Modal parameters to estimate the dynamic response of footbridges considering the human-structure interaction

Lightweight, low damping and slender footbridges are prone to human-structure interaction (HSI) effects, by which a new mechanical system is composed whenever walking subjects couple to the structure, imposing apparent modal properties, different from those of the empty structure. Codes and guidelines typically provide harmonic load models (HLM) in a procedure that does not take into account HSI effects. To do so, a modal analysis of the footbridge structure as a SDoF model characterized by apparent modal parameters equal to those of the coupled system may be employed. Therefore, the main contribution of this paper is the establishment of simple equations to calculate the apparent damping ratio and the apparent natural frequency of footbridges excited by the first harmonic of the human walking loads (1.7 Hz - 2.3 Hz), as functions of the modal parameters of the empty structure and the crowd density. The developed numerical tools are presented and validated with results from the literature, as the crowd model, the human-structure interaction mathematical model and the free vibration analysis of the coupled system. Comparisons between the results of the equivalent SDoF model of the coupled system subjected to a crowd moving load model and the system composed of the footbridge coupled to the moving biodynamic models of the pedestrians showed that the first procedure adequately simulates the HSI effects. Finally, it is shown that the proposed equations are suitable to estimate the dynamic responses of simply support footbridges allowing the consideration of the HSI effects in a straigthforward procedure.