Closure to “Torsional-Flexural Buckling of Thin-Walled Members”

1966 ◽  
Vol 92 (5) ◽  
pp. 320-320
Author(s):  
Alexander Chajes ◽  
George Winter
Keyword(s):  
Flexural Buckling ◽  
Thin Walled

Torsional and Flexural Buckling of Bars of Thin-Walled Open Section Under Compressive and Bending Loads

1942 ◽  
Vol 9 (3) ◽  
pp. A103-A107 ◽  
Author(s):  
J. N. Goodier
Keyword(s):  
Lateral Buckling ◽  
Flexural Buckling ◽  
Open Section ◽  
Bending Loads ◽  
Thin Walled ◽  
General Section ◽  
Observed Behavior

Abstract The observed behavior of torsionally weak columns in buckling by twisting rather than, or as well as, bending is analyzed in this paper on the basis of a hypothesis due to Wagner. The theory is simplified, and extended to the general section, where results simpler than some already obtained by Kappus are given. It is further extended to bars, restrained by flexible sheets, and bars with constrained axes of rotation. Wagner’s hypothesis is applied to the problem of lateral buckling, where it yields the accepted theory for symmetrical sections, but indicates results of novel form for unsymmetrical cases. Similar results are obtained in the problem of eccentric thrust, whatever the section.

scholarly journals Elastic Critical Axial Force for the Torsional-Flexural Buckling of Thin-Walled Metal Members: An Approximate Method

2015 ◽  
Vol 23 (1) ◽  
pp. 23-32 ◽  
Author(s):  
Michal Kováč
Keyword(s):  
Differential Equations ◽  
Approximate Method ◽  
Axial Force ◽  
Reference Method ◽  
Critical Force ◽  
Buckling Mode ◽  
Flexural Buckling ◽  
Coupled Equations ◽  
Thin Walled ◽  
Critical Axial Force

Abstract Thin-walled centrically compressed members with non-symmetrical or mono-symmetrical cross-sections can buckle in a torsional-flexural buckling mode. Vlasov developed a system of governing differential equations of the stability of such member cases. Solving these coupled equations in an analytic way is only possible in simple cases. Therefore, Goľdenvejzer introduced an approximate method for the solution of this system to calculate the critical axial force of torsional-flexural buckling. Moreover, this can also be used in cases of members with various boundary conditions in bending and torsion. This approximate method for the calculation of critical force has been adopted into norms. Nowadays, we can also solve governing differential equations by numerical methods, such as the finite element method (FEM). Therefore, in this paper, the results of the approximate method and the FEM were compared to each other, while considering the FEM as a reference method. This comparison shows any discrepancies of the approximate method. Attention was also paid to when and why discrepancies occur. The approximate method can be used in practice by considering some simplifications, which ensure safe results.

Torsional-Flexural Buckling of Thin-Walled Members

1965 ◽  
Vol 91 (4) ◽  
pp. 103-124
Author(s):  
Alexander Chajes ◽  
George Winter
Keyword(s):  
Flexural Buckling ◽  
Thin Walled

scholarly journals Catastrophic Influence of Global Distortional Modes on the Post-Buckling Behavior of Opened Columns

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3314
Author(s):  
Andrzej Teter ◽  
Zbigniew Kolakowski
Keyword(s):  
Cross Sections ◽  
Carrying Capacity ◽  
Strong Interactions ◽  
Load Carrying Capacity ◽  
Buckling Modes ◽  
Flexural Buckling ◽  
Load Carrying ◽  
Post Buckling ◽  
Global Modes ◽  
Thin Walled

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.

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