Train-Bridge Dynamic Interaction: Development of Simplifi ed Analysis Techniques

초록

The analysis of vibrations of trains crossing bridges is a complex dynamics problem that is typically handled using finite-element techniques. Such techniques have been found to be accurate and are useful in validating designs. There is a need, however, for simplified methods that can be used by bridge designers in the early design phases. The basic theory of train-bridge interaction started from Timoshenko’s work on moving loads on single-span, simply supported beams. This work was generalized by using dynamic models of trains on beam structures with multiple spans, as summarized in Fryba’s text and papers. With the advent of computational techniques the theory has branched into two main directions: The first is in the evolution of more realistic models of trains and bridges based on the finite-element technique, as mentioned above. The second direction is in developing simplified methods that can be used by bridge designers in the conceptual and early stages of design. The two approaches to the train-bridge interaction analysis are both of practical importance, and both approaches appear in current design codes. Simplified methods are used primarily for relatively simple bridge structures, such as simply supported beams, and for trains at conventional speeds (typically less than 200 km/hr or 125 mph). Such methods are based on impact factors, where static loads are amplified to represent the effect of dynamic interaction. For more complex bridges, such as continuous multi-span structures, or for higher speeds, computational approaches are needed. There has been recent work in extending simplified methods to continuous bridges and/or higher speed trains (summarized in the collection of papers in Bridges for High-Speed Railways, Calcada, et al., 2008). One challenging aspect of this work is in estimating the effects of possible resonance. The most basic approach uses a Fourier series representation, where the dynamic behavior is approximated by using only the resonance frequencies. Other approaches use a decoupled analysis that involves the dynamic signature of the train and the properties of the bridge. In the present paper, a set of analytical and semi-empirical results are presented which provide further insight into the train-bridge interaction problem and which complement existing simplified analysis methods. These results show the conditions when interaction can be significant, requiring somewhat more complex coupled analysis. In cases where the interaction is minor, then it is shown how this dynamic effect can be approximated or neglected altogether. The results are compared with vibration data taken from conventional inter-city and high speed trains in South Korea.