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Flexural-Torsional Buckling and Vibration Analysis of Composite Beams

E.J. Sapountzakis1, G.C. Tsiatas2
Assistant Professor, School of Civil Engineering, National Technical University, Zografou Campus, GR-15780, Athens, Greece. Email:
Dr. Eng., School of Civil Engineering, National Technical University, Zografou Campus, GR-157 80, Athens, Greece. Email:

Computers, Materials & Continua 2007, 6(2), 103-116.


In this paper the general flexural-torsional buckling and vibration problems of composite Euler-Bernoulli beams of arbitrarily shaped cross section are solved using a boundary element method. The general character of the proposed method is verified from the formulation of all basic equations with respect to an arbitrary coordinate system, which is not restricted to the principal one. The composite beam consists of materials in contact each of which can surround a finite number of inclusions. It is subjected to a compressive centrally applied load together with arbitrarily transverse and/or torsional distributed or concentrated loading, while its edges are restrained by the most general linear boundary conditions. The resulting problems are (i) the flexural-torsional buckling problem, which is described by three coupled ordinary differential equations and (ii) the flexural-torsional vibration problem, which is described by three coupled partial differential equations. Both problems are solved employing a boundary integral equation approach. Besides the effectiveness and accuracy of the developed method, a significant advantage is that the method can treat composite beams of both thin and thick walled cross sections taking into account the warping along the thickness of the walls. The proposed method overcomes the shortcoming of possible thin tube theory (TTT) solution, which its utilization has been proven to be prohibitive even in thin walled homogeneous sections. Example problems of composite beams are analysed, subjected to compressive or vibratory loading, to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. Moreover, useful conclusions are drawn from the buckling and dynamic response of the beam.


Flexural-torsional buckling, Flexural-torsional vibration, Composite beam, Boundary integral equation, Analog equation method, Free vibrations, Forced vibrations

Cite This Article

E. . Sapountzakis and G. . Tsiatas, "Flexural-torsional buckling and vibration analysis of composite beams," Computers, Materials & Continua, vol. 6, no.2, pp. 103–116, 2007.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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