Comparison of the Known Hypotheses of Lateral Buckling in the Elastic-Plastic States of Thin-Walled Semi-Slender Columns

Stability of structures, as known, is a challenging issue, especially in critical engineering, i.e., in designing structures which in a wrong design process could cause a catastrophe. The avoidance of possible stability troubles is mandatory. In this study, the simplifications and hypotheses of loss of stability by lateral buckling in elastic-plastic states of semi-slender columns axially compressed by force are presented. The Tetmajer-Jasiński’s and Johnson-Ostenfeld’s simplifications as well as Engesser-Kármán-Shanley’s, Ylinen, Březina, Pearson-Bleich-Vol’mir’s and author’s approximated hypotheses are analysed. The graphs of surface functions of the compressing critical stress σ_cr depending on the ratios μ = a/t or δ = R/t and χ = L/t are presented as the theoretical examples of thin-walled cylindrical and square columns made of steel R35. In order to compare the results of the author’s approximated hypothesis, i.e., the modified Engesser-Kármán-Shanley’s hypothesis with others simplifications and hypotheses are shown in adequately ranges for elastic-plastic states as the graphs of the functions σ_cr(λ).