James Boam jdb21@bath.ac.uk

Proceedings of Bridge Engineering 2 Conference 2007 27 April 2007, University of Bath, Bath, UK

CRITICAL ANALYSIS OF THE LONDON MILLENNIUM FOOTBRIDGE

James D. Boam

University of Bath

Abstract: This paper is a subjective assessment of the aesthetics, choice of design, construction method and refinements of the Millennium Bridge in London. The paper explains what caused lateral vibrations in the bridge earning it the name ‘The Wobbly Bridge’ and how this problem was rectified. In addition the success of the bridge and its affect upon London will be discussed. The paper also contains simplified calculations in order to perform a basic structural analysis of the bridge.

Keywords: London Millennium Bridge Suspension Bridge Lateral Vibrations Aesthetics

1 Introduction

The Millennium Bridge in London is a steel footbridge across the River Thames between the Southwark Bridge, downstream, and Blackfriars Railway Bridge, upstream. The bridge is a suspension bridge and runs from the Tate Modern on the south bank towards St. Paul’s Cathedral north of the river. The bridge was originally opened in June 2000 but shut soon after due to unexpected swaying. After modifications and testing, the bridge was reopened in February 2002.

2 Bridge Aesthetics

Analysis of the Millennium Bridges’ aesthetic qualities shall be done by considering Fritz Leonhardt’s ten areas of aesthetic design.

2.1 Fulfilment of Function

To satisfy this aspect of bridge aesthetics it must be clear when looking at the bridge how the structure works. Unfortunately with this bridge it is not particularly clear how the bridge works. The shallow profile and suspension cables running beneath the level of the deck makes them hard to see which is unlike most other suspension bridges

which are dominated by tall towers and noticeable main cables.

Without the clear load paths that are seen on most suspension bridges it would not be unreasonable for users to assume that this bridge was long, slender and unsupported along its spans. From an engineering point of view it is difficult, despite the subtle nature of the cables, to look at the cables and not instantly appreciate their structural importance.

Figure 1: Slender profile of the bridge makes its structure

less conspicuous

2.2 Proportions of the Bridge

The shallow profile of the bridge is easy on the eye. The cables running both above and below the level of the deck does not make the bridge appear unusually thick as plenty of light is allowed to pass through the cables and deck connections.

The piers for the bridge are thick concrete to protect the bridge from collisions with boats. This has the potential to spoil the proportions of the bridge but is cleverly avoided by using elliptical shaped piers. Here the slender appearance from the side is maintained, but as the bridge is viewed along its length the shape of the piers keeps the bridge in proportion.

None of the bridge members look oversized, with a nice transition in thickness being achieved on the columns that connect the concrete pier to the rest of the bridge.

The low profile of the bridge aids in preventing shadow upon the bridge. . With no towers or cables above the line of the deck it prevents casting the bridge areas of the bridge into shadow. Shadowed regions along the bridge would be undesirable due to the metallic finish and this shows a lot of attention has been devoted to combining the structure and aesthetics.

2.3 Order

The main cables of the bridge follow an elegant parabolic shape between the piers and gently fall down to their anchors at each end of the bridge. The cables do not only curve in a vertical direction, when viewed head on they curve horizontally too. This adds shape to the bridge from all angles but keeps the overall appearance smooth on the eye.

The connections between the main cables and the deck sections are regular but not so close that they make the bridge look busy. As the connections gently rotate from the vertical along the length of the bridge it helps to move the eye across the whole bridge.

The rounded piers and column forks help with the smoothness of the bridge and the continuity of curved edges and surfaces.

Figure 2: Elegant Shape of the bridge

2.4 Refinements

The innovative feature of this bridge is its low profile considering it is a suspension bridge. This allows for clear views up and down the River Thames and of buildings on

both sides of it. There is little thickness to the bridge as it is steel so there are few visibility issues.

The piers have been tapered which avoids them looking thicker at the top than the base and the central span is much larger than the side spans. The structure of the bridge and its setting do not leave it susceptible to finer aesthetic issues.

2.5 Integration into the Environment

Throughout London there is a large variation in architectural styles based on the cities development through time. The bridge compliments some of the nearby buildings, the modern offices and apartments, and in the skyline to the north the impressive modern financial buildings of the city.

In contrast, the bridge stands out wildly to the nearby Globe theatre and St. Paul’s Cathedral that it points to in the north. The metallic surface of the bridge is wildly dissimilar to the timber framework ad thatched roof of the Globe and the masonry cathedral.

