Probabilistic analysis of serviceability of a grandstand under dynamic crowd loading
J. Knibbe 1, 2, R. de Vries 2, 3, R.D.J.M Steenbergen 2, 4
1 Delft University of Technology, Faculty of Technology, Policy and Management, Delft, the Netherlands
2 Netherlands Organisation for Applied Scientific Research (TNO), Reliable Structures, Delft, the Netherlands
3 Delft University of Technology, Faculty of Civil Engineering and Geosciences, the Netherlands
4 Ghent University, Faculty of Engineering and Architectures, Ghent, Belgium
In this paper, a novel method is developed for determining the reliability of a complex structure under dynamic crowd loading, combining a Finite Element model of a structure and a frequency-domain load model in a reliability analysis. The method is applied on a representative case of a grandstand under dynamic crowd loading. Excited crowds jumping up and down on a grandstand can cause noticeable vibrations, which negatively affect the serviceability of the structure due to discomfort. The FE model consists of linear beam elements, with a distributed dynamic load along the seating deck, described in the frequency domain. The amplitude spectrum of this load is parameterized using a number of stochastic parameters, of which the distribution is determined by sampling a dataset of experimentally measured crowd loads. With this load model, the amplitude spectrum of the acceleration response of the grandstand is determined, from which a serviceability criterion based on acceleration intensity is evaluated. Through a Monte Carlo analysis, an exceedance probability Pf of 0.3264 is calculated, with a coefficient of variation of 0.025. A more advanced reliability calculation method, DARS, was also applied, resulting in a value of Pf between 0.400 and 0.444.
Key words: Structural dynamics, crowd loads, finite element model, reliability, serviceability