Analytical and simplified models for dynamic analysis of short skew bridges under moving loads

Skew bridges induce inherently coupled bending and torsion response. The actual relevance of this coupling for the dynamic response under moving loads such as those arising in high-speed railways is not well known, introducing uncertainties unless costly three-dimensional dynamic models are used. In this work, models are developed based on beam theory and analytical extraction of vibration modes, which are both simple and fast. First, a general three-dimensional beam model is derived, involving both bending and torsional modes. In the following, a simplified beam model is proposed involving only bending modes. In both cases, the eigenfrequencies, eigenmodes and orthogonality relationships are determined analytically from the boundary conditions, and the dynamic response is obtained numerically in the time domain. Both models are validated through representative realistic examples by comparing with two types of finite element models: a stick model with three-dimensional beams and a full three-dimensional model with shell elements. Finally, parametric studies are performed with the simplified beam model for identifying parameters that influence the dynamic response under traffic loads. The results show that the degree of skewness has an important influence on the vertical displacement, but hardly on the vertical acceleration of the bridge. The torsional stiffness has a significant effect on the vertical displacement when the skew angle is large. Finally, the span length reduces the skewness effect on the dynamic behaviour of the bridge