Probabilistic modeling of spectator jumping loads for temporary grandstands: Insights from experiments and load simulation

Jumping loads are the most significant form of crowd-induced dynamic loading on temporary grandstands. This study presents experimental results from subjects jumping at frequencies between 1.0 Hz and 3.0 Hz on force plates, analyzing three key parameters: peak load ratio, jumping period, and contact time. A widely used mathematical model for simulating vertical jumping loads is reviewed and refined based on these experiments. The analysis also includes two-person jump dynamics and associated horizontal loads. Results show that the peak load ratio and contact parameters follow truncated normal distributions and can be used to simulate quasi-periodic jumping loads. A Gaussian-based multi-peak model significantly improves computational efficiency for non-single-peak jumps. The combined jumping load from two individuals is approximately 85% of the linear superposition of individual loads. Horizontal loads were also quantified, with front-to-back forces averaging 45% of body weight and side-to-side forces 10%. These findings support more accurate load simulations for safer grandstand design under dynamic crowd conditions and the models are convenient to be applied in the vibration serviceability assessment of stadium stands.