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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

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
Vibration problem on cantilever grandstand

Flexible structure with large span and lightweight

Synchronised crowd loadings 1.5 ~ 2.8 Hz

+

dynamic analysis of cantilever grandstand
Dynamic analysis of cantilever grandstand

Human-structure interaction

Active crowd

Load model

Passive crowd

Crowd model

contents
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
passive crowd model 1

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:
passive crowd model 2
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

active crowd model 1
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
active crowd model 2
Active crowd model (2)

Average impulse of each individual

Load-time history at 2 Hz

Average impulse of all individuals => Crowd jumping load

active crowd model 3
Active crowd model (3)

Crowd jumping load

Fourier coefficients

High FC => Better synchronisation

analysis 1
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

analysis 2
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

case study cardiff millennium stadium
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
results
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
concluding remarks
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