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Shock and Vibration
Volume 2016, Article ID 4070627, 12 pages
Research Article

Application of Volterra Integral Equations in Dynamics of Multispan Uniform Continuous Beams Subjected to a Moving Load

The Faculty of Environmental Engineering and Geodesy, Wrocław University of Environmental and Life Science, Grunwaldzka 55, 50-365 Wrocław, Poland

Received 30 March 2016; Revised 6 September 2016; Accepted 8 September 2016

Academic Editor: Salvatore Russo

Copyright © 2016 Filip Zakęś and Paweł Śniady. 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.


The dynamic behavior of multispan uniform continuous beam arbitrarily supported on its edges subjected to various types of moving noninertial loads is studied. Problem is solved by replacing a multispan structure with a single-span beam loaded with a given moving load and redundant forces situated in the positions of the intermediate supports. Redundant forces are obtained by solving Volterra integral equations of the first or the second order (depending on the stiffness of the intermediate supports) which are consistent deformation equations corresponding to each redundant. Solutions for the beam arbitrarily supported on its edges (pinned or fixed) due to a moving concentrated force and moving distributed load are given. The difficulty of solving Volterra integral equations analytically is bypassed by proposing a simple numerical procedure. Numerical examples of two- and three-span beam have been included in order to show the efficiency of the presented method.