LONDON MILLENNIUM BRIDGE: PEDESTRIAN-INDUCED
LATERAL VIBRATION
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By Pat Dallard,1 Tony Fitzpatrick,2 Anthony Flint,3 Angus Low,4 Roger Ridsdill Smith,5
Michael Willford,6 and Mark Roche7
ABSTRACT: The London Millennium Footbridge is located across the Thames River in Central London. At its
opening on June 10, 2000, the bridge experienced pedestrian-induced lateral vibration. Observations on the day
of opening and studies of video footage revealed up to 50 mm of lateral movement of the south span and 70
mm of the center span. The north span did not move substantially. The bridge was closed on June 12, 2000,
pending an investigation into the cause of the unexpected lateral movements. This paper highlights the phenomenon of pedestrian-induced lateral vibration on footbridges and the current state of knowledge of the lateral
loading effect. Modification of the bridge, introducing extensive passive damping, is currently underway with
completion scheduled for the end of 2001.
INTRODUCTION
The highly publicized closure of the London Millennium
Footbridge due to excessive lateral vibration at its opening on
June 10, 2000 has highlighted a potentially critical loading
effect not currently considered in adequate detail in international bridge design codes. This paper highlights to designers
the phenomenon of laterally-induced pedestrian forces. The
initial design of the bridge was completed by Arup in 1999.
The retrofit, currently under construction and due for completion at the end of 2001, has also been designed by Arup.
This paper does not include either details of the static or
dynamic analysis, wind tunnel testing, performance criteria
used in the design of the bridge, or descriptions of its behavior,
as this is not the intention of the paper. It should, therefore,
be recognized that this paper is not intended as anything close
to exhaustive—other more detailed papers will be published
at a later data once construction is complete and restrictions
are lifted. Further information can be obtained from the authors on an individual basis.
Finally, it is highlighted that the bridge represents an extreme in its form and it therefore does not fall directly within
the limits outlined in many codes. Comparisons to code provisions, as included in the text following, are therefore included for information purposes only—as benchmarks. Analysis and design of the bridge was conducted on a performance
rather than a prescriptive basis.
DESCRIPTION OF THE BRIDGE
The bridge site is located across the Thames River in Central London and links two features of London that have become the city’s leading tourist attractions: St. Pauls Cathedral
and the new Tate Gallery (Fig. 1).
The bridge is a shallow suspension structure crossing the
Thames in London. The total width of the river crossing between the abutments is 332 m (1,088 ft), is divided into a
central span of 144 m (472 ft), a northern span of 80 m (263
ft), and a southern span of 108 m (353 ft). The cable geometry
is such that:
• The 4 cables on each side of the bridge are arranged side
by side.
• The central span cable dips 2.3 m (7.5 ft).
• The centerline of the cables move 1.73 (5.66 ft) towards
the center of the bridge in plans at midspan.
The cables are anchored at each abutment so that they are
free to rotate, but are fixed against translation in any direction.
Over each saddle on the river piers, the cables are allowed to
slide during construction in order to ensure that the out-ofbalance forces in the river piers due to the dead load are minimized. Thereafter, they are fixed against translation but are
free to rotate in any direction.
The 4.0 m (13.1 ft) bridge deck is supported solely by the
cables at 8.0 m (26.2 ft) intervals, which does not touch the
piers as it passes between the V brackets. The deck edge members are pinned; they are free to slide in the direction of the
bridge span at 8.0 m intervals but fixed against translation in
the other two directions.
Each river support comprises a prefabricated steel V bracket
that supports the cable saddles, is fixed to a reinforced concrete
elliptical pier supported on driven steel tubular piles, and that
cantilevers from the pier pilecap situated just below the elevation of the riverbed. The abutments are founded on groups
of bored, cast-in-place concrete piles. Loads are applied to the
piles using deep reinforced concrete pilecaps.
1
Assoc., Arup, 155 Avenue of the Americas, New York, NY 10013.
Dir., Arup, 155 Avenue of the Americas, New York, NY 10013.
