Power Spectral-Density Model for Pedestrian Walking Load

Intensive vibrations may occur in slender structures like footbridges and long-span floors due to movement of pedestrians. Problems are usually treated in the time domain as Fourier series models of the forcing function, but most methods have disadvantages of neglecting the stochastic character of human walking, being computationally inefficient for random vibration analysis, and overestimating responses in the case of resonance. Meanwhile, frequency-domain models of other types of structural loading are efficient while being a more acceptable approach widely adopted for dealing with stochastic response problems. Hence, an experiment-based power spectral-density (PSD) model normalized to walking frequency and order of harmonic is proposed. To construct this model, 1,528 individual walking-load time histories were collected from an experiment on a rigid floor. These records were then linked to obtain a smaller number of longer samples for a good frequency resolution in spectral analysis. Using the linked samples and for a frequency normalized to mean walking frequency, PSD models in the range 1±0.05 for the harmonic and subharmonic are suggested as a Gaussian mixture with eight model parameters. Via the stationary and nonstationary stochastic vibration theory, the proposed model is used to predict the structural response in terms of root-mean square and peak of acceleration. The framework is finally tested via field measurements demonstrating applicability in practical design work.