The bridge is right in front of the Tate Modern gallery and this is the perfect setting for the bridge. The contemporary styling of the bridge almost warrants it being classed as art and is an ideal route into the gallery.

The bridges boldness and diversity is the reason why it fits into the surroundings. The mesh of different architectural styles within London means that by being ‘of the time’ it integrates very well into the environment.

Figure 3: Millennium Bridge in front of the Globe theatre

and Tate Modern gallery

2.6 Texture

The bridge’s all over smooth metallic finish is striking but it is dull so the bridge does not shimmer or give off any glare when it is sunny. This contemporary finish fits in well with the ethos of the Tate Modern as mentioned before. The piers have a rough concrete finish which looks fine, but the harsh transition in finishes between the piers and the smooth metallic forked columns does not look right. For a bridge with such smooth flowing lines the abrupt cut off between the steel and the concrete does stand out, although the similar colours go some way to reduce this effect.

2.7 Colour

James Boam jdb21@bath.ac.uk

The shallow profile of the cables that run alongside the deck for a vast majority of the bridge are coloured the same as the deck so they are highlighted as little as possible. The metallic finish is an effective way of ensuring a modern appearance for the bridge and making sure that it stands out amongst many brick, masonry and concrete structures. At night, the lighting along the length of the bridge displays the ‘Blade of Light’ concept of the bridge.

Figure 4: Bridge at night showing ‘Blade of Light’

Concept

2.8 Character

Bridges with character all seem to have something unusual about them that set them apart but without being too ridiculous. The Millennium Bridge does posses a lot of character and this is down to its unusual form. It is a very flat suspension bridge and when comparing it to others it does stand out.

2.9 Complexity

The most complex feature of this bridge is the path of the main cables. They weave through both horizontal and vertical planes unlike ordinary suspension bridges which does fascinate the viewer most notably when looking along the length of the bridge. The innovative connectors between the bridge deck and the cables, although more complex, do not have the same affect. Their complexity is ignored by the viewer due to their apparent necessity.

2.10 Nature

Given the bridges setting, its modern appearance and that it is a suspension bridge it is unlikely to show any likenesses with nature. There is one similarity and it is best shown when beneath the level of the deck. The saddle shaped connectors between the deck and the cables look like vertebrae making the bridge seem like a spine.

Figure 5: Spine like underside of the bridge

2.11 Aesthetic Summary

The Millennium Bridge is an aesthetically pleasing bridge and its alternative form is fitting for both its immediate visual surroundings and the entire city of London. Although its structural function may not be entirely clear the bridge is still well proportioned and easy on the eye.

3 Design and Construction

The choice of suspension bridge to cross a body of water of this size is not an irregular one, even for footbridges. The irregularity comes in the form of the suspension bridge, and this irregular shape adds a few problems into the design and construction. As it is so slender in profile, it requires the cables to be under unusually high tensile forces. These high forces have to be transferred into the ground and will require large and therefore expensive foundations.

An arch bridge of three spans could have been used over the bridge but this would also have created large horizontal forces at the abutments. A tied arch central span, with the deck as the base, with simple beam bridge outer spans could also be used, but this would sacrifice the views. A similar problem would be encountered with a cable stayed bridge. Truss bridges would be too thick for the ‘Blade of Light’ concept the designers envisaged. For a slender deck with few piers only suspension and cable stayed bridges are an option. To maintain the views the innovative low cable suspension design works but a similar cable stayed design seems to be less feasible.

3.1 Abutments

The first stage of construction, as with almost all structures, is the foundations for the bridge piers and abutments. The foundations for the north and south abutments are both pile foundations with the sixteen piles at the north abutment and twelve piles at the south abutment. All piles are 2.1metres in diameter and are 28metres long and both sets of piles have a 3metre pile cap [1]. The horizontal forces from the cable at the north abutment are transferred to the pile cap via reinforced concrete beam which is connected to 1metre thick vertical shear walls. The proximity to the river and the need to transfer very large forces into the soil meant that footings

James Boam jdb21@bath.ac.uk

and other shallow foundations would have been impossible to use. An area in front of the abutment below the steps up to the bridge is used as a basement and car park for the nearby school which also would have limited the plan area of the foundations.

