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PROCEEDINGS OF THE ELEVENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Shear Deformation Effect in Flexural-Torsional Buckling Analysis of Beams using the Boundary Element Method
E.J. Sapountzakis and J.A. Dourakopoulos
School of Civil Engineering, National Technical University, Athens, Greece
E.J. Sapountzakis, J.A. Dourakopoulos, "Shear Deformation Effect in Flexural-Torsional Buckling Analysis of Beams using the Boundary Element Method", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 103, 2007. doi:10.4203/ccp.86.103
Keywords: flexural-torsional buckling, Timoshenko beam, nonuniform torsion, warping, bar, twist, boundary element method, shear deformation.
Elastic stability of beams is one of the most important criteria in the design of structures subjected to compressive loads. This beam buckling analysis becomes much more complicated in the case the cross section's centroid does not coincide with its shear center (asymmetric beams), leading to the formulation of the flexural-torsional buckling problem. Moreover, unless the beam is very "thin" the error incurred from the ignorance of the effect of shear deformation is substantial, and an accurate analysis requires its inclusion.
In this investigation, an integral equation technique is developed for the solution of the general flexural-torsional buckling analysis of Timoshenko beams of arbitrarily shaped cross section. The beam is subjected to a compressive centrally applied load together with arbitrarily axial, transverse and torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing the concept of the analog equation. The essential features and novel aspects of the present formulation compared with previous ones are summarized as follows:
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