Deterministic and stochastic approaches in the vibration serviceability assessment of pedestrian bridges

Modern footbridges are very slender structures, characterized by natural frequencies in the vertical and lateral directions within the range of the dominant walking harmonics; thus, they may be very sensitive to walking-induced vibrations. Design codes dealing explicitly with the footbridge serviceability issue commonly impose a dynamic analysis of footbridges having the natural frequency of the fundamental vertical mode of vibration up to 5 Hz, assuming a force model constituted by a resonant sinusoid moving across the bridge with velocity related to the frequency. However, during the design working life of a footbridge, different scenarios can occur. Depending on the pedestrian traffic expected on the footbridge, an average pedestrian flow based on a daily occurrence rate or an occasional significant stream of pedestrians can be expected. These scenarios are studied on a case-study of footbridge simplified model, first analysing the dynamic response to a series of resonant moving loads with uniform time-lag; then, a stochastic analysis taking into account the normal distribution of pedestrian pacing frequency is performed. Comparisons among the vibration levels generated by the different scenarios are finally proposed.