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Pedestrian Loads and Dynamic Performances of
Lively Footbridges: an Overview
CSHM – 2 Workshop, 28th September – 1st October 2008, Taormina Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
Fiammetta Venuti
Luca Bruno
Politecnico di Torino (Italy)Department of Structural Engineering and Geotechnics
Pedestrian loads and dynamic perform
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/332 Introduction
ROAD BRIDGES
� Increase of traffic
� Increase of vehicles weight
Critical performances of existing
structures � reduced safety and stability
PEDESTRIAN BRIDGES
� Increasing strength of materials
� Increase of slenderness
Critical performances of new
structures
� reduced serviceability
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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� reduced safety and stability� reduced serviceability
� high costs for dynamic
assessment after construction
The dynamic behaviour should be considered in a very early design stage
� Need for comfort criteria
� Need for suitable and predictive load models
� Need for practical design rules
Pedestrian loads and dynamic perform
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/333 Introduction
Human-induced vibration problems on footbridges were
discovered in the 19th century � collapse of a footbridge
in Broughton due to marching soldiers
Attention focused on vertical vibrations in the 20th century
From 2000, with the closure of the London Millennium
Bridge, the attention is focused on lateral vibrations due to synchronisation phenomena (a few episodes had been
already reported from the Seventies)
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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London Millennium Bridge opening day, July 2000Auckland Harbour bridge, 1975
already reported from the Seventies)
Pedestrian loads and dynamic perform
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/334 Introduction
In the last decade, increasing attention to human-induced vibrations
on footbridges testified by:
� Specific international conference
� International reseach projects and guidelines
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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FIB Federation International du Beton. Guidelines for the design of footbridges, fib Bulletin No. 32, Lausanne, 2006.
SETRA/AFGC. Passerelles piétonnes – Evaluation du comportement vibratoire sous l’action de piétons. Guide méthodologique. Paris, 2006
BUTZ C. et al., Advanced load models for synchronous pedestrian excitation and optimised design guidelines for steel footbridges (SYNPEX), Final report, RFS-CR 03019, Research Fund for Coal and Steel, 2007
European Project SINPEX
Pedestrian loads and dynamic perform
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/335 Introduction
Objective
state-of-the-art about human-induced vibrations on footbridges
Summary
� Phenomenological analysis of pedestrian loading
� pedestrian on a rigid surface
� pedestrian on a vibrating surface � human-structure interaction
Pedestrian loads and dynamic perform
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F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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� Comfort criteria
� Pedestrian load models
� single pedestrian
� groups of pedestrians
� crowds
� Experimental tests
� laboratory tests
� field tests
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6
PHENOMENOLO
GICAL A
NALYSIS
Pedestrian loads and dynamic performances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. – 1 Oct.2008, Taormina
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7Pedestria
n walking on a rig
id su
rface
100
50
Ex
p.
Theo
r.
Number of people
lpF
HF
L
FV
FVF
V
Pedestrian loads and dynamic performances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. – 1 Oct.2008, Taormina
1.2
1.6
2.0
2.4
fVMatsu
moto et a
l. (1978)
Hz
12/
≅=
VH
ff
Walking fre
quency
Hz
2/
≅=
pV
lv
f
FH
Andriacchi et al. (1997)
FL
FL
Walking fre
quency ra
nges fo
r diffe
rent a
ctivitie
s afte
r Bachmann (2
002)
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/338 Pedestrians walking on a vibrating surface
Human-structure interaction
Modification of the footbridge dynamic properties
Change in natural frequencies due to pedestrians mass
Change in damping (the effect of moving people is still unexplored)
Synchronisation between the pedestrians and the structure
The phenomenon is much more probable in the horizontal direction
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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T-bridge
Japan 1993
Millennium Bridge
London 2000
Synchronous Lateral Excitation (SLE)
Passerelle Solferino
Paris 2000
Auckland Harbour
New Zealand 1975
Groves Bridge
Chester (UK) 1977
“[..] the phenomenom could occour on any bridge with a lateral frequency below about 1.3 Hz loaded with a sufficient number of pedestrians.” (Dallard et al., 2001)
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/339 Synchronous Lateral Excitation
KEY FEATURES OF THE PHENOMENON
The probability of lock-in grows for increasing amplitude of the deck motion
� The deck lateral motion triggers the
synchronisation between the pedestrians and
the structure � LOCK-IN
2 kinds of synchronisation:
Pedestrian loads and dynamic perform
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F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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Dallard et al. (2001), Bachmann (2002), Nakamura (2003)
� High crowd density causes
synchronisation among pedestrians
Venuti et al. (2005), Ricciardelli (2005)
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/3310 Synchronous Lateral Excitation
� The lateral force grows for increasing amplitude of the deck
motion
Self-excitation:
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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Dallard et al. (2001)
Nakamura (2003)
� Pedestrians detune or stop walking when vibrations exceed a threshold value
Self-limitation:Pizzimenti (2003)
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11
