Dr Khosru Rahman

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.

Train configurations give rise to a primary wagon pass forcing frequency and their multiples. When any one of these frequencies coincides with the natural frequency of vibration of the bridge, a resonant response can occur. This condition can amplify the dynamic response of the bridge, leading to increased levels of displacement, stresses and acceleration. Increased stress levels on critical bridge structural elements increases the rate at which fatigue damage accumulates. Increased bridge acceleration levels can affect passenger comfort, noise levels, and can also compromise train safety. For older bridges the effects of fatigue, and being able to predict the remaining life, has become a primary concern for bridge engineers. Better understanding of the sensitivity of fatigue damage to the characteristics of the passing train will lead to more accurate remaining life predictions and can also help to identify optimal train speeds for a given train-bridge configuration. In this paper, a mathematical model which enables the dynamic response of railway bridges to be assessed for different train configurations is presented. The model is based on the well established closed from solution of the Euler-Bernoulli Beam (EBB) model, for a series of moving loads, using the inverse Laplace-Carson transform. In this work the methodology is adapted to allow different train configurations to be easily implemented into the formulation in a generalised form. A generalised equation, which captures the primary wagon pass frequency for any train configuration, is developed and verified by presenting the results of the bridge response in the frequency domain. The model, and the accuracy of the equation for predicting the primary wagon pass frequency, is verified using independently obtained measured field train-bridge response data. The main emphasis of this work is to enable the practicing engineer, railway operators and bridge asset owners, to easily and efficiently make an initial assessment of dynamic amplification, and the optimal train speeds, for a given bridge and train configuration. This is visually presented in this work using a Campbell diagram, which shows dynamic amplification and compares this with those calculated based on the design code, across a range of train speeds. The diagram is able to identify train speeds at which a resonance response can occur, and the wagon pass frequency, or its multiples, which are causing the increased dynamic amplification. The model is implemented in Matlab and demonstrated by analysing a range of short- to medium-single span simply supported plate girder railway bridges, typically found on the UK railway network, using the standard BS-5400 train configurations. The model does not consider the effects of the train mass and suspension system as this would require a non-closed form numerical solution of the problem which is not practical for the purposes of an initial assessment of the train-bridge interaction problem.