Keywords: bridge-train dynamics, bridge-train interaction, dynamic response, finite element analysis, parametric study, dynamic amplification, skewed bridge.

This paper reports on the application of the DBTI model described in the accompanying Part I paper, to a parametric study, as well as to the analysis of three-dimensional dynamic responses of an existing railway bridge. The main aim of the parametric study was to identify key parameters governing the dynamic response of bridge-train systems and to assess the importance of the bridge-train interaction in relation to these parameters. The dynamic response of the bridge-vehicle system was found to be sensitive to the frequency and mass parameters. It was found that, for the practically applicable range of speed parameters, an increase in the frequency parameter increases the bridge response. The bridge-vehicle interaction was found insignificant only for low values of either speed or frequency parameters. Increasing the mass parameter was found to increase the dynamic amplification factor at low speed parameters, but to significantly reduce the amplification at higher speeds. Effects of the interaction on the dynamic response were found to be negligible for calculating the dynamic amplification factor when either the mass or the speed parameter is low.

The dynamic analysis of an existing railway bridge was performed using the DBTI package. The bridge under investigation was a simply-supported and skewed structure made of wrought-iron. A modal analysis was carried out first in order to establish the natural frequencies and corresponding mode shapes of the bridge. This was followed by a transient analysis, where the bridge was subjected to passages of different passenger and freight trains travelling at a range of speeds. Generally, dynamic amplification of displacements was moderate and did not exceed 10%, except for responses at speeds close to the critical speeds. This dynamic amplification was found to compare very favourably with that recommended by Eurocode 1. Therefore, refined values of dynamic factors can be obtained through the dynamic analysis with network-specific service trains. This finding is of high practical importance, as it allows for more efficient methods of dealing with existing dynamically underperforming bridges. At train speeds close to critical speeds, the bridge responses grew considerably as resonance occurred. This phenomenon was reflected by significant peaks in displacements of the bridge. Resonance produced by the freight trains occurred at critical speeds far beyond the maximum operational speeds of these trains. However, the analysis demonstrated the risk of excessive vibrations that can be produced by these trains in bridges with lower fundamental frequencies. The effects of moving trains on the bridge were found to be strongly dependent on the type of the load model used in the analysis, particularly at resonance. The moving force load model produced far greater response than the moving system model that incorporated bridge-train interaction. Therefore, the use of complex models for bridge-train dynamics was found to produce refined dynamic responses. This could provide gains in situations where bridges assessed in a traditional manner fail the assessment criteria.

Finally, the analysis that was carried out with the use of skewed and straight three-dimensional bridge models, as well as straight two-dimensional model showed that neglecting the skewness of this bridge can yield considerably different dynamic response. The skewness was found to increase the fundamental frequency of the bridge. This led to a shift in the dynamic amplification factor towards higher speeds and alterations of its magnitude. Three-dimensional models were found necessary for accurate prediction of this response.

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