Dynamic analysis of bridge girders submitted to an eccentric moving load

The cross-section warping due to the passage of high-speed trains can be a relevant issue to consider in the dynamic analysis of bridges due to (i) the usual layout of railway systems, resulting in eccentric moving loads; and (ii) the use of cross-sections prone to warping deformations. A thin-walled beam formulation for the dynamic analysis of bridges including the cross section warping is presented in this paper. Towards a numerical implementation of the beam formulation, a finite element with seven degrees of freedom is proposed. In order to easily consider the compatibility between elements, and since the coupling between flexural and torsional effects occurs in non-symmetric cross-sections due to dynamic effects, a single axis is considered for the element. The coupled flexural-torsional free vibration of thin-walled beams is analysed through the presented beam model, comparing the results with analytical solutions presented in the literature. The dynamic analysis due to an eccentric moving load, which results in a coupled flexuraltorsional vibration, is considered in the literature by analytical solutions, being therefore of a limited applicability in practice engineering. In this paper, the dynamic response due to an eccentric moving load is obtained from the proposed finite element beam model that includes warping by a modal analysis.