COMFORT C
RITE
RIA
Pedestrian loads and dynamic performances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. – 1 Oct.2008, Taormina
Pedestrian loads and dynamic perform
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/3312 Comfort requirements
The reaction of pedestrians to vibration is very complex:
� different people react differently to the same vibration condition
� an individual reacts differently to the same vibrations on different days
� a pedestrian alone is more sensitive to vibration than in a crowd
� a pedestrian who expects vibrations is less sensitive
Comfort requirements:
� Limit values for structural � the bridge natural frequencies should fall outside
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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� Limit values for structural
frequencies� the bridge natural frequencies should fall outside
the pedestrian loading frequencies
� Limit values of accelerations � If the limit on frequencies is not satisfied, a
dynamic calculation with suitable load models is
required
Code/Standard Vertical [Hz] Horizontal [Hz]
Eurocode 2
Eurocode 5
Eurocode 1 (UK NA)
1.6 – 2.4
< 5
< 8 (unloaded bridge)
0.8 – 1.2
0.5 – 2.5
< 1.5 (loaded bridge)
Seldom fulfilled in new footbridges
Pedestrian loads and dynamic perform
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/3313 ISO 10137 – Eurocode 5
Bases for design of structures – Serviceability of buildings and walkways against vibrations.
ISO 10137 (2007):
The limit values are obtained by multiplying the base curves of rms accelerations by
a factor 60 (pedestrians) or 30 (standing persons)
vertical
RMS [m/s
2]
horizontal
RMS [m/s
2]
Pedestrian loads and dynamic perform
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F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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f [Hz]
a v-RMS [m/s
f [Hz]
a h-RMS [m/s
av,rms
av,rms
ah,rms 212.0
843.0
41/6.0
≤≤=
≤≤=
≤≤=
f
f
ff
Limit values for pedestrians
Eurocode 5: av,max= 0.7 m/s2 ah,max= 0.2 m/s2
Pedestrian loads and dynamic perform
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/3314 SETRA Guideline
Comfort requirements are not absolute but depend on the comfort level specified
by the Owner.
TrafficClass
Density d(P=person)
I
II
urban footbridge linking up high pedestrian density areas or that is frequently used by dense crowds, subjected to very heavy traffic
urban footbridge linking up populated areas, subjected to heavy traffic and that may occasionally be loaded throughout its bearing area
Description
d=1.0 P/m2
d=0.8 P/m2
Stage 1: determination of the footbridge class
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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Comfortlevel
Degree of comfort
1
2
3
< 0.5
0.5 – 1.0
1.0 – 2.5
Acceleration levelVertical [m/s2]
4 > 2.5
maximum
average
minimum
discomfort
Acceleration levelHorizontal [m/s2]
< 0.1
0.15 – 0.3
0.3 – 0.8
> 0.8
Lock-in
III footbridge for standard use, occasionally crossed by large groups ofpeople but that will never be loaded throughout its bearing area
IV seldom used footbridge, built to link sparsely populated areas
d=0.5 P/m2
Stage 2: choice of the
comfort level
Stage 3: determination
of frequencies (risk of
resonance)
Stage 4: dynamic calculation (if necessary)
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/3315 SYNPEX Guideline
� Acceleration checks should be performed if:
Hz 3.23.1 ≤≤ vf Hz 2.15.0 ≤≤ hfvertical horizontal
� Definition of design scenarios, characterised by a traffic class and a comfort level
TrafficClass
Density d(P=person)
TC 1
TC 2
TC 3
Very weak traffic: 15 single persons
Weak traffic: comfortable and free walking
Dense traffic: unresctricted walking, overtaking can inhibit
Description
15 P
d=0.2 P/m2
d=0.5 P/m2
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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TC 3 Dense traffic: unresctricted walking, overtaking can inhibit
TC 4
TC 5
Very dense traffic: uncomfortable situation, obstructed walking
Exceptional dense traffic: crowding begins
d=0.5 P/m
d=1.0 P/m2
d=1.5 P/m2
Comfortlevel
Degree of comfort
CL 1
CL 2
CL 3
< 0.5
0.5 – 1.0
1.0 – 2.5
Acceleration levelVertical [m/s2]
CL 4 > 2.5
maximum
medium
minimum
discomfort
Acceleration levelHorizontal [m/s2]
< 0.1
0.1 – 0.3
0.3 – 0.8
> 0.8
Lock-in
Pedestrian loads and dynamic perform
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/3316 UK National Annex to EN 1991-2
� Limit on the vertical acceleration: 24321lim m/s 0.1 kkkka = 2
lim m/s 0.25.0 ≤≤ a
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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� Comfort criterion on synchronous
lateral excitation:
pedestrian
bridge
m
mD
ξ=
Pedestrian excitation mass damping parameter
k4=1 exposure factor
Pedestrian loads and dynamic perform
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/3317 Comments
� Standard codes and new guidelines has different approaches
Absolute values of
comfort requirements
Comfort requirements decided
by the owner as a function of
the footbridge traffic class and
required level of comfort
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
� UK National Annex has a different approach towards the avoidance
of SLE � mass damping parameter instead of limit on the lateral
acceleration
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18
LOAD M
ODELS
Pedestrian loads and dynamic performances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. – 1 Oct.2008, Taormina
Pedestrian loads and dynamic perform
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/3319 Classification of load models
TIME DOMAIN FORCE MODELS
Assumption: both feet produce exactly the same periodic force
� Deterministic
� Probabilistic
general force model for each type of human activity
take into account that some parameters which influence
human force (e.g. frequency, person’s weight) are
random variables whose statistical nature should be
considered in terms of their probability distribution
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
FREQUENCY DOMAIN FORCE MODELS
considered in terms of their probability distribution
functions.
