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Dealing with dynamics

As bridges become more extreme, the limiting factor is no longer the strength or durability of the materials used. Dynamic response to wind, earthquakes and traffic loads dominate the design process. Dave Parker reports on how designers have dealt with dy

Why read this

Structural dynamics of three extreme bridges analysed

Active damping considered - and rejected

The way forward for footbridge dynamics

Record breaker

Spanning 2.3km across the typhoon haunted waters of the Bali Sea, the Java-Bali Bridge will be the longest in the world - if it opens before the giant Messina crossing (see p50).

There is still no certainty the landmark structure will ever be built, but the concept design has posed some interesting challenges for structural engineer Flint & Neill, not least on the dynamic front.

Flint & Neill partner Ian Firth explains: 'We chose a hybrid cable stay/suspension bridge design because this effectively reduces the suspended span to 1,600m. And the cable stayed backspans with their multiple piers are very stiff. So the natural frequencies of the deck are higher, amplitudes of motion are lower and it responds much better to wind loads.'

Given the high probability of typhoons in the area the aerodynamic characteristics of the structure were crucial. Deck design was made no easier by the client's decision that only two traffic lanes in each direction were needed. A conventional single deck girder would have been unfeasibly narrow for the recordbreaking span. To achieve the necessary lateral stiffness Flint & Neill went for a cross-braced twin box design, with a 16m central slot between the aerofoil cross-section steel boxes.

'Messina style slotted decks are very efficient aerodynamically, ' Firth points out. 'And the separation helped us develop a very efficient tower design with a distinctly Balinese flavour.'

Unusual they may be, but Firth insists the 300m high towers have much greater transverse stiffness than conventional portal frame designs. He also expects that once detail design begins the real challenge will be fine tuning the cross sections of each box in the wind tunnel.

'Vortex shedding is the key issue - predicting how curved soffit box girders will behave is really difficult.' Aerolastic testing - modelling the dynamic response of the structure to high winds - will also include the effect of local topology, Firth adds.

Lateral and torsional motion on long span structures is a problem for which Firth sees no simple solutions. Active damping and 'intelligent' aerodynamic control fail to impress. He sees the risk of power or equipment failure as too high. But passive aerodynamic damping - 'flat plates paddling air' - is another matter. Such appendages would make Java-Bali an even more dramatic crossing.

Fink rethink

Had it been built with active damping, the Royal Victoria Dock footbridge in London's Docklands would have weighed 25% less. So says structural engineer Tekniker director Matthew Wells, adding: 'The original intention was to react to deflections caused by the passenger gondola which will eventually run below the deck.

'The system could in theory have coped with all imposed loads - the problem was defining which frequencies to damp.'

A mini transporter bridge design was architect Lifschutz Davidson's response to a design brief from the then London Docklands Development Corporation for a landmark 130m span pedestrian crossing over a stretch of water which was being developed as a regional sailing centre.

A 13m minimum clearance below the deck seemed to imply that pedestrians would need some form of weather protection - but at the same time the structure had to cause as little wind turbulence as possible.

'Some form of tube would have been a possibility, ' says Wells. 'But who would want to cross it late on Saturday night?'

The transporter bridge alternative would allow pedestrians to enjoy the views from the open top deck in fine weather, with the option of skimming across the dock in a 40 passenger enclosed car in less clement conditions.

An inverted Fink truss was the chosen structural form, partly because of its inherent lightness and flexibility, partly because it invoked both the dockyard cranes and the forest of masts and cables that once filled the dock. Five fabricated 'whale backbone' steel box girders linking the six masts were spigoted together around the mast feet.

This simple to erect pin-jointed arrangement also significantly increased the structure's inherent lateral damping.

Beneath this backbone runs the track for the passenger gondola, which weighs 11t fully loaded. Wells says the gondola only increases midspan deflection by a maximum of 75mm.

'Dynamically, there was no problem with the gondola swinging beneath the deck, as its 'bouncing' frequency is very much lower than that of the bridge. And in high winds it will be able to winch itself close up under the deck during the crossing.'

Doubts about development time for an actively damped solution meant Techniker went for a 'static' solution at competition stage. As design development began, tests revealed a potential aerodynamic problem - the first torsional and first vertical frequencies were very close together, less than 0.5Hz apart.

'Normally you would expect vertical to be around 1Hz with torsional three or four times higher, ' Wells comments. 'When they're this close you could be facing a Tacoma Narrows situation.'

Aerodynamic damping via a perforated balustrade proved to be the solution to this particular problem. Meanwhile, Techniker worked up two alternative active damping designs, using adapted Formula One self-levelling suspension technology applied to the backstays. This promised a massive weight reduction and a cut in the maximum depth of the box girders from 1,650mm to 1,250mm. There was a downside, however.

Wells explains: 'With full active damping it would be impossible to use the bridge in high winds if there was any equipment failure. Then there was the ongoing cost of maintenance. But the real problem was the time needed to decide on the sampling window - which motions to monitor and to correct.'

Jointless swinger

It may have been abandoned at the foundation stage when the private developer client ran out of money, but the 1,080m long, 360m main span Ah Kai Sha cable stay crossing over the Pearl River in Guangzhou, southern China, set new dynamic challenges for structural engineer Robert Benaim & Partners. A massive double deck concrete truss carrying eight lanes of high speed traffic on the top deck and six lanes of local traffic inside the truss had interesting aerodynamics in its own right. But it was Benaim's interest in minimising vulnerable deck joints that really set the design apart.

'We initially planned to use conventional towers, ' says Benaim technical director David Collings. 'But when we did our sums we felt we could make this an integral structure, with deck and towers monolithic.'

With such a stiff deck truss the towers would need to have high lateral bending stiffness and low shear stiffness in the longitudinal plane. A bonus would be that the stiff deck would distribute live loads more effectively between the cables, minimising traffic induced cable vibrations.

Final tower design was an elegant 127m high optimised double lozenge cross section solution with a lightweight upper crossmember. Standard static wind tunnel testing showed the deck design needed no modification. However, the design team suspected the slender towers might be at risk at some point in the construction sequence. The stiff deck truss made it possible for the deck to cantilever out 50m from the tower before stays were needed.

'There would be a very long period of motion, ' Collings points out. 'And the longer the period of motion, the more energy the wind can put in.'

Dynamic wind tunnel testing was commissioned. All stages of construction were modelled.

'We even added model tower cranes, ' Collings comments.

'The worst case came just before the crossmember went in. It was a torsional mode, in which one leg effectively remained stationary while the other oscillated about it.'

Estimated to cost around $150M, the Ai Ka Sha Bridge would have opened next year.

But Collings says the exercise was far from wasted. 'It convinced us that the A13 viaduct at Dagenham could be built without joints, ' he insists.

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