Dir., Consultant, Flint & Neill Partnership, Dartmouth Street, London,
UK.
4
Dir., Arup, 155 Avenue of the Americas, New York, NY 10013.
5
Assoc., Arup, 155 Avenue of the Americas, New York, NY 10013.
6
Dir., Arup, 155 Avenue of the Americas, New York, NY 10013.
7
Assoc., Arup, 155 Avenue of the Americas, New York, NY 10013.
Note. Discussion open until May 1, 2002. To extend the closing date
one month, a written request must be filed with the ASCE Manager of
Journals. The manuscript for this paper was submitted for review and
possible publication on June 4, 2001; revised July 10, 2001. This paper
is part of the Journal of Bridge Engineering, Vol. 6, No. 6, November/
December, 2001. 䉷ASCE, ISSN 1084-0702/01/0006-0412–0417/$8.00
⫹ $.50 per page. Paper No. 22594.
2
3
FIG. 1(a).
412 / JOURNAL OF BRIDGE ENGINEERING / NOVEMBER/DECEMBER 2001
J. Bridge Eng., 2001, 6(6): 412-417
London Millennium Bridge Looking North
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OBSERVATION ON THE OPENING WEEKEND
FIG. 1(b).
London Millennium Bridge Looking South
The bridge was open for three days, between Saturday, June
10 and Monday, June 12. At times it was very crowded, with
about 2,000 people along its length, at densities of between
1.3 and 1.5 people per square meter. An estimated 80,000–
100,000 people crossed the bridge on the opening Saturday.
When the bridge was crowded, movement of the south and
center spans became sufficient enough that pedestrians had to
hold onto the balustrades, or stop walking to retain their balance.
The movement of the south span, between Bankside and the
first river pier, was a combination of horizontal and torsional
(twisting) oscillations. Observations on that day and studies of
video footage show that up to 50 mm (2 in.) of lateral movement occurred, although this depended on the number of people walking along the bridge. The frequency of the movement
was about 0.77 cps. The center span moved by 70 mm (3 in.)
at a frequency of 0.95 cps, mainly in the horizontal plane. This
part of the bridge was observed to oscillate when occupied by
more than about 200 people. The north span did not move
substantially.
It was decided to limit the rate at which people could cross
the bridge, and access was limited from noon onward on that
Saturday. The main concern was the safety of individuals when
movements became uncomfortable, rather than any risk of
structural failure of the bridge itself. Arup is not aware of any
injuries to members of the public over the opening weekend,
even during the times when the movement was the greatest.
The bridge was closed on June 12, pending an investigation
into the cause of the unexpected movements.
DESCRIPTION OF THE LOADING EFFECT
FIG. 1(c).
London Millennium Bridge River Pier
It is well known that a pedestrian applies dynamic forces to
the surface on which he/she walks. The vertical component is
applied at the footfall frequency (typically around 2 Hz) and
is about 40% of their body weight. The lateral component is
applied at half the footfall frequency and on a stationary surface is about 10 times smaller than the vertical component.
Structural engineers have paid more attention to the vertical
components of the dynamic forces, since almost all documented problems with footbridges and floors have been associated with vertical forces and vibrations. There are codes
describing how to assess and design for these effects; whether
these codes are adequate is discussed further in a later section.
However, what was seen at the Millennium Bridge was
caused by a substantial lateral-loading effect, which appears
to arise in the following way. Chance footfall correlation, combined with the synchronization that occurs naturally within a
crowd, may cause the bridge to start to sway horizontally. If
the sway is perceptible, a further effect can start to take hold.
It becomes more comfortable for the pedestrians to walk in
synchronization with the swaying of the bridge. The pedestrians find this makes their interaction with the movement of the
bridge more predictable and helps them maintain their lateral
balance. This instinctive behavior ensures that the footfall
forces are applied at a resonant frequency of the bridge, and
with a phase such as to increase the motion of the bridge. As
the amplitude of the motion increases, the lateral force imparted by individuals increases, as does the degree of correlation between individuals. This frequency ‘‘lock-in’’ and positive force feedback caused the excessive motions observed at
the Millennium Bridge.
