Pedestrian-Induced Vibrations of Footbridges: An Extended Spectral Approach

The vibration serviceability assessment of footbridges under pedestrian traffic requires a probabilistic approach considering the uncertainty in the dynamic behavior of the structure and the variability of multiple load parameters, such as the pedestrians' arrival time and step frequency. In view of engineering applications, a major challenge lies in the development, verification, and validation of efficient prediction models. With this challenge in mind, this paper uses a spectral approach to predict the dynamic response induced by unrestricted pedestrian traffic. A spectral load model available in the literature is extended to account for multiple harmonics of the vertical walking load and for application to arbitrary mode shapes. Furthermore, a closed-form expression is proposed to estimate the variance of the multimode structural response taking into account both resonant and nonresonant contributions. The performance of the proposed approach is evaluated for a simply supported beam as well as a real footbridge where multiple modes considerably contribute to the overall structural response. The results show that the proposed approach allows a good and mildly conservative estimate of the structural response to be obtained.