An extended spectral approach for the vibration serviceability assessment of footbridges

To assess the vibration serviceability of footbridges, a methodology is required that accounts for the variability of multiple load parameters, such as the pedestrians’ arrival time and step frequency. To this end, generally the method of Monte Carlo simulation is applied. This method is, however, computationally expensive and not suitable for practical applications. An alternative method offering great potential towards the development of efficient and user-friendly prediction methods, is found in spectral approaches. In a spectral approach, the pedestrian-induced loading is modeled as a stationary random process by means of a suitable power spectral density function. In this contribution, a spectral load model for unrestricted pedestrian traffic available in the literature is extended to account for multiple harmonics of the vertical walking load and for application to arbitrary mode shapes. In addition, a closed-form expression is proposed to estimate the structural response taking into account the resonant and non-resonant contribution of multiple modes. The performance of the proposed approach is evaluated for a real footbridge where multiple modes considerably contribute to the overall structural response. It is shown that the proposed approach allows to obtain a good and mildly conservative estimate of the structural response.