and are bound by the theoretical limits of the local buckling stress of the isolated critical plates with simply-supported and fixed boundary conditions along the adjoined edges. A range of standard European and American hot-rolled structural steel profiles, including I-sections, square and rectangular hollow sections, channel sections, tee sections and angle sections, as well as additional welded profiles, are considered. The analytical formulae are calibrated against results derived numerically using the finite strip method. For the range of analysed sections, the elastic local buckling stress is typically predicted to within 5% of the numerical value, whereas when element interaction is ignored and the plates are considered in isolation with simply-supported boundary conditions along the adjoined edges, as is customary in current structural design specifications, the local buckling stress of common structural profiles may be under-estimated by as much as 50%. The derived formulae may be adopted as a convenient alternative to numerical methods in advanced structural design calculations (e.g. using the direct strength method or continuous strength method) and although the focus of the study is on structural steel sections, the functions are also applicable to cross-sections of other isotropic materials.

Design of structural steel members by advanced inelastic analysis with strain limits

“…However, most structural members are subjected to a combination of loads. For this reason, the authors have recently developed closed-form expressions to predict the full cross-section local buckling stress of standard steel profiles subjected to compression, bending and combined loading [47]. The underlying concept is that the buckling stress of the full cross-section lies between the buckling stresses of the isolated critical plates with simply-supported and fixed boundary conditions.…”

“…Conservatively, standard plate theory can be used to estimate the cross-section slenderness based on the most slender isolated plate of the cross-section with simply-supported boundary conditions, though this approach is not recommended. Herein, the functions developed by the authors [47] have been used to predict the cross-section local bucking stress σ cr,cs and hence the cross-section slendernessλ p .…”

“…CUFSM [45]) or approximate analytical expressions [35]. The expressions presented in [35] are based on the same concept as used to predict the full cross-section local buckling stress [47] and are hence used herein as they require minimal additional calculation effort. Note that a conservative prediction of the full cross-section local buckling stress tends to lead to an over-prediction of the associated half-wavelength [35].…”

Stability and design of stainless steel structures – Review and outlook

“…The observed behaviour, together with existing and emerging design treatments, are described in this section. respectively, where y=fy/E is the yield strain and p  is the cross-section slenderness, calculated as / y cr f  , in which cr is the elastic local buckling stress of the full cross-section under the applied loading conditions, which may be determined using simplified analytical expressions [33,34] or numerical tools such as the finite strip software CUFSM [35].…”

“…Only cross-section capacity checks will typically be required when the structure is simulated using beam elements, and a geometrically and materially nonlinear analysis with imperfections (GMNIA) is employed. An alternative to carrying out cross-section checks is to limit the maximum strain that arises in the structure based on the local slenderness of the adopted cross-sections [34,90]; the maximum strain can be determined from the CSM base curve [31,32].…”