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What can pedestrians do on a bridge?
Auckland bridge
(lateral vibration due to crowd load)
Stana Živanović
Aleksandar Pavić
Iván Muñoz Díaz
Vibration Engineering Section
Escuela Técnica Superior de Ingenieros Industriales
Universidad de Castilla-La Mancha
The University of Sheffield
Av. Camilo José Cela s/n, Ciudad Real, 13071,
United Kingdom
Spain
9-12 Febraury, Orlando, Florida
9-12 Febraury, Orlando, Florida
Influence of Walking and Standing
Crowds on Structural Dynamic
Properties
Department of Civil & Structural Engineering
Lock-in (vertical direction)?
Time history
gradually increasing crowd
?
TEST11
40
20
0
Negative damping!
-20
-40
-60
-80
0
200
400
600
Time [s]
800
1000
1200
9-12 Febraury, Orlando, Florida
Acceleration [milli-g]
Does it exist?
Ma(t)+Cv(t)+Kd(t)=300v(t)
60
9-12 Febraury, Orlando, Florida
Usually this is a vibration serviceability (comfort) problem.
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Lock-in (lateral direction)
80
A lot of research since
Millennium footbridge
problem occurred in
2000
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Literature: might happen if vibration amplitude >1cm?
Experimental data lacking.
4
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2.0
1.0
2x1.0m=2.0m
2.0m
• response of empty structure
to a shaker induced force
• response of the structure to a
shaker induced force and six
people walking over
0.5
0.0
-0.5
19
Plan view 20
21
22
23
24
25
26
10
11
12
13
14
15
16
17
1
2
3
4
7
8
-1.0
9-12 Febraury, Orlando, Florida
Acceleration [m/s2]
9-12 Febraury, Orlando, Florida
Tested structure
-1.5
-2.0
0
10
20
30
40
50
60
70
Time [s]
Willford (2002) and Brownjohn et
al. (2004) felt this might be the
case
Positive damping?
Lock-in impossible?
(strongly perceptible vibration
levels)
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5
6
10.8m
11.2m
8x1.35m=10.8m
Elevation
27
18
9
0.275m
Lock-in (vertical direction)?
1.5
6
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Mode shapes
Modal testing
1] Empty structure
2] Structure with 2, 4, 6 or 10 standing (passive) people
3] Structure with 2, 4, 6 or 10 walking (active) people
Only one lowfrequency mode
(at 4.5Hz)
9-12 Febraury, Orlando, Florida
9-12 Febraury, Orlando, Florida
• Chirp excitation 3.5-5.5Hz by electrodynamic shaker
• Duration of a data block 64s (excitation 80%)
• 5 or 15 averages
8
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9-12 Febraury, Orlando, Florida
Standing/walking people arrangements
4.48m
105
106
107
101
102
103
0.92m 0.92m
108
104
1.78m
2.7m
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FRF fitting
FRFs for human-structure systems
10
FRF phase [degree]
6 people
walking
2.5
2.0
6 people
standing
1.5
1.0
6 people
walking
120
6 people
standing
80
40
0.5
3.5
4.0
4.5
Frequency [Hz]
5.0
5.5
0
3.5
4.0
4.5
Frequency [Hz]
5.0
5.5
200
empty sla b
8
empty sla b
6
2 people
stand ing
4
4 people
stand ing
6 people
stand ing
2
2 people
walking
160
2 people
walking
2
160
3.0
0.0
FRF magnitude [(m/s )/N]
measured
model
9-12 Febraury, Orlando, Florida
9-12 Febraury, Orlando, Florida
200
measured
model
2
FRF magnitude [(m/s )/N]
4.5 x10-3
4.0
3.5
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FRF phase [degree]
1.0m
5.4m
2.0m
9-12 Febraury, Orlando, Florida
Modal testing setup
5.4m
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4 people
walking
6 people
walking
10 peopl e
walking
2 people
stand ing
120
4 people
walking
4 people
stand ing
6 people
stand ing
80
10 peopl e
stand ing
40
6 people
walking
10 peopl e
walking
10 peopl e
stand ing
0
3.5
4.0
4.5
Frequency [Hz]
5.0
5.5
0
3.5
4.0
4.5
Frequency [Hz]
5.0
5.5
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Dampening effect of people
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Podgorica footbridge
4.0
standing
walking
3.5
2.5
2.0
9-12 Febraury, Orlando, Florida
Damping ratio [%]
9-12 Febraury, Orlando, Florida
3.0
1.5
1.0
0.5
0
2
4
6
8
10
Number of people
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Conclusions
Acknowledgements
• University of Sheffield staff and students
• Under strong vertical vibration, lock-in does not seem to
occur (opposite to what happens in the lateral direction)
• People can be considered as dampers
• Financial support by the UK Engineering and Physical
Sciences Research Council (EPSRC)
• More studies needed to quantify the damping increase
(probably dependent on vibration level and natural
frequency, apart from the number of active people)
• Conserjería de Educación y Ciencia of Junta de
Comunidades de Castilla-La Mancha and European
Social Fund
9-12 Febraury, Orlando, Florida
9-12 Febraury, Orlando, Florida
Nat. freq.=2.0Hz
damping=0.26%
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9-12 Febraury, Orlando, Florida
6 people walking
6 people standing
THANK YOU!