Abstract
The multimodal buckling of thin-walled isotropic columns with open cross-sections under uniform compression is discussed. Column lengths were selected to enable strong interactions between selected eigenmodes. In the case of short columns or very long ones subjected to compression, single-mode buckling can be observed only and the effect under discussion does not occur. In the present study, the influence of higher global modes on the load-carrying capacity and behavior in the post-buckling state of thin-walled structures with open cross-sections is analyzed in detail. In the literature known to the authors, higher global modes are always neglected practically in the analysis due to their very high values of bifurcation loads. However, the phenomenon of an unexpected loss in the load-carrying capacity of opened columns can be observed in the experimental investigations. It might be explained using multimode buckling when the higher global distortional-flexural buckling modes are taken into account. In the conducted numerical simulations, a significant influence of higher global distortional-flexural buckling modes on the post-buckling equilibrium path of uniformly compressed columns with C- and TH-shaped (the so-called “top-hat”) cross-sections was observed. The columns of two lengths, for which strong interactions between selected eigenmodes were seen, were subject to consideration. Two numerical methods were applied, namely, the semi-analytical method (SAM) using Koiter’s perturbation approach and the finite element method (FEM), to solve the problem. The SAM results showed that the third mode had a considerable impact on the load-carrying capacity, whereas the FEM results confirmed a catastrophic effect of the modes on the behavior of the structures under analysis, which led to a lack of convergence of numerical calculations despite an application of the Riks algorithm. All elastic-plastic effects were neglected.
Highlights
Cold-formed isotropic columns under compression are commonly used as load-carrying elements in structures of any type
We focus only on recent publications devoted to the interactive buckling of thin-walled beams with open cross-sections by
Multimodal buckling of the C- and TH-section columns, made of further intensive investigations with respect to modeling and the methods applied
Summary
Cold-formed isotropic columns under compression are commonly used as load-carrying elements in structures of any type. In the SAM, all analyzed buckling modes corresponding to bifurcation loads and the number of halfwaves along the longitudinal direction are calculated based on equilibrium equations and boundary conditions with the modified numerically strict transfer matrix method. FEM analyses were conducted to validate the proposed SAM model and to verify the post-buckling equilibrium paths and load-carrying capacity attained Such a comparison enables the scope to which the method can be applied to be determined, when the secondary global mode should be considered regarding the secondary global buckling mode and the range of beam lengths. It is worth mentioning that higher buckling loads are huge, but considering it in SAM leads to the significant decrease in the post-buckling equilibrium path and load-carrying capacity It might be explained using multimode buckling when the higher global distortional-flexural buckling modes are taken into account.
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