Vertical Footbridge Vibrations: The Response Spectrum Methodology

In this paper, a novel, accurate and readily codifiable methodology for the prediction of vertical footbridge response is presented. The methodology is based on the well-established response spectrum approach used in the majority of the world’s current seismic design codes of practice. The concept of a universally applicable reference response spectrum is introduced, from which the pedestrian-induced vertical response of any footbridge may be determined, based on a defined “event” and the probability of occurrence of that event. A series of Monte Carlo simulations are undertaken for the development of a reference response spectrum. The simulations use known statistical data for pedestrian and population walking characteristics to generate loads for a 50m long simply-supported bridge, with a fixed level of damping and a mean pedestrian flow rate of 1 pedestrian / sec. The response obtained from the reference spectrum is then modified to take into account actual span length, bridge damping, pedestrian pacing frequency, variation on mode shapes and predicted bridge-specific flow rates. Furthermore, the response is modified to account for a specific event return period. The concept of a cumulative event period is introduced and its implication on the calculation of footbridge response is discussed. Finally, a brief comparison is made between the theoretically predicted pedestrian-induced vertical response of an 80m long RC footbridge (as an example) and actual field measurements. The comparison shows that, unlike current codes of practice and other response-prediction approaches, the proposed methodology offers theoretical predictions within 7% of those experimentally measured.