Horizontal Vibration Of Grandstand Induced By Rhythmic Crowd Loads

In recent years, with wide acceptance and high expectation of fast design, efficient construction and environmental protection, the designers tend to use steel to build the grandstand. However, since the steel grandstand is relatively long-span and large-scale, its natural frequencies are generally low, thus the dynamic crowd loads may excite the resonance frequency along the vertical direction, more than that, there is research showing that along the horizontal direction of grandstand, the resonance frequencies could be excited as well by the vertical crowd loads. The current project is financially supported by National Natural Science Foundation Project(No 51178126)titling "Study on Safety and Serviceability of Steel-structured Gymnasium Stands Induced by Rhythmic Crowd Loads". The project aims at providing the technology for safety and serviceability of steel-structured gymnasium Stands base on the present study of the horizontal vibration of the grandstand. The main content in this thesis are described briefly as follows:(1) The mechanism of how vertical loads produce horizontal displacement was explored. A vertical-horizontal coupling vibration model was built and the static and dynamic equations under the vertical loads were derived to calculate the horizontal displacement. Besides, the model of horizontal displacement under the horizontal load was built as well to analyze the factors of the horizontal displacement induced by the vertical load. Results show that the loads and structures are the main factors to affect the horizontal displacement caused by the vertical load.(2) The horizontal vibration testing model(a symmetric steel plate supported by four legs) was manufactured and tested. The natural frequencies along the horizontal direction were measured and the exciter was used to apply the cycled loads on the testing frame specimens. Total 9 specimens, with 5 loads and 3 different excitation locations were measured. The results show that the symmetric stand model can produce horizontal displacement s with vertical load. In particular, when the frequency of vertical load is close to the natural frequency of the model, the testing model will vibrate in resonance. Besides, the factors that affect the horizontal displacement induced by vertical load were analyzed based on the measurements.(3) The experimental results were compared to those from ANSYS simulation. To validate the mechanism theory and the model testing, a finite element model of the symmetrical steel frame was built using commercial software ANSYS. The FE model was used to calculate the horizontal displacement under the vertical linearly-swept loads. The comparison between the experimental and numerical results shows that both match reasonably well, so that the model testing and the computational simulation were validated to be correct.(4) The existing vertical crowd load was added to a cantilever grandstand model to analyze the coupling phenomenon between vertical load and the horizontal displacement. The simulation results show that the horizontal displacement is quite obvious. Besides, the factors affecting the vibration of the cantilever grandstand model were studied as well.