This paper is concerned with modelling the loads generated by groups of people jumping rhythmically. The principal objective is to replicate the results that were obtained in an earlier experimental study in which measurements were made with groups of up to 64 people. The experiments showed how the Fourier components of the loads attenuate with increasing group size and this defines a load model which can be used to calculate structural response. The measurements also showed the variations that can occur for similar sized groups.
A model for the loads produced by an individual jumping is used as the basis of this study, with variations to three main parameters being examined. The first parameter being the jump height which the individual selects subconsciously; the second is the jumping frequency which may not align perfectly with the requested frequency; and finally the phase differences between individuals in a crowd. It is assumed that the variations in jump height and frequency will follow normal distributions and that the standard deviations of the distributions can be determined from the available measurements. A load-time history can then be generated for an individual jumping using the basic load model but including the chosen variables selected at random from the distributions. Groups of people are represented by the combination of the appropriate number of individual load-time histories and here the phase difference between individuals can be introduced. The variation in phase difference can be determined from the experimental data.
The modelling is based upon the measurements and attempts to reproduce the experimental data. Although this provides a method for determining a load model, it is not suggested that this should be used for calculating structural response because the model derived directly from the experiments is far easier to use. However, this serves to explain some of the characteristic variations that were observed in the experiments and provides a better understanding of this important load case. It also enables the loads produced by larger groups to be calculated.
B. R. Ellis, BSc, PhD, CEng, MIStructE
BRE Centre for Structural and Geotechnical Engineering
T. Ji, BSc, MSc, PhD, CEng, MIStructE
Manchester Centre for Civil and Construction Engineering, UMIST.