A frequency-domain approach to model vertical crowd-structure interaction in lightweight footbridges

Load models that account for Human-Structure Interaction (HSI) may be preferable to accurately predict the dynamic response of lightweight footbridges subjected to pedestrian actions. Representing each person within a crowd may not be practical in engineering design calculations as time-variant models with a large number of degrees of freedom have to be managed. In addition, high computational time may be required to achieve the steady-state response. In this sense, this paper proposes a novel approach to calculate the vertical steady-state response of footbridges from a time-invariant coupled crowd-structure system. Considering the model of the structure and a feedback model of the crowd, a total closed-loop Transfer Function (TF) of the coupled system is derived. Based on this frequency-domain interacting methodology, a step-by-step procedure is set to asses the vibration serviceability of lightweight footbridges due to harmonic excitations through simple algebraic operations. The proposal is used to study a Fibre Reinforced Polymer footbridge subjected to two streams of walking pedestrians. For this structure, a good compromise between experimental and numerical results is obtained in terms of vertical vibrations and TFs. To further validate the proposed approach, a pre-stressed concrete laboratory facility is also analysed, obtaining a satisfactory agreement between the experimental and numerical TFs. Thus, the proposed approach allows to evaluate lightweight footbridges under crowd-induced loads considering HSI in a simple and accurate manner, which is clearly geared to practice.