Explicit equations for distortional buckling of cold-formed steel lipped channel columns

In this work, the development of rational explicit equations for distortional buckling critical stress of lipped channel columns subject to uniform compression is presented. An energy-based approach is adopted along with two different assumed buckled shapes (models) to obtain the analytical expressions. In Model 1, stiffened flange is assumed rigid, i.e., transverse wall bending is neglected, whereas in Model 2 the flange plate flexibility is taken into account. An analytical procedure to determine warping stresses based on cross-section displacements and considering that flange-stiffener assembly rotation center does not coincide with web-flange fold-line is described. To validate proposed equations, a parametric analysis is carried out for lipped channels with flange-to-web width ratio, bf/bw, ranging from 0.2 to 1.0 and lip-to-web width ratio, bs/bw, from 0.1 to 0.4. Results are compared to those obtained with a generalized beam theory (GBT) software for ‘pure’ distortional mode and it is shown that, within the range of typical geometries used in industry, average differences are approximately 1.062 ± 0.073 and 0.998 ± 0.001 for Models 1 and 2, respectively. The linear (natural) coupling of pure distortion and local/global deformation modes is also briefly described and its influence on the critical loads is discussed. Finally, comparison is made to benchmark methodologies currently used in design standard and specifications. The obtained results indicate that proposed equations are reliable and valuable for practical design applications.