Bending-torsional and flat forms of instability of an I-beam with variable wall height
https://doi.org/10.22227/1997-0935.2025.12.1839-1852
Abstract
Introduction. The aim of the study is to investigate the problem of bending-torsion and flat-form loss of stability of a thin-walled open-section element. A refinement of V.Z. Vlasov’s technical theory for thin-walled rods is presented. The refined differential equations obtained describe the stability conditions of an I-beam with variable wall height. Closed solutions based on refined differential equations are presented using the Bubnov–Galerkin analytical method. The paper provides comparative graphs that allow the differences between analytical solutions and finite element analysis to be assessed.
Materials and methods. The technical theory of V.Z. Vlasov and the Bubnov–Galerkin method were used.
Results. Based on the clarifications made, a closed-form solution was obtained for the problem of elastic buckling of a rod with a linearly varying wall height. An analytical method was proposed for calculating the bending-torsional and flat forms of buckling of a thin-walled open-section element.
Conclusions. The theoretical work presented demonstrates that the solution to the problem of the plane shape and bending-torsional instability of a beam-column with a linearly varying wall height of an open section can be achieved by refining the differential equations and presented in a closed form similar to that for beams-columns of constant section, but with additional corrections in the form of formula coefficients.
About the Author
A. O. Ilyushenkov
Territorial Design Institute “Khabarovskpromproekt”
Russian Federation
Russian Federation
Alexander O. Ilyushenkov — civil and industrial engineer
2 Ussuriysky Boulevard, Khabarovsk, 680000
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Review
For citations:
Ilyushenkov A.O. Bending-torsional and flat forms of instability of an I-beam with variable wall height. Vestnik MGSU. 2025;20(12):1839-1852. (In Russ.) https://doi.org/10.22227/1997-0935.2025.12.1839-1852
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