Contribution of tracks to dynamic behaviour of railway bridges

The design of (single-span) railway bridges has to meet the challenge of reliable assessment of potential resonance risks. A simplified resonance check based on a bridge's fundamental frequency is provided in the European standard BS EN 1991-2. However, filler beam bridges often do not fulfil the requirements when assessed by calculation only. Measurements usually reveal much higher fundamental frequencies, thus indicating that the calculated frequencies are inaccurate. The difference between calculations and measurements is strongly connected to the mostly unconsidered stiffness contributions of non-structural elements such as ballast or maintenance workways connected to the deck. BS EN 1991-2 provides recommendations for modelling and calculation of the combined track/structure system for the determination of load effects, thus introducing restraining effects of the tracks in the model. In this paper, substitutional rotational springs are derived from the parameters given in DIN EN 1991-2. These can be added to a simple beam single-span model, reducing the modelling complexity significantly while providing equivalent results. Furthermore, a formula for calculation of the fundamental frequency is derived from an equivalent single degree-of-freedom system considering the rotational spring stiffness. Measured and calculated natural frequencies of existing filler beam bridges are used to demonstrate the achievable improvements in calculation.