Impact factors derived from internal forces in Timoshenko beams subjected to concentrated moving loads

The aim of this work is to analyse the impact factors in the Timoshenko beams response under moving loads in terms of both displacements and internal forces, particularly bending moments. The dynamic response is determined by modal analysis, which consist in representing the absolute displacement field by means of a weighted combination of the undamped system eigenfunctions. This paper presents a finite-element based approach that can be used to compute the dynamic internal forces, both in Bernoulli-Euler and Timoshenko beams models under moving loads. Firstly, this methodology has been validated against an analytical solution for a single-span bridge. Afterwards, the impact factors in a real four-span bridge are presented with a discussion of several issues which come up with the resolution of this kind of problems, such as the damping level and the difference between positive and negative bending moments. Finally, conclusions about the similarities in the dynamic amplification factors for different magnitudes are discussed, including one case of visible resonant behaviour.