FREQUENCY RANGE
FIG. 1(d).
London Milllennium Bridge Sofit
Normally individuals crossing a footbridge will walk at their
own forward speed and footfall rate. However, if a bridge is
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J. Bridge Eng., 2001, 6(6): 412-417
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very congested this is not possible, and the mass of people
must move at a similar forward speed, generally slower than
the average speed at which free individuals would walk.
The typical footfall rate for purposeful walking is around 2
steps per second. In large crowds and in the absence of vibrations this rate drops to 1.4 steps per second or lower. This
means that the vertical forcing frequency is generally in the
region of 1.2–2.2 Hz. Since alternate footsteps apply forces
in opposite lateral directions, the predominant lateral forcing
frequencies are half of these values, so are in the range of
0.6–1.1 Hz. When locked-in to a lateral vibration mode within
this frequency range, the pedestrian footfall rate will tend to
be twice the lateral frequency of the bridge, even though this
footfall rate may not be typical for that crowd density.
On the Millennium Bridge, even the lowest lateral mode at
0.475 Hz was excited. It is possible that low frequencies are
excited by pedestrians adopting a snaking walk, again to help
them balance, but with a footfall rate higher than twice the
frequency of the lateral vibration mode.
PREVIOUS OBSERVATIONS OF THIS BEHAVIOR
It appears little has been recorded of this phenomenon in
the literature. A documented case is that of a footbridge in
Japan connecting a sports facility to a bus terminus. The bridge
suffered strong lateral motions when crowds crossed it at the
end of an event (Fujino et al. 1993).
More recently, it appears that lateral vibrations were among
several reasons behind the closure of the new Solferino Bridge
in Paris immediately after its opening in December 1999. A
100 year-old footbridge in Ottawa experienced strong lateral
vibrations in July 2000, also when subjected to crowd loading,
in this case by spectators of a fireworks display.
Since the opening of the Millennium Bridge we have received reports of some other footbridges that appear to have
exhibited strong lateral vibrations. None of these incidents is
recorded in the technical literature.
3.0 Hz. This, however, can be omitted if it is shown that the
minimum supported structure weight is greater than that which
can be calculated from the formula provided. Should this formula have been the only criterion adopted for the Millennium
Bridge, vibration would not have been identified as in need of
further attention. The specification is therefore in need of modification to account for the range of the vibration phenomena
observed at the Millennium Bridge.
Other codes, notably the British (BSI 1978) and Ontario
(Ontario 1983) code, contain clauses that limit the acceleration
(0.25 m/s2) that can be experienced by a single pedestrian.
Each of these codes was analyzed in the design of the bridge
prior to construction for which the results indicated acceptable
behavior, contrary to that which occurred.
ACCEPTANCE CRITERIA
Existing criteria defining acceptable limits to dynamic motion of footbridges relate to pedestrian comfort. For bridges
these have been derived from subjective tests, mainly for vertical movement at frequencies above 1 Hz. Vertical acceleration limits, determined from testing, are typically in the range
of 0.5–1.0 m/s2 (1.6–3.2 ft/s2). Criteria for lateral motion are
less well developed, but we consider values in the range of
0.2–0.4 m/s2 (0.65–1.3 ft/s2) to be appropriate.
RESEARCH REQUIRED
In order to develop design rules suitable for codification,
further research is required. A fundamental understanding of
the loading effect would require the following to be quantified:
• the variation in walking speed, footfall rate, and footstep
synchronization in crowds crossing bridges
• the probability of pedestrian footfall frequency lock-in as
a function of the amplitude and frequency of bridge motion, for a range of initial pedestrian footfall rates
• the effective lateral excitation forces induced by pedestrians as a function of frequency and amplitude of bridge
motion
• the reduction in correlation in higher order modes, due to
the pedestrians having to change phase as they move from
one half-wavelength to the next, if they are to remain
correlated
CURRENT STATE OF KNOWLEDGE OF THE LATERAL
LOADING EFFECT
Loading effect parameters are not well quantified. While the
literature reports a few measurements of the magnitude of lateral forces due to walking, these are all made on unmoving
surfaces. We have not found any conclusive documented measurements of the effect of motion of a walkway on the magnitude of footfall forces, nor of the magnitude of motion at
which lock-in occurs. However, our own observations indicate
that a significant proportion of pedestrians can start to lock-in
when the amplitude of the walkway motion is only a few millimeters. Lock-in is generally not achieved perfectly and individuals readjust their footfall rate and phase periodically to
maintain comfortable walking.
