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Shock and Vibration
Volume 15, Issue 2, Pages 147-162

Finite-Element Formulae for Calculating the Sectional Forces of a Bernoulli-Euler Beam on Continuously Viscoelastic Foundation Subjected to Concentrated Moving Loads

Ping Lou

School of Civil Engineering and Architecture, Railway Campus, Central South University, 22 Shao-shan-nan Road, Changsha, Hunan 410075, China

Received 9 November 2006; Revised 2 January 2007

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the finite element method, there are shortcomings using the conventional formulae to calculate the sectional forces, i.e., the bending moment and the shear force, at any cross-section of Bernoulli-Euler beam under dynamic loads. This paper presents some new finite-element formulae overcoming the shortcomings of the conventional ones to calculate the sectional forces at any cross-section of a Bernoulli-Euler beam on continuously viscoelastic foundation subjected to concentrated moving loads. The proposed formulae can easily degenerate into the formulae for calculating the sectional forces of a simply supported or a continuous Bernoulli-Euler beam subjected to concentrated moving loads, and into the formulae for calculating the sectional forces of a Bernoulli-Euler beam on Winkler foundation under static loads. Five numerical examples including static and dynamic analyses are chosen to illustrate the application of the proposed formulae. Numerical results show: (1) compared with the conventional formulae, the proposed formulae can improve the calculation accuracy of the sectional forces of beam; (2) one should use the proposed formulae, not the conventional formulae, to calculate the sectional forces at any cross-section in Bernoulli-Euler beam.