Elastic buckling of thin-walled beam-columns based on a refined energy formulation

Giżejowski, M.; Barszcz, A.; Uziak, J.

doi:10.1201/9781003132134-19

Cited by 1 publication

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“…Such an assumption is valid only for beam-columns laterally and torsionally unrestrained (ULT) between end points and having a narrow flange I-section (NFI). In order to account for the effect of prebuckling displacements and second order effects, one has to use the energy equation derived from the displacement field in which the circular trigonometric functions of twist rotation are maintained up to the final stage of the strain energy derivation as shown in [13] and used in this study. Such an approach is desired for beam-columns restrained laterally and torsionally (RLT) between end points and/or having wide flange I-sections (WFI).…”

Section: Discussionmentioning

confidence: 99%

“…The starting point for strain components evaluation of the nonlinear buckling problem of thin-walled beam-columns is the formulation presented by Gizejowski et al [13]. The displacement field relationship developed there enabled to express coupling between the torsion deformation state and those of bending and axial states, therefore extending the formulation of Pi and Bradford in [17,18] which neglected the effect of axial deformations on the torsion state.…”

Section: Refined Energy Equationmentioning

confidence: 99%

“…Comparison of the displacement field relationship developed in [1] and that presented herein yields the conclusion that both formulations are identical as far as LBA problems of thinwalled members are concerned. The difference between the above formulation, presented also in [13], and that developed by Pi and Bradford in [17,18] may arise only when the nonlinear buckling problems (NBA) of thin-walled members are dealt with.…”

Section: Refined Energy Equationmentioning

confidence: 99%

“…This paper presents a continuation of research undertaken in [13] where the theoretical basis has been developed. The general formulation shown in the background paper is further developed towards its practical application in solving the flexural-torsional problems.…”

Section: Acknowledgementsmentioning

confidence: 99%

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Refined energy method for the elastic flexural-torsional buckling of steel H-section beam-columns Part I: Formulation and solution

2023

Archives of Civil Engineering

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Closed form solutions for the flexural-torsional buckling of elastic beam-columns may only be obtained for simple end boundary conditions, and the case of uniform bending and compression. Moment gradient cases need approximate analytical or numerical methods to be used. Investigations presented in this paper deal with the analytical energy method applied for any asymmetric transverse loading case that produces a moment gradient. Part I of this paper is devoted entirely to the theoretical investigations into the energy based out-of-plane stability formulation and its general solution. For the convenience of calculations, the load and the resulting moment diagram are presented as a superposition of two components, namely the symmetric and antisymmetric ones. The basic form of a non-classical energy equation is developed. It appears to be a function dependent upon the products of the prebuckling displacements (know from the prebuckling analysis) and the postbuckling deformation state components (unknowns enabling the formulation of the stability eigenproblem according to the linear buckling analysis). Firstly, the buckling state solution is sought by presenting the basic form of the non-classical energy equation in several variants being dependent upon the approximation of the major axis stress resultant 𝑀 𝑦 and the buckling minor axis stress resultant 𝑀 𝑧 . The following are considered: the classical energy equation leading to the linear eigenproblem analysis (LEA), its variant leading to the quadratic eigenproblem analysis (QEA) and the other non-classical energy equation forms leading to nonlinear eigenproblem analyses (NEA). The novel forms are those for which the stability equation becomes dependent only upon the twist rotation and its derivatives. Such a refinement is allowed for by using the second order out-of-plane bending differential equation through which the minor axis curvature shape is directly related to the twist rotation shape. Secondly, the effect of coupling of the in-plane and out-of-plane buckling forms is taken into consideration by introducing approximate second order bending relationships. The accuracy of the classical energy method of solving FTB problems is expected to be improved for both H-and I-section beam-columns. The outcomes of research presented in this part are utilized in Part II.

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Section: Discussionmentioning

confidence: 99%