Analytical Model for Beams on Elastic Foundations Considering the Coupling of Horizontal and Vertical Displacements
Publication: Journal of Engineering Mechanics
Volume 139, Issue 12
Abstract
An analytical method is introduced to deal with the coupling problem for Euler-Bernoulli beams on elastic bidimensional foundations by considering the horizontal and vertical displacements of the beam-foundation system. The approach is an extension of the modified Vlasov model. With separation of the variables, the horizontal and vertical displacements are expressed as the displacement function at the ground surface and the attenuation function along the depth of the foundations, respectively. The governing equations and the corresponding boundary conditions of the model are obtained via the variational principle. Then, the differential operator method is used to uncouple the governing equations and boundary conditions. An iterative procedure is executed to accomplish the numerical implementation. A parametric study is conducted to illustrate the effects of the applied loadings and the physical and geometry properties on the static responses of the beam and foundations. The numerical results show that the coupling elasticity should be taken into account in cases of flexible beams and high soil Poisson ratios. Moreover, the horizontal loads on the beam significantly affect the response of the beam-foundation system.
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Acknowledgments
The authors gratefully acknowledge support from the Science and Technology Project of Hunan Province under Grant No. 2011FJ3124 and the Research Funds for the Young Teachers of Hunan University.
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Published In
Journal of Engineering Mechanics
Volume 139 • Issue 12 • December 2013
Pages: 1757 - 1768
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jul 5, 2012
Accepted: Mar 18, 2013
Published online: Mar 20, 2013
Published in print: Dec 1, 2013
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