Foundations for the south abutment of the bridge were not restricted by any underground developments, but their proximity to the river and magnitude of forces meant that pile foundations had to be used. The cables posed more of a problem, as given the geometry of the bridge, the cables and bridge deck reach the position of the abutment but approximately 3.5metres above ground level. This is what has formed the ‘needle’ at the south end where the deck bifurcates and then doubles back down to ground level. Where the deck doubles back it sits on top of a large concrete ramp which is connected to the pile cap. The cables, however, are anchored back using a strut and tie. This is a clever way of gaining height without requiring extra land to bring the bridge down or materials for extra lengths of deck and cables. However, by cantilevering the cables out past the foundations, the large axial forces may try to overturn them. This is an undesirable effect as it induces moments and puts a lot of strain on the ground.

Figure 6: South Abutment and cable strut and tie

Both sets of foundations and the abutments on top of

them were constructed in situ. This is a lot more viable than trying to transport twenty-eight 28metre long piles into the centre of London.

3.2 Piers

For each of the pier foundations two 6metre diameter caissons were dug to a depth of 18metres below the river bed within a sheet pile cofferdam [2]. The caissons were backfilled with reinforced concrete and connected to the pier by a 3metre pile cap. The original design used driven pile foundations for the piers. Presumably it was decided the bulkier caissons would ensure better resistance to a collision with a vessel and provide a stiffer support for the cables.

Each pier was constructed from three prefabricated sections each 5metres tall with gradually reducing cross sections. The steel forks at the top of the piers are connected to the concrete using sleeved high strength steel bars. As the cables move away from the supports

horizontally it would have made it very difficult to have vertical piers.

Figure 7: Bridge foundations and structure

3.3 Cables

Once the foundations, piers and abutments are in place the next phase of construction is to add and anchor the cables. The cables used for the Millennium Bridge are Lock-Coil Cables. A galvanized, interlocking outer layer of wires holds all the interior trapezoidal and circular wires in position and prevents muck and grime getting in to them [3]. The choice of these cables could be an attempt to protect them from the corrosive moisture in the air, increasing their life and reducing the likelihood of replacement. Other types of cable, like wire strand core and structural core may have been a better choice. Although not as impermeable to the weather they would have been much easier to make, requiring only one or two different types of wire making it much more economical.

Figure 8: Spinning of the cables about to begin after

the piers are in place The cables themselves are all 120mm in diameter and

run in two groups of four on either side of the deck. If this is the required area of steel then the proportions of the cables are about right. Two cables on each side may have still looked reasonable but a single coil would appear oversized. A problem with having four cables on each side is that each saddle has to have four different

James Boam jdb21@bath.ac.uk

connection points on each side, which is very unusual and will add cost in fabrication. Should any of the cables be damaged, by an accident or not, the number of cables means that the structure should have more chance resisting failure.

The cables were most probably wound on site. Guide lines would lead the cable spinner over the route of the cable gradually building up the cable thickness. This seems much more practical than spinning the cable offsite and attempting to hoist it in to place and anchor it afterwards. Once completely spun and anchored back, the cables were fixed at the top of the piers using saddles. This is necessary as the piers do not add much stiffness to the deck, so under live loading the bridge would deflect a lot if the cables were allowed to slide at each pier. This also means the spans can act with some independence should a span collapse.

Figure 9: Cabling fixing at pier

3.4 Deck and Saddles

There are four main components to the bridge deck and saddles; the arms, the edge tubes, the aluminium deck and the movement joints.

The arms that connect the deck to the cables occur at every 8metres along the deck and are hollow box section. They vary in pitch to account for the cable paths and taper down from 450mm square at the deck to 225mm square at the cables [4]. The use of rigid arms instead of cables had to be done, as at parts of the bridge the cables hang below the height of the deck. Connecting cables would not be able to support the bridge as they would hold no tension. The rigid arms will have been used along the whole length of the bridge for aesthetic continuity.

Spanning between each of the arms are steel edge tubes. These hollow circular tubes are approximately 350mm in diameter and hold up the bridge deck and the bridge lighting and balustrades [5].

The aluminium deck is 4metres wide and formed from extruded box sections. As the balustrades and the lighting are directly attached to the steel edge beams, the deck only has to cope with the live load. The design of the lighting means that, even from foot level, there is enough light at night time to negate the need for overhead lights. This aids the aesthetics of the bridge tremendously and keeps the profile slender. The choice of aluminium as a bridge deck is simply a compromise. Aluminium is more resistant to corrosion to steel but is more expensive and

not as strong. This decision will have a relatively small effect on the overall cost of the project considering the extensive earth works. If it reduces the long term maintenance costs of the bridge then it may prove to be a wise decision.

