A simplified method for estimating bridge frequency effects considering train mass

The dynamic response of a railway bridge depends on several parameters; the primary parameter is the fundamental natural frequency of vibration of the bridge itself. It is considered a critical parameter of the bridge as the driving or the forcing frequencies arising from moving trains may coincide with the fundamental frequency of the bridge and initiate a resonant response amplifying the bridge load effects. This condition may adversely affect the stresses experienced on bridge members and, consequently, the remaining fatigue life of the structure. Because the train adds additional time-varying mass to the bridge, this introduces a time-varying change in the bridge’s fundamental natural frequency of vibration. As a result, train critical speeds will have a certain range depending on the train configuration. This article presents a simplified method using a power-law relationship to predict the frequency characteristics of a bridge as a function of the train-to-bridge mass ratio. The method is presented in a generalized form, which enables the frequency characteristics to be determined for any given combination of trains and simply supported bridges of short to medium span typically found on the UK rail network. The method is then demonstrated in a case study of a single-span, simply supported plate girder bridge. By considering the BS-5400 train traffic types, the proposed method is used to calculate bridge frequency effects, dynamic amplification, and train critical speed bandwidth for each train type. The simplicity of the proposed method, as it does not require any complex computational modeling, makes it an ideal and effective tool for the practicing engineer to carry out a quick and economical assessment of a bridge for any given train configuration.