Simple formulae for distortional buckling loads of cold-formed thin-walled rack members upright with rear flange and additional lip stiffeners

The determination of the elastic distortional buckling loads of the cold-formed lipped channel sections upright with rear flange and additional lip stiffeners subjected to the pure bending was performed based on the analytic solutions combined with CUFSM. The parameter analyses were carried out under the extreme load case of pure bending, leading to approximate formulae for predicting the buckling half-wavelength and the modified factor to take into account the effect of the shear and distortional deformation of the flange section. The rotational restraint, provided by the web to the flange during buckling deformation, was then examined, and a more accurate linear approximate expression for the rotational restraint and the web stress was proposed. Based on these approximate formulae, simplified formulae were finally developed to predict the elastic distortional buckling loads of the cold-formed lipped channel sections upright with rear flange and additional lip stiffeners subjected to the pure bending. The proposed formulae are shown to be accurate through comparison with the results of CUFSM, easy to be applied, may be used in practical applications and taken account into design codes and guidelines.