The irregular path of the cables at shallow profile means that the deck gets a lot of its stiffness from the cables. This means that the deck does not to be braced to resist deflections from lateral wind loads [2]. With the cables being under so much tension and without much stiffness from the piers the deck is subject to quite large vertical deflections under live loading. To accommodate this, the bridge deck is not continuous. The deck is prefabricated into 16metre sections that are connected by movement joints. This clever design not only eliminates any stresses that would be caused by movement of the cables, but from temperature variations too. Construction is simplified too as these sections can be relatively easily slotted together. To fit these sections in place they were probably lifted into place from a barge once the cables were fitted.

Figure 10: Movement joint

Another feature of the bridge deck is the bifurcating

section as the bridge moves over the south abutment. The effective widening of the bridge reduces its torsional restraint and this is balanced by increasing the size of the steel edge beams. As mentioned before this is a sophisticated way of reducing the amount of materials and foot print of the bridge even though it creates some added problems. There is space behind the existing bridge that could have been used to bring the bridge down in a more conventional manner. The problem with this, apart from more materials, is that it takes the bridge entrance away from the south bank walkway and would detract from people using the bridge. Although not used for any particular purpose the ground behind the bridge is a nice open space in front of the Tate Modern, another possible reason not to build upon it.

4 Loading

The Millennium Bridge will have a relatively small dead load due to the lightweight deck and steel edge

James Boam jdb21@bath.ac.uk

beams. The super-imposed dead load is also relatively low as only the balustrades and tube lighting contribute to this. The live load acting on the bridge is only pedestrians as it is a footbridge. Wind was anticipated to have a minimal effect due to the deck structure and stiffness from the cables, but was modeled anyway. Temperature effects are also lessened by the deck movement joints but this still needs to be checked for differential movements and overall expansion or shrinkage. As this is a steel bridge it is unaffected by creep and can therefore be ignored.

4.1 Dead, Super-Imposed Dead and Live Loads

Some of the dimensions for different structures will have to be assumed from drawings as exact figures are unavailable [5]. Due to the voided nature of a lot of the elements of the deck, specific unit weights were also taken from technical drawings [5] and shown below. We are assuming g = 10N/Kg and that the unit weight relates to half of the bridge as there are two cables.

James Boam jdb21@bath.ac.uk

Table 1: Weight of Materials in Bridge Material Weight (kN/m) Balustrades 1.22 Aluminium Decking 1.12 Steel Edge Beams 1.24 Steel Arms 0.29 Cables 3.60

Note that the bridge cross section varies, especially where the deck bifurcates and for calculations on the individual spans more accurate dead load measurements will be taken.

For each different span of the bridge the overall dead and super-imposed dead loads are as follows. Despite the change in section the loads are assumed to act as uniformly distributed loads (U.D.L’s). The bridge spans are numbered 1 for the North span, 2 for the central span and 3 for the southern span.

Table 2: Dead and Super-Imposed Dead Loads on Each

Bridge Span Span Dead Load (kN/m) Super-Imposed Dead

Load (kN/m) 1 6.25 1.22 2 6.25 1.22 3 7.87 2.12

The bridge is designed to carry a maximum of five

thousand pedestrians. Assuming that the average person weighs 750Newtons, and taking the bridge length at 333metres it equates to a live load of 11.3kN/m.

4.2 Wind Loading

Wind loading for this project was analysed in a wind tunnel during the early design stages but a simple worst case check can be performed. The movement joints in the deck should allow for deflections due to the wind, it shall be assumed that they have all seized up. The analysis treats the wind acting as a point load on the centroid of the section of the bridge being analysed. This is an unrealistic

assumption as the wind will in all likelihood work upon the entire bridge. First the wind speed must be calculated using Eqs (1) and applying reduction factor m for footbridges. This is being calculated for span 2 which would feel the greatest wind force.

211 SSvKvc = . (1)

Table 3: Values for Eqs (1) 126 −= msv 44.11 =K

11 =S 02.12 =S

82.0=m 131 −= msvc

From here the total wind force on the bridge is calculated using Eqs (2).