Fujino (1993) provides some tentative design force values.
These are based on back-calculation of the measured response
of a bridge. Eurocode 5 (CEN 1995) includes pedestrian loading models and acceleration limits, for both vertical and lateral
vibrations. The provisions for vertical vibration were derived
using a combination of theory and experiment. The lateral provisions were not based on experimental data, but were inferred
from the provisions for vertical vibration.
We have performed tests on the Millennium Bridge that
show that for dense pedestrian traffic both references would
significantly underestimate the effective lateral dynamic loading. The tests also show that the lateral loading increases with
bridge response, indicating a potential for instability.
The AASHTO (1997) guide specification for the design of
pedestrian bridges recommends a dynamic performance evaluation of bridges with a fundamental frequency of less than
It is recognized that there will be considerable variation of
these parameters between individuals and in different circumstances. It is likely that a statistical description would be required. Studies into these effects were initiated as part of our
work to design measures to reduce the motions of the Millennium Bridge. Work has been carried out at Imperial College,
London; at the Institute of Sound and Vibration Research,
Southampton; and at the University of Sheffield.
We are wary of the difficulties involved in assembling a
fundamental model for this loading effect. For practical purposes, it is likely that the correlated dynamic force can be
quantified most readily by back-analysis from actual bridge
motions recorded during the passage of a crowd.
Preparation of design guidance for the effect is currently
under consideration by the CEN Project Team for drafting
European Codes.
ASSESSMENT OF VULNERABILITY
OF FOOTBRIDGES
In view of the range of frequencies at which horizontal footfall forces are applied, footbridges with lateral natural frequencies below 1.3 Hz are potentially the most vulnerable to
being excited into excessive lateral vibration. In practice, many
414 / JOURNAL OF BRIDGE ENGINEERING / NOVEMBER/DECEMBER 2001
J. Bridge Eng., 2001, 6(6): 412-417
longer span pedestrian bridges are likely to have a natural
mode in this frequency range and their frequencies may be
modified by the presence of crowds.
The damping required in a potential problem mode is proportional to the number of pedestrians and inversely proportional to mass. Hence, the vulnerability of a bridge is increased
if its mass and damping are low, and most importantly, if it is
subject to use by crowds of people.
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INDICATIVE QUANTITATIVE INFORMATION
It may be useful to give some quantitative information on
the solution developed for the Millennium Bridge. The solution is based on a crowd density of 2 people per m2 and provides more than 18% critical damping in the lateral modes
below 1.3 Hz. This level of damping limits the lateral accelerations to 0.2 m/s2 under an effective correlated lateral dynamic load of 20 N (5 lbs) per person. This acceleration limit
and corresponding design load were chosen to ensure both
comfort and stability. The degree of damping is a reflection of
the need to cover all possible normally and deliberately induced vibration—as the bridge vibrations on initial opening
were well publicized, control of the behavior of the bridge
under extreme ‘‘vandal’’ conditions has been included in the
solution adopted.
We shall be collating and publishing the research work as
soon as possible to allow more widespread discussion, along
with detailed descriptions of the proposed solution and options
considered for the modification works to the Millennium
Bridge itself. Meanwhile, we would be pleased to make information available to designers currently involved in projects
that might be affected.
person due to lateral spacing of the feet and the inclination of
the cables are a very small fraction of those shown to be exerted horizontally by the feet. The static weight of a pedestrian
or group of pedestrians crosses a span over a period of at least
40 s, so this effect is essentially static and cannot cause a
resonant response.
