Stochastic analysis of footbridge vibrations using an analytical moving pedestrian model

In the design of footbridges, the pedestrian load is often simplified by a fixed single load in the middle-span of the bridge. With this assumption, the bridge can be simplified to a single-degree-of-freedom-system (SDOF) and analyzed very efficiently with simple equations. If a moving load is considered, usually a more complex finite element model is necessary and the analysis requires generally a much more demanding numerical time integration. Within this paper, we will present an analytical model for a moving pedestrian load along a simplified footbridge with given cross-section properties. The load model assumes a constant pedestrian stream across the bridge and is represented as a periodic load within the time domain. With help of Fourier series, we will transfer this load-time-history into the frequency domain. The simplification of the original dynamical system to a series of SDOF system is possible and the solution for the periodic load can be achieved by analytical formulas. Based on this analytical model, we will analyze a footbridge under a pedestrian stream with random load amplitudes and varying phase angles. As reference, we will compare the solution with a finite element model with full time integration. The results are compared to recommended formulas in typical footbridge design guidelines.