Dt CqAP 1= . (2) Where q is defined in Eqs (3)

2613.0 cvq = . (3)

Table 4: Values for Eqs (2) and Eqs (3) 2/589 mNq = 2

1 72mA =

8=DC kNPt 339=

PL and PV are being ignored. The slender profile of

the bridge and pedestrian function creates a negligible PL and the interaction between the three spans from vertical loading greatly minimizes the effect of the already small force PV. A downward force on the central span causes the outer spans to rise. This cancels out the bending moment in the spans and the small value of PV means it will have little effect on any hogging moments at the piers

.4.3 Temperature Effects

For assessing temperature effects it must again be assumed that all the movement joints along the length of the bridge have been clogged up. Now the bridge must expand as an entire entity when exposed to heat. As one end of the bridge cantilevers away from the abutment it shall be assumed that overall expansion or contraction will cause little effect in the stress state of the bridge.

Were the bridge restrained at both ends, and assuming that the bridge was built at fifteen degrees Celsius, the maximum temperature variation in London for a footbridge would be 25degrees Celsius. This equates to 300micro strain (300 x 10-6) and total bridge shrinkage of about 10cm. This results in an additional 60N/mm2 of tensile stress being carried by the bridge. The 20 degree increase in temperature results in 48N/mm2 of additional compressive stress in the bridge.

For differential temperature across a section a group must be assumed. As the bridge is steel and aluminium it shall be considered as a group 1 bridge. This gives a

Positive temperature difference shown in Fig. (10) and Table 5.

James Boam jdb21@bath.ac.uk

Figure 11: Positive Temperature Differences for Steel Bridge

Table 5: Values of Tx for Fig. (10)

T1=24°C T2=14°C T3=8°C T4=4°C

This distribution can be assumed to be linear between

0°C and 24°C. This gives linear strain and therefore linear stress variation through the section adding 58N/mm2 of tension at the extreme fibres of the deck.

4.4 Strength of Components and Load Combinations

First the deck must be analysed to see if it can tolerate the imposed load from the bridge users combined with its own self weight. The aluminium decking would also need to resist some additional stresses from temperature variation, but due to the thin deck these would not have a great affect.

The Steel Edge beams have to be checked that they could carry the dead weight of themselves, the bridge deck and the imposed-dead load of the balustrades combined with the live load. There will be a minor affect from the wind but most of this will be taken by the suspension cables. By combining the loads with their relevant factors of safety, the 8metre hollow circular tubing can be checked in bending. By combining differential temperature effects with these loads it should show the worst case loading for this member.

Table 6: Loads acting on each steel edge beam

Member Load Factor Load (kN/m) Aluminium Deck 1.05 1.18 Balustrade 1.75 2.13 Steel Edge Beam 1.05 1.30 Live Load 1.50 16.95

The combined load to be carried by the steel edge

beam is 21.56kN/m of beam. The maximum moment, assuming the edge beam is simply supported is calculated using Eqs. (4).

82lM MAX

ω= . (4)

MMAX is 172kNm. The edge beam is circular hollow and has an outer diameter of 350mm. By assuming a reasonable thickness of 14mm and a maximum permissible stress of 355N/mm2, it is possible to estimate the stress in the extreme fibres of the beam due to dead and live loads using Eqs. (5).

h

h1

h2

h3

T1

T2

T3

T4

0

ZM MAX

MAX =σ . (5)

Z, the plastic modulus of the section is 1250cm3

meaning σMAX is 138N/mm. The effect of the differential temperature chance needs to be added too. As the beam is only 350mm deep the temperature change is in fact only 16°C. This means the strain is only 192 micro strains. This in tern means that the additional stress in the bridge is only another 38N/mm2. The total estimated stress is therefore 176N/mm2 and below the permissible level. It is likely that the circular section is thinner and it is possible that a more standard strength of mild steel (σ=275N/mm2).

The saddles then have to be checked to make sure that they can carry each 8metre section of the deck onto the cables. The saddle arms appear to be thick enough to carry the loads. Combined temperature with dead and live loads would most probably be the worst load and would need to be analysed.

The Cables are the next part of the structure to be analysed. Many assumptions must be made to estimate the tension in the cables. First we must assume that under the loads the cables do not deflect but we know they will deflect quite heavily as there is little stiffness in the supporting piers. We are also assuming that the each individual cable span is independent of the other and unaffected by the change in geometry and stiffness of the deck. Applying loads to different spans of the bridge will have a large affect on the tensions in the cables even though the cables are fixed at the piers. The lengthening of the cables is also neglected in the analysis. With such a shallow profile and therefore such high forces in the tension cables it is possible that the tension cables could stretch quite a lot.