During the investigations of the Millennium Bridge a number of other instances of bridges suffering excessive lateral
vibration under crowd loading have been brought to our attention. The forms of some of these bridges are shown in Fig.
2. It can be seen that the structural forms have nothing in
common with that of the Millennium Bridge, or with each
other. There is, therefore, good reason to suppose that this
problem can exist on a footbridge of any structural form. All
that is required is that there is a lateral mode of a low enough
natural frequency, i.e., below around 1.3 Hz, and that the
bridge is subjected to traffic by a sufficiently large crowd of
pedestrians. Fig. 3 shows the lateral natural frequencies reported in the literature for a number of footbridges, as a function of span. It can be seen that the natural frequencies of the
Millennium Bridge span are quite normal; it does not have
particularly unusual dynamic properties.
Why, therefore, are problems of excessive lateral vibration
not seen more often on footbridges and why has this effect
not been picked up by the Code Committees or in the design
literature? The answer may lie in the results of the tests into
pedestrian loading commissioned in order to develop a solution for the Millennium Bridge. It has been shown clearly in
the laboratory that the magnitude of lateral force imparted by
a pedestrian increases as the sway motion of the walkway
RELEVANCE OF MILLENNIUM BRIDGE
STRUCTURAL FORM
The Millennium Bridge is a tension ribbon bridge and the
geometric stiffness of the cables provides almost all of the
stiffness of the bridge in both the vertical and lateral directions. It is therefore necessary for geometric change to occur
as the bridge responds to any applied loads. The question of
lateral torsional response to eccentrically applied vertical loads
was studied and understood by the design team during the
design process. The dynamic properties of the bridge (natural
frequencies, modal masses and mode shapes) measured by an
extensive modal testing program were determined to be very
similar to those predicted at the design stage; this includes
coupling of lateral and torsional motions in some modes.
The excess lateral vibration was a resonant response with
the resonant lateral motions caused almost entirely by dynamic
forces exerted horizontally by pedestrians. When walking in a
straight line the lateral forces imparted by a pedestrian occur
at half the footfall rate. This frequency range is therefore typically 0.7–1.0 Hz. We have also observed that people moving
over the lowest frequency mode on the bridge (0.48 Hz) adopt
a slightly meandering path, instinctively changing direction
slightly every 3 or 4 footfalls. This behavior is similar to that
of someone walking along the deck of a rocking ship, which
means that lateral modes with natural frequencies lower than
half the footfall rate can also be susceptible to pedestrian excitation.
Generation of response requires the repeated application of
forces at a frequency close to the natural frequency of the
mode in question. The modes in which this behavior was observed on this bridge have frequencies of 0.48, 0.78, 0.95, and
1.05 Hz. Alternate footfall vertical forces could have been applied at these frequencies by pedestrians creating a resonant
torsional input. However, calculations for the Millennium
Bridge show that the resulting fluctuating lateral forces per
FIG. 2(a).
Alexandra Bridge, Ottawa, Canada
FIG. 2(b).
T-Bridge, Tokyo, Japan
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J. Bridge Eng., 2001, 6(6): 412-417
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increases. The probability that a pedestrian will notice the motion of the walkway and synchronize his/her footfall rate to
that of the walkway motion also increases with increasing
walkway amplitude. The lateral forces induced by a crowd
increase strongly with increasing motion of the bridge. This
leads to a highly nonlinear overall loading effect from a crowd
of pedestrians.
FIG. 2(c).
Queens Park Bridge, Chester, U.K.
The controlled tests on the Millennium Bridge during December 2000 demonstrates very clearly an effect predicted using a nonlinear model. A group of people were instructed to
walk in a circulatory route on one span of the bridge. The
number of people in the group was gradually increased and
the lateral motion of the bridge observed. The acceleration
time history during a typical test is shown in Fig. 4. It can be
seen that the dynamic response of the bridge is stable until a
critical number of people are walking, and then it increases
very rapidly. The same pattern of behavior was observed during tests on each of the spans in turn.
