Pedestrian Loads and Dynamic Performances of Lively Footbridges an Overview

Pedestrian loads and dynamic perform

ances of lively footbridges: an overview

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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


F. Venuti,, L. Bruno, CSHM-2, 28 Sept. –1 O

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Fiammetta Venuti

Luca Bruno

Politecnico di Torino (Italy)Department of Structural Engineering and Geotechnics



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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




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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



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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)




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London Millennium Bridge opening day, July 2000Auckland Harbour bridge, 1975

already reported from the Seventies)



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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




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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



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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




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� Comfort criteria

� Pedestrian load models

� single pedestrian

� groups of pedestrians

� crowds

� Experimental tests

� laboratory tests

� field tests

Pedestrian loads and dynamic performances of lively footbridges: an overview

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/33

6

PHENOMENOLO

GICAL A

NALYSIS


F. Venuti,, L. Bruno, CSHM-2, 28 Sept. – 1 Oct.2008, Taormina



/33

7Pedestria

n walking on a rig

id su

rface

100

50

Ex

p.

Theo

r.

Number of people

lpF

HF

L

FV

FVF

V



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




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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:




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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:




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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





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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




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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



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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]




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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



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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




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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




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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



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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




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� Comfort criterion on synchronous

lateral excitation:

pedestrian

bridge

m

mD

ξ=

Pedestrian excitation mass damping parameter

k4=1 exposure factor



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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




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� 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





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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




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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)



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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




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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)



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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




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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) - -



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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




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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.



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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




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Second harm.

UK N.A. EN1991-2 )( vfk

vf

Population factor

Only for vertical vibration



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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:




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Setra (2006)



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EXPERIM

ENTA

L TESTS





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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:




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� 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



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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).




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INSTRUMENTED SHOES

Sole with force transducers, allows to measure vertical

forces during gait over a great number of steps

TREADMILL



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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




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Pizzimenti, 2005University of Reggio Calabria

SETRA, 2006

7m-long platform to recreate the same condition of a footbridge



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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




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Passerelle Simone de Beauvoire, 2006, Paris



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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.




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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.



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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




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T-bridge, Fujino et al. 1993



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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




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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



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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




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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.)



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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




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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



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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




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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 −−=

Documents

Pedestrian Loads and Dynamic Performances of Lively Footbridges an Overview