Simplified methods to calculate the dynamic response of railway-bridges under crossing trains

In this paper, two different methods to calculate the dynamic response of single-span bridges under moving forces are presented. The work is focused on beam bridges with constant cross-section in underdamped condition. In the first method, referred to as, Impulse-method, the effective impulse resulting from the load is approximated by simple analytical functions. The bridge is modelled as a single degree of freedom system by means of modal analysis. For this simplified system describing bridge and load, closed analytical formulae to calculate the dynamic response can be setup. The "Impulse-method" is exemplified by the HSLM-A1 load train given in Eurocode 1 (EC1). In the second method the response spectrum analysis widely used in earthquake engineering is adopted for the present problem. The calculation of response spectra for beam bridges under the HSLM-A load models is demonstrated. An example shows how this method is deployed.