A spectral density approach for modelling continuous vertical forces on pedestrian structures due to walking

Existing walking models used for vibration serviceability assessment of structures carrying pedestrians are typically based on measurements of single footfalls replicated at precise intervals. This assumed perfect periodicity allows walking forces to be modelled as a Fourier series based on the walking pace and its integer multiples. This paper examines real continuous walking forces obtained from an instrumented treadmill and the effect of their random imperfections through time simulations of structural response and shows that there are significant differences between responses due to the imperfect real walking forces and the equivalent perfectly periodic simulation. These differences are most significant for higher harmonics where the simulated vibration response is overestimated. As a realistic representation of imperfect walking is an auto-spectral density function, the random character naturally leads to a stochastic approach to treatment of pedestrian loading applied in the frequency domain. The approach can be used for single pedestrians as well as crowd loading where correlation between pedestrians as well as statistics of their pacing rates is used.