Closed-form solutions for the structural response to train loads

Exact analytic solutions for uniform, equally spaced sequences of travelling point loads, loading a continuous finite-length structure, are found. A general procedure to reduce any train to this kind of sequence, whilst preserving the essential features of its dynamic load, is also introduced. The analytic expressions provided make it possible to derive the main choices for both structural designs and monitoring tests. A comparison between analytic predictions and numerical results for a case study is presented and discussed.