VERTICAL FOOTBRIDGE VIBRATIONS: THE RESPONSE SPECTRUM METHODOLOGY Christos T. GEORGAKIS Associate Professor Department of Civil Engineering Technical University of Denmark Kgs. Lyngby, Denmark Einar Thór INGÓLFSSON PhD Student Department of Civil Engineering Technical University of Denmark Kgs. Lyngby, Denmark Summary 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 = λ 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. Details regarding the response spectrum methodology are presented by Ingólfsson et al. [1]. Keywords: Footbridge, vertical vibrations, response spectrum, peak acceleration, return period, codification 1. Introduction Although pedestrian loading on footbridges is largely stochastic, most international codes of practice treat it, in principal, deterministically. The extent to which the assumptions associated with this are applied has led to a large variation in load models and footbridge response prediction from one code to another. This often leads to the inaccurate prediction of vertical response, particularly when the fundamental vertical frequency of the bridge differs from the mean walking frequency of the anticipated pedestrian population. Several researchers have worked on presenting probabilistic models that consider important load characteristics relating to the variability of pedestrian characteristics in crowd morphology [2],[3],[4]. Nevertheless, these probabilistic models – although generally more accurate – tend to be difficult to execute when obtaining bridge response, thus making their use by engineers and their implementation into codes of practice unlikely. In this paper, a simple and codifiable methodology for the accurate evaluation 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. A series of Monte Carlo simulations are undertaken to establish a universally applicable reference response spectrum from a probabilistic pedestrian load model. The response spectrum allows for the determination of the modal peak acceleration of a reference bridge, with a specific mean pedestrian flow