Vibrations of sports stadium grandstand structure due to crowd-jumping loads

Abstract

In recent years the destiny of stadiums has much changed. Formerly the stadiums were used occasionally. The present stadiums are much more versatile; take place in them may concerts and a variety of sporting events, while inside grandstands are located commercial units. As a result, the requirements for the design of these structures are more rigorous, in particular for dynamic loads. The design of grandstands has also evolved. This is due to the requirements of spectators who wish to have a perfect, direct and unobstructed view of anything, and be as close as possible playing action. In parallel, economic considerations limit grandstands supporting structure while maximizing sitting places. This combination leads to longer and more flexible brackets which in combination of spontaneous human behavior raises problems of vibration of the structure. A crowd of people can generate significant dynamic loads especially when it involves rhythmic jumping. Such situations occur during sporting events or concerts. The rhythm of music leads to synchronization behavior of people gathered in the grandstands. Such harmonic force may raise the issue of a resonant vibration, resulting in exceeding the limit states. The paper refers to computational examination of theoretical model of one grandstand in stadium in Krakow. The dynamic interaction function is applied as the dynamic loading reflects to actual behavior of the fans in the grandstands. The calculation of the dynamic response is carried out in the Abaqus 6.12 code. To best replicate reality, a numerical model was built based on a construction project taking into account the actual properties of the structural materials. The study analyzed the convergence of solutions determining the first three natural frequencies of the structure. The first calculated natural frequency (f = 3.24Hz) is close to frequency (f = 2.8Hz) which can generate fans crowd. On the other hand the second natural frequency of the structure (f=4.5Hz) is almost twice of frequency of "Labado" dance. The applied dynamic force cause increasing of stresses in structural elements about 40-60%. The level of calculated stresses as well as displacements of grandstand is safe for the structure.