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Response of a joint passive crowd-SDOF system subjected to crowd jumping load

University of Oxford. Response of a joint passive crowd-SDOF system subjected to crowd jumping load. Jackie Sim, Dr. Anthony Blakeborough, Dr. Martin Williams Department of Engineering Science University of Oxford. Vibration problem on cantilever grandstand.

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Response of a joint passive crowd-SDOF system subjected to crowd jumping load

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  1. University of Oxford Response of a joint passive crowd-SDOF system subjected to crowd jumping load Jackie Sim, Dr. Anthony Blakeborough, Dr. Martin Williams Department of Engineering Science University of Oxford

  2. Vibration problem on cantilever grandstand Flexible structure with large span and lightweight Synchronised crowd loadings 1.5 ~ 2.8 Hz +

  3. Dynamic analysis of cantilever grandstand Human-structure interaction Active crowd Load model Passive crowd Crowd model

  4. Outline Passive crowd model How to model the seated and standing crowds? Active crowd model How to model the jumping crowd? Analysis of active + passive crowds on SDOF structure What is the structural response? 4. Results 5. Case study Contents

  5. y2 DOF 2 m2 k2 c2 y1 DOF 1 m1 k1 c1 F Passive crowd model (1) • Griffin et al. – experimental tests and model development • Measure the apparent mass of 24 seated and 12 standing men:

  6. Curve-fitting the crowd apparent mass response Crowd model represented as transfer function Seated: Standing Passive crowd model (2) Fourth order polynomial i.e. 2DOF system

  7. Active crowd model (1) Experimental tests - University of Surrey - 100 test subjects - Each individual jumping on rigid force plates • Metronome at 4 beat frequencies (1.5, 2, 2.67 and 3.5 Hz) • Synchronised test results were analysed

  8. Active crowd model (2) Average impulse of each individual Load-time history at 2 Hz Average impulse of all individuals => Crowd jumping load

  9. Active crowd model (3) Crowd jumping load Fourier coefficients High FC => Better synchronisation

  10. Passive crowd-SDOF system subjected to crowd jumping load Feedback system representation + SDOF structure Crowd jumping load _ Interaction force Seated / Standing crowd ms F x Analysis (1) Displacement Acceleration

  11. Analysis (2) Frequency domain analysis Parameters Natural frequency of empty structure: 1 ~ 8Hz Structural damping ratio: 2% Passive crowd mass ratio, g: 0 ~ 0.3 (increment of 0.05) Subjected to crowd jumping load at 1.5, 2, 2.67 and 3.5Hz

  12. Results - Maximum displacement

  13. Results – RMS Acceleration

  14. First mode at 2.9 Hz Crowd mass = 16800 kg per bay Assume g = 0.3 Structure mass = 56000 kg for one bay Structure stiffness; Case study – Cardiff Millennium Stadium

  15. Rugby match between Australia and France in Nov 1999 Displacement of approximately 50mm reported after the match Half full capacity Mass ratio, g = 0 ~ 0.15 Maximum displacement (mm) RMS Acceleration (times g = 9.81m/s2) Results

  16. Concluding remarks • Passive crowd adds significant damping to the system and alters the resonance frequency • Preliminary analysis on the Cardiff Millennium Stadium gave good results • Current work – statistical model of the crowd jumping load – taking into account the timing of each individual

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