� pedestrian loads modelled as random processes
� walking forces represented by power spectral densities (PSD)
Pedestrian loads and dynamic perform
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/3320 Single pedestrian load model
∑=
−+=n
i
vertipvertivert tfGGF1
,, )2sin( ϕπα
∑=
−=n
i
latiplatilat tfGF1
,, )sin( ϕπα
vertical
lateral
G = 700 N pedestrian weight
αi = Dynamic Load Factor (DLF) of the ith harmonic
∑=
−=n
i
longiplongilong tfGF1
,, )2sin( ϕπα longitudinal
Framework: Fourier decomposition of the three force components
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
Load models in codes and guidelines usually considers only the first harmonic and
the resulting sinusoidal force is applied in resonance to the footbridge natural
mode of interest
vertical
lateral
longitudinal
Bachmann & Ammann (1987)
Pedestrian loads and dynamic perform
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/3321 Crowd load models: framework
ψπ ⋅⋅= nftFtF )2sin()(
Assumption:
the action of a group of pedestrians or a crowd is generally modelled by
multiplying the action of a single pedestrian by an effective number of
pedestrians neff
effective number
of pedestrians
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
ψπ ⋅⋅= effnftFtF )2sin()( 0
action of a single
pedestrian
reduction
coefficient
The action should be applied in resonance with the footbridge natural frequency
DLF0 ⋅= GF
Vertical Longitudinal Lateral
SETRA - SYNPEX
UK N.A. EN1991-2
F0 [N]
280 140 35
280 (walk) – 910 (jogging) - -
Pedestrian loads and dynamic perform
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/3322 Effective number of pedestrians
It can be interpreted as a synchronisation factor � it represents the percentage of
people in the crowd that, by chance, walk in step
nneff =Matsumoto et al.
(1978)
Uncorrelated pedestrians
ISO 10137
� This model is not suitable to model SLE
arriving on the bridge with a Poisson distribution, with resonant frequencies and random phases
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
SETRA – SYNPEX ξnneff 8.10= for d<=1 P/m2
nneff 85.1= for d>=1.0 P/m2
from probabilistic assumptions:
� account for synchronisation due to
high density
number of pedestrians who, walking in step with the footbridge
natural frequency and equally distributed along the deck,
produce the 95% fractile of the peak acceleration due to
random pedestrian streams.
Pedestrian loads and dynamic perform
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/3323 Reduction coefficient
Reduction factors to account for the probability of occurrence of step frequencies
First harm.Second harm.
longvert ,ψlatψ
SETRA – SYNPEX
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
Second harm.
UK N.A. EN1991-2 )( vfk
vf
Population factor
Only for vertical vibration
Pedestrian loads and dynamic perform
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/3324 Load distribution along the deck
The distributed oscillating loading should be applied in order to obtain the most
unfavourable effect � the amplitude of the load has the same sign as the mode
shape configuration
Pulsating force F[N] moving across the span at constant speed v
Single pedestrian or group:
Crowd:
Pedestrian loads and dynamic perform
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F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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Setra (2006)
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25
EXPERIM
ENTA
L TESTS
Pedestrian loads and dynamic performances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. – 1 Oct.2008, Taormina
Pedestrian loads and dynamic perform
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/3326 Objectives of tests
� the intensity of the force exerted by a pedestrian on a rigid surface
� the intensity of the force exerted by a pedestrian on a moving
surface
� the probability that a pedestrian synchronises to the motion of the
walking surface
Measurement of:
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
� the frequency and velocity of people walking
� the crowd characteristic quantities (e.g. density, velocity)
� the probability of synchronisation among pedestrians
done
partially done
to be done
Pedestrian loads and dynamic perform
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/3327 Force on a rigid surface: laboratory tests
FORCE PLATE
four tri-axial force sensors
that measure the force
acting between the foot
and the ground in 3 axes:
X Y
Z
TREADMILL
transverse (X),
anteroposterior (Y)
and vertical (Z).
