Walking-induced vibration of a footbridge

In the last years, the need for structures able to link the functional and aesthetic role has led engineers and architects to design footbridges characterized by long span, light materials and increasing slenderness. The low ratio between permanent and variable loads makes recent footbridges more sensitive to the dynamic loads, such as the forces transmitted by pedestrian. Excessive vibrations may arise when the bridge natural frequencies are very close to those characterizing the human activities: walking, jogging and running. This issue became relevant after the Millenium Bridge inauguration, when an excessive lateral sway motion was triggered by the synchronization between bridge and pedestrian movements. The dynamic behavior of a lively footbridge over-passing the Serio river near Seriate (about 50 km far from Milan), Italy, is investigated in this paper. The suspension bridge, 63.75 m long, is composed of a timber deck on a steel grid. The footbridge model, based on the as-built design data, is implemented in the ANSYS framework. The numerical frequencies computed through the FE model match those identified from the results of the experimental campaign of ambient vibration measurements in a fully satisfactory way. Since the bridge displays several frequencies in the range excited by human activities, its response to crossing pedestrians is investigated. The dynamic interaction pedestrians-footbridge is analyzed for different classes of traffic with two approaches. First, the FE model developed in ANSYS is excited by the distributed harmonic load model for a pedestrian stream, applied on the bridge coherently with the corresponding mode shape, as suggested by the Hivoss Guideline. Second, an ad-hoc developed numerical code is adopted to compute the bridge dynamic response to moving forces. This code reads as input data the structural matrices computed in ANSYS and integrates the equations of motion of a system in which the pedestrian is modeled as a constant vertical travelling force along the footbridge deck. The vibration serviceability under the vertical component of pedestrian load is assessed by comparison to comfort criteria. The results of the Hivoss guideline show accelerations exceeding the value of comfort. The transient analysis predicts lower values within the limits. The two sets of values can be interpreted as an upper and lower bound of the actual response.