Modelling of crowd-induced vibrations in stadium terraces



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University of Cape Town

Human-induced vibrations are increasingly becoming an issue of great concern in the design of civil engineering structures. In this research work, three major trends that contribute to the prevalence of human-induced vibrations in public structures were identified. While the focus has been mainly on sports stadia, the known effects of humans on the vibration behaviour of structures in general were also reviewed. Existing design and theoretical models for predicting the effects of humans on structures were examined with two issues being raised. Firstly, the existing force model for describing load impulses resulting from jumping has been found to be unable to predict the correct shape of the impulse or its dominant harmonic for jumping frequencies that are significantly less than 2 Hz. Secondly, there is experimental evidence to show that active humans not only excite a structure through footfall-induced forces, but that they also affect the dynamic properties of the structural system, namely its natural frequencies and damping. However, the existing modelling approach assumes that humans engaged in continuous movement can act only as an input force in the dynamics of the vibrating system. To address both these issues, a new modelling approach, termed 'the pseudo-variable mass model' has been proposed in this study. This method is based on the treatment of the structure-jumper system as a pseudo-variable mass system. The predictions of both the existing and the proposed models were compared with the actual results of experimental investigations involving 10 jumpers, jumping on a lightweight-flexible structure at frequencies of 1 Hz and 1.5 Hz. Comparisons with other findings in the literature were also made. This study showed that the proposed model can adequately predict four observed phenomena, namely, the impulse shape, the dominant harmonic of the impulse, the dominant harmonic in the acceleration response and the effect on the fundamental frequency. Thus, for safe and economic design of lightweight and flexible structures, the proposed model may be used to simulate the effects of jumping at frequencies that are significantly less than 2 Hz.