By applying the right load factors we can find the total load taken by one bank of four cables. Temperature effects are less likely to affect the cable as much as wind. The geometry of the cable means it has stiffness in both horizontal and vertical planes. To simplify the example the cables will be modeled as two separate cables, one in the vertical plane taking the bridge loading and the other in the horizontal plane taking the wind loading. The tensions of these imaginary cables will be resolved into the plane of the actual cable. Note that the wind blows from the side and will only be carried by one set of cables for worst case analysis as the other set will be assumed to not be in tension.

The loads acting on the cable are shown in Table 7. The wind load has been converted into a U.D.L. to make it possible to analyse. The point load was simply divided by the span to get its force per unit length. This is more like wind loading which is evenly distributed and should not be modeled as a point load.

Table 7: Loads acting on each bank of Cables Member Load Factor Load (kN/m) Aluminium Deck 1.05 1.18 Balustrade 1.75 2.13 Steel Edge Beam 1.05 1.30 Cables 1.05 3.78 Live Load 1.25 14.13 Wind Load 1.10 2.35

James Boam jdb21@bath.ac.uk

The horizontal length of the cable in the centre span

is 144metres and the sag is 2.3 metres. The total vertical load carried by the cable is 22.52kN/m. Using the cable geometry it is possible to calculate the horizontal force needed at each support to hold the cable in shape with Eqs. (6).

flH 8

2ω= . (6)

The horizontal force comes out at 25.4MN. To get the

tension in the ‘vertical’ cables the force must be resolved with the vertical reaction at one node of the cables. This is simply half of the applied vertical load which is 1.62MN. Using a triangle of forces the tension in the cables is 25.5MN

The ‘horizontal’ cables only have to take the wind load. The effective sag of these cables is approximately 1.75metres and the horizontal length is again 144metres. Using Eqs. (6). again the horizontal reaction is 3.48MN. The ‘vertical’ reaction is half the total load, 169kN. Using the triangle of forces the tension in these horizontal cables is 3.48MN.

Now these two tensions can be resolved to get the final tension of the actual cables. The final force carried by the worst case four cables is 25.7MN.

The cables now need to be checked to see if they can resist this force. The force in each cable is a quarter the total force, assuming it is distributed evenly among the cables. We know the area of each cable, and it is reasonable to assume that the cables will be high tensile steel, with a strength of around σ=1600N/mm2. Using Eqs. (7) we can calculate the stress in the cables.

AF=σ . (7)

From this we get a stress of 568N/mm2 which is well

below the permissible stress level. To check these results a similar analysis of the two edge spans can be done to verify the tensions in the cable.

With tensions in the cables found it is now possible to calculate the force acting on each pier. The cables running over the pier are almost flat so this means that very little force is transferred into the piers. Assuming an angle of around 5degrees between the cables and the horizontal it is possible to calculate the forces. Acting down on each fork of a pier is two lots 25.7Mn multiplied by the sine of 5degrees. This gives a force acting down on each fork of 4.48MN. As the forks are at approximately 45degrees to the horizontal it can be assumed that 3.17MN of the downward forces act axially through the forks and 3.17MN of the force will be acting perpendicularly to the

end of the forks. The bases of the forks are approximately 2.5metres in diameter and are heavily anchored into the concrete section of the pier. At this size the piers will have no trouble in supporting the cables.

5 Serviceability and Refinements

The bridge was well designed to stand up under ultimate limit state and had no problems coping with the large crowds on its opening. One well documented and very noticeable flaw were the large lateral vibrations experienced by the bridge after opening. Some people on the bridge were unable to continue walking and the vibrations started to become hazardous to bridge users. These were unacceptable serviceability conditions and this forced the bridge to close only two days after opening.

5.1 Wobbly Bridge Phenomenon

At first it was thought that wind buffeting had caused the lateral vibrations but this was quickly dispelled. It had also been suggested that it was the foot soldier effect, synchronization of the footsteps of large groups, but this was well understood and designed out of the bridge.

The problem lay in the low damping and high live loads of the bridge as shown in Ref. [6]. Walking along the bridge caused small vibrations that could be perceived by some bridge users. As some users noticed the bridge vibrations they start to walk in step with the vibrations setting up resonant forces. This, coupled with the previously mentioned foot soldier effect, meant that more and more people start to walk in stride with the sway of the bridge. With large crowds, like on the opening day of the bridge the vibrations have large amplitude. The resonant frequencies of the individual spans were in a range similar to that of peoples strides which leant itself to lateral vibration.