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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INSTRUMENTED SHOES
Sole with force transducers, allows to measure vertical
forces during gait over a great number of steps
TREADMILL
Pedestrian loads and dynamic perform
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/3328 Force on a moving surface and lock-in: laboratory tests
Treadmill laterally moving with different frequencies and amplitudes � measure the
force on a moving platform and estimate the degree of synchronisation
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
Pizzimenti, 2005University of Reggio Calabria
SETRA, 2006
7m-long platform to recreate the same condition of a footbridge
Pedestrian loads and dynamic perform
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/3329 Pedestrian-structure synchronisation: field tests
� measure the footbridge dynamic response to different crowd conditions and the
triggering of the lock-in
� measure the pedestrian lateral motion
Nakamura & Kawasaki, 2003 M-bridge, Japan
London Millennium Bridge 2001
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
ina
Passerelle Simone de Beauvoire, 2006, Paris
Pedestrian loads and dynamic perform
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/3330 Crowd characteristic quantities
Available techniques:
� Counting: flow measured by counting the number of persons at a
specific cross-section in a certain time interval; speed and
frequency measured by noting down the number of steps
and time taken by randomly selected pedestrians to cross
a given length.
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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measure velocity, step frequency, step length
count people moving across a line, extract complete
pedestrian trajectories.
� Videos:
� GPS:
� Infrared:
observation to measure crowd density and velocity.
Pedestrian loads and dynamic perform
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/3331 Synchronisation among pedestrians
� measure the motion of pedestrians’ heads and the motion of the deck
� allow the percentage of synchronised pedestrians to be estimated
Observation of videos recorded during crowd events
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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T-bridge, Fujino et al. 1993
Pedestrian loads and dynamic perform
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/3332 What has to be done
� Measure the probability of synchronisation among pedestrians as a
function of the crowd density
� Measure the way in which walking velocity (and frequency) are
modified by the motion of the walking surface
� Measure the forces exerted on real footbridges for different crowd
conditions
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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conditions
Adaptation of W.I.M. to pedestrian loads?
Critical aspects:
� Pedestrians do not walk in lanes
� More than 1 pedestrian in the same deck cross-section
� Need to measure the lateral force component
Pedestrian loads and dynamic perform
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/3333 Conclusions
� Footbridge serviceability under human-induced excitation is still an open
research topic;
� Standard codes are still based on outdated assumptions, while design
guidelines provide new design methodologies, load models and comfort
criteria;
� Human-structure interaction is a complex phenomenon: it need further
Pedestrian loads and dynamic perform
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F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
ct.2008, Taorm
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� Human-structure interaction is a complex phenomenon: it need further
research to be deeply understood with contributions from different
research fields
� Need for experimental tests to
� propose and validate load models
� statistichally characterise pedestrian walking behaviour (e.g. velocity,
frequency, synchronisation, etc.)
Pedestrian loads and dynamic perform
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/3334 A proposal for a different approach for SLE
� Description of the synchronous lateral excitation phenomenon through the
proposal of a crowd-structure interaction model;
� model the crowd as a dynamical system instead of as a simple load.
ttt ∆+=
The model is based on:
� PARTITIONED APPROACH
� decomposition of the dynamic coupled system into two subsystems
� “TWO-WAY” INTERACTION
Pedestrian loads and dynamic perform
ances of lively footbridges: an overview
F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O
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FORCE MODELStructure-to-Crowd
action
Crowd-to-Structure
action
ttt ∆+=
CROWD
STRUCTURE
VENUTI F., BRUNO L., BELLOMO N., Crowd dynamics on a moving platform: mathematical modelling and application to lively footbridges, Math. Comput. Model., n. 45, 2007
Pedestrian loads and dynamic perform
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/3335 A proposal for a different approach for SLE
function of the footbridge lateral acceleration and of the ratio between the step and the structure frequency
=F
psF
F
+
Component due to n pedestrians
Component due to nps pedestrians
synchronised to the structure
psps nSn =z&&
Force due to n pedestrians
FORCE MODEL VENUTI F., BRUNO L., P. NAPOLI, Pedestrian lateral excitation on lively footbridges: a new load model, SEI vol. 17 n.3, 2007
Pedestrian loads and dynamic perform
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function of the crowd density
ppF
sF
+
Component due to npp pedestrians
synchronised to each other
)1( pspppp SnSn −=
Component due to ns uncorrelated
pedestrians
pppss nnnn −−=