Finite-element formulae for calculating the sectional forces of a Bernoulli-Euler beam on continuously viscoelastic foundation subjected to concentrated moving loads

Article type: Research Article

Authors: Lou, Ping

Affiliations: School of Civil Engineering and Architecture, Railway Campus, Central South University, 22 Shao-shan-nan Road, Changsha, Hunan 410075, P.R. China. Fax: +86 731 5571736; E-mail: pinglou@mail.csu.edu.cn or pingloucsu@126.com

Abstract: 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.

Keywords: Sectional forces, bending moment, shear force, finite element, Bernoulli-Euler beam, concentrated moving loads

Journal: Shock and Vibration, vol. 15, no. 2, pp. 147-162, 2008