Figure 12: Crowds on the Millennium Bridge on opening

day experience the lateral vibrations

5.2 Research and experiments

Experiments with pedestrians walking over moving surfaces was carries out by Southampton and Cambridge universities to find out what caused the movement of the bridge. To truly replicate the conditions of the

Millennium Bridge, however, testing needed to be done on the deck itself. Engineers monitored the movements as pedestrians walked on a variety of different paths and around the bridge in an attempt to recreate the behaviour of the opening days of the bridge.

Figure 13: Two pictures of Engineers testing the bridge

5.3 Removing the Vibrations

After much research a large number of dampers were designed to be retrofitted to the bridge. 37 fluid-viscous dampers were designed to run along the underside of the bridge and elsewhere along the bridge to control lateral vibrations of the bridge. These increased the natural frequency of the bridge by around three times and eliminating the change of pedestrian induced lateral vibrations. Although no vertical vibrations were experienced during the opening days of the bridge, a decision was taken to ensure that none could happen in the future. 52 Tuned Mass Dampers were installed between the saddles and the decks [7]. This retrofit programme took two years and cost five million pounds. This was a massive blow to the bridge and to London. It was seen as another Millennium project that had gone wrong and detracted from the pioneering design and striking styling of the bridge.

Figure 14: Two Fluid-Viscous dampers attached to an

arm of a saddle. With the need to keep the Thames in operation during

the retrofit and a large amount of the works requiring access to the underside of the bridge the installation of the dampers was a very slow process. The scaffolding and

temporary works needed for the installation process were very complicated. This is a lesson to the designers and hopefully any other minor or otherwise considered trivial issues were addressed during the extensive improvements to the bridge.

Figure 15: Tuned Mass Damper on the underside

of the bridge

6 Impact of the Bridge on London

Despite at first appearing to be a massive failure, and not being in use for the first two years of its life, the Millennium Bridge has turned out to be quite popular in the capital. The main reason for its success lies within its positioning along the River Thames. With St. Paul’s Cathedral dominating the skyline to the north, and the Tate Modern and Globe theatre right next the bridge on the south it is a perfect cultural route from one side of the city to the next.

With the arts lovers and culturally stimulated people attracted to area it gives the bridge a chance to be appreciated for its architectural quality and striking aesthetic qualities. Some may disagree with the bridges proximity to such traditional buildings, like the globe, given its modern styling. All over London, however, there are contradictions of styles and building principles and it is what makes the city so unique.

7 Summary

The innovative design of the Millennium Bridge is a bold and outstanding piece of architecture. With a design issue so difficult to get spot on as aesthetics the Millennium Bridge excels. Although its structure is not clear its smooth lines and clever use of colour and lighting and exceptional proportions make it a truly wonderful bridge to view. The eye is never disinterested by the shape and intricacy of the bridge.

The design itself is a very clever way of maintaining slenderness but allowing views of the cityscape. The foundations make good use of the space they are in, especially considering some of the nearby buildings. The construction process was essentially standard for a suspension bridge and the right choice of materials for the structure. The one overhanging issue is the lateral vibrations that closed the bridge for two years and required costly repair works. Now it is safe to call it a successful bridge and is firmly settled as a landmark of the capital and country.

James Boam jdb21@bath.ac.uk

James Boam jdb21@bath.ac.uk

8 Acknowledgements

The guideline notes on the presentation method of this document provided by Professor Tim Ibell were informative, clear and easy to use. They proved an invaluable aid in forming this document. The lecture series’ that ran alongside project, both Bridge Engineering 1 and the Drop-in sessions for this module, proved essential in gaining the knowledge required to attempt this project.

9 References

[1] Fitzpatrick, T., Linking London: The Millennium Bridge

[2] Dallard et al, The London Millennium Footbridge

[3] Gagnon, C.P., Stahl, F.L., Cable Corrosion in

Bridges and Other Structures, pp. 13-14. [4] http://www.arup.com/MillenniumBridge/project/

decking_section.html [5] http://www.arup.com/MillenniumBridge/indepth/

drawings.html [6] Newland, D.E., Vibration of the London

Millennium Footbridge: Part 1 – Cause [7] Taylor, D.P., Damper Retrofit of the London

Millennium Footbridge – A Case Study in Biodynamic Design