The implication of this effect is that unless a particular
bridge has experienced its critical number of pedestrians there
will not have been any evidence that there may be a potential
problem. Many bridges, which have been in place for years
and have only experienced moderate pedestrian traffic, will be
considered perfectly acceptable. However, if they were to be
loaded by perhaps only a slightly greater pedestrian density
they could suffer strong lateral vibrations.
This sequence is what happened on the Inter-Provincial road
bridge in Ottawa, which swayed strongly when loaded by
crowds of pedestrians after a fireworks display in July 2000
(a few weeks after the Millennium Bridge opened). This bridge
(Fig. 2) had been in service for 100 years before this event.
Similarly, the Queen’s Park Bridge in Chester (Fig. 2) was
opened in 1923. It existed uneventfully until a rowing regatta
took place beneath it in 1977, when it experienced strong lateral motions.
We have concluded that the observed excessive lateral motion of the Millennium Bridge was not caused by the particular
structural form of the bridge, but was due to the combination
of the high pedestrian density and the presence of lateral
modes of vibration below 1.3 Hz. The same two factors in
combination could cause similar motions on any other footbridge of whatever form.
SOLUTION
FIG. 2(d).
Pont du Solferino, Paris, France
FIG. 3.
The solution for the Millennium Bridge has been to add a
large amount of damping, which increases the critical number
of pedestrians required to cause excessive response beyond the
number that can physically walk across the bridge. This solution has been accompanied by several physical investigations
both on the bridge itself and at various academic institutions
Lateral Natural Frequencies of Bridges
416 / JOURNAL OF BRIDGE ENGINEERING / NOVEMBER/DECEMBER 2001
J. Bridge Eng., 2001, 6(6): 412-417
many persons crossing the bridge together must be catered for
in the design. The appropriate combination of modal mass and
damping can then be determined.
The Millennium Bridge is unusual in that its spectacular
form and location will ensure large numbers of people will
want to cross. Hence, we have taken the physical walking
capacity of the bridge as our design case. In many other cases
this could be considered an unnecessarily high level, although
the reactions of client bodies to this decision is as yet untested.
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ACKNOWLEDGMENTS
FIG. 4.
Lateral Acceleration of Bridge Deck and Number of Pedestrians
to further quantify the loading, investigate and evaluate solutions, and determine the final arrangement and magnitude of
dampers. Design of the dampers and an implementation program was completed in February of 2001 and presented to the
client body for approval. Construction and final testing are
scheduled for the winter of 2001.
Details of the solution will be presented as part of other
publications.
CONCLUSION
Designers must be made aware of the need to maintain lateral bridge frequencies above 1.0 Hz. Where stiffening to raise
the lowest lateral frequency above 1.3 Hz is not an option,
then designers and their clients will need to decide on how
In carrying out this work, we have been very grateful for the collaboration of Prof. Bachmann of the Swiss Federal Institute of Technology,
Zurich; Prof. Fujino of Tokyo University; and Prof. Kreuzinger of the
Technical University, Munich.
REFERENCES
American Association of State Highway and Transportation Officials
(AASHTO). (1997). Guide specification for design of pedestrian
bridges, Washington, D.C.
British Standards Institution (BSI). (1978). ‘‘British Standard Specification for loads; Steel, Concrete and Composite Bridges, Part 2.’’ BS
5400, London.
European Committee for Standardization (CEN). (1995). ‘‘Design of timber structures, DD ENV 1995-1-1.’’ Eurocode 5, Brussels.
Fujino, Pacheco, Nakamura, and Warnitchai. (1993). ‘‘Synchronisation of
human walking observed during lateral vibration of a congested pedestrian bridge.’’ Earthquake Engineering and Structural Dynamics,
Vol. 22, 741–758.
Ontario Highway Bridge Design Code. (1983). Ministry of Transportation
and Communications, Highway Engineering Division, Ontario.
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