Screening analysis of continuous beams under moving loads by Residual Influence Line methods: a Matlab toolbox implementation

This contribution presents an efficient methodology for the dynamic analysis of continuous two-span beam bridges subjected to moving loads, based on the Residual Influence Line approach (LIR, from its acronym in French). A combined analytical-numerical formulation is proposed to capture the dominant, resonant response of these railway bridges, whose modal behaviour is characterized by a first cluster of two coupled modes. The key aspects of the method are: no time-integration is required to obtain an estimate of the maximum response; and is easily extendable to bridges with a larger number of spans. Based on this new theoretical foundation, a toolbox named TB2S (train-bridge-2spans) is developed and implemented in MATLAB. The toolbox is designed as a rapid calculation tool for structural screening, of particular interest in (a) preliminary design stages, and (b) large dynamic compatibility analysis of existing bridges. It allows one to estimate the dynamic response with minimal computational cost, integrating common modal combination rules such as the SRSS and CQC methods. With few simple data—total length and mass, bending stiffness, load and axle distances, etc.—the user obtains reliable estimates of the response of the bridges of interest. The validation of the method, carried out through comparisons with analytical and semi-analytical solutions across a wide range of train-bridge configurations, demonstrates accuracies exceeding 95% in resonance peaks. Furthermore, a demonstrative case study applied to the Förslov Bridge using the HSLM-A model, a reference for high-speed (HS) trains, is included and made available in the following open-source repository developed by the authors (https://github.com/carlosriascosUPV/TB2S_desktop). The results confirm that the LIR approach constitutes a robust strategy for the dynamic screening of railway multi-span structures, providing a versatile tool to support the design process in accordance with Eurocode standards.