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Torsional Buckling of Restrained Thin-Walled Bars of Open Bisymmetric Cross-section

Kujawa M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2012

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Vol. 16, No 3-4

301--306

EN

The problem of torsional budding of restrained thin-walled bars of an open constant bisymmetnc cross-section was solved using the minimum total stationary elastic energy condition (J. S. Przemieniecki 1968 Theory of Matrix Structural Analysis McGraw-Hill, New York) and the Newton-Raphson method (S. C. Chapra and R. P. Canale 1998 Numerical Methods for Engineers McGraw-Hill Book Company). The consideration was restricted to the elastic structures. The example presented in the paper helps to assess the correctness of the proposed solution. This article is an addition to the author's considerations contained in M Kujawa 2012 TASK Quart. 16 (1/2) 5.

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Torsion of Restrained Thin-walled Bars of Open Constant Bisymmetric Cross-section

Kujawa M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2012

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Vol. 16, No 1-2

5-15

EN

Elastic and geometric stiffness matrices were derived using Castigliano’s first theorem, for the case of torsion of restrained thin-walled bars of open constant bisymmetric cross-section. Functions which describe the angles of torsion were adopted from the solutions of the differential equation for restrained torsion. The exact solutions were simplified by expanding them in a power series. Numerical examples were taken from Kujawa M 2009 Static and Sensitivity Analysis of Grids. . . 97, GUT Publishing House, and Szymczak C 1978 Engineering Transaction 26 323. Convergence of the solutions was analyzed using the matrices derived for torsion angles, warping, bimoments and critical forces.

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The effect of nonlinear restraint on torsional buckling and post-buckling behaviour of a thin-walled column

Szymczak C.

Foundations of Civil and Environmental Engineering

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2006

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No. 7

333-342

EN

Torsional buckling and post-buckling of a simply supported axially compressed thin-walled column of open bisymmetric cross-section with a central restrain has been investigated. The nonlinear behaviour of the restraint against the rotation angle of the cross-section has been assumed. The stability consideration is based upon the classical theory of beams with nondeformable cross-section. The solution of the buckling and post-buckling behaviour problem formulated has been found with the perturbation approach. The critical load and the initial post-buckling path of equilibrium for I - column for the cubic relation of the restraint reaction and the rotation angle have been determined. The results show the considerable effect of nonlinearity of the restraint behaviour on the post-buckling path of equilibrium of the column in comparison with the linear restraint.

4

Torsional buckling paradox : extended studies

Chróścielewski J., Lubowiecka I., Szymczak C., Witkowski W.

Biuletyn Wojskowej Akademii Technicznej

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2004

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Vol. 53, nr 6

89-97

EN

Torsional buckling of I-beam columns with variable cross section has been investigated. It has been shown that critical torsional buckling load may exceed the limits prescribed by torsional buckling loads of I-beam columns with constant minimum/maximum fIange width. This paradoxical result has been obtained on the grounds of the classical theory of thin-walled members with non-deformable cross section. In this study, this paradox is investigated further for fIange widths taken from 10 cm to 20 cm. The obtained FEM resuIts confirm the existence of the paradox.

PL

Analizowano wyboczenie skrętne pręta cienkościennego o dwuteowym przekroju poprzecznym ze zmienną szerokością półek. Wykazano, że siła krytyczna wyboczenia skrętnego może przekraczać granice wyznaczone przez siły odpowiadające prętom o stałych ekstremalnych szerokościach półek. Ten paradoksalny wynik uzyskano w ramach teorii prętów cienkościennych o przekroju nieodkształcalnym. Przeanalizowano siłę krytyczną wyboczenia skrętnego dwuteowników cienkościennych dla szerokości pasów od 10 do 20 cm, dla różnych kształtów pasów. Wyniki analizy MES potwierdzają istnienie paradoksu.