A Simplified Method for Estimating Bridge Frequency Effects Considering Train Mass Provisionally Accepted

Aminur K. Rahman^{1, 2} Boulent Imam^{1, 2*} Donya Hajializadeh^{1, 2}

• ¹University of Surrey, United Kingdom
• ²School of Sustainability, Civil and Environmental Engineering, United Kingdom

The dynamic response of a railway bridge depends on a number of parameters of which the primary one 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 the 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. Since the train adds additional time varying mass to the bridge, this introduces a time varying change of 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 paper presents a simplified method, using a power-law relation, to predict the frequency characteristics of a bridge as a function of the train to bridge mass ratio. The method is presented in a generalised 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 on a case study 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 modelling, 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.