Probability distribution of footbridge peak acceleration to single and multiple crossing walkers

The scenarios of a single and of multiple walkers crossing a footbridge are considered by many Standards and design Guidelines for vibration serviceability assessment. Accordingly, this study analyzes the probability distribution of footbridge peak accelerations induced by these two load cases. In particular, single span footbridges with uniform mass distribution are considered, with different values of span length, natural frequencies, and structural damping. Only lateral vibrations are considered, and the load is modeled as a moving sinusoidal force corresponding to the first harmonic. The randomness of the dynamic characteristics of walkers is modeled using probability distributions taken from the literature; so doing a standard probabilistically-modeled population is defined. The footbridge is analyzed by means of modal analysis, considering only the first mode. In the case of multiple crossing walkers, arrival time is modeled as a Poisson distribution and different number of walkers, therefore different walkers densities, are considered. Numerical analyses of the transient response to the moving harmonic load were carried out, and the peak acceleration was evaluated. The probability distribution of the peak acceleration induced by the crossing of walkers belonging to the Standard Population is evaluated through Monte Carlo simulations. Finally, the empirical probability distributions are fitted to a Generalized Extreme Value (GEV) distribution and its characteristic parameters are discussed with reference to six case-study footbridges.