Few things are more galling than having your penthouse office suite shaken by high winds or the odd overgrown ape. Arup’s solution to wobbly building syndrome is dependable and cost-effective – though we’re not sure if it’s been tested on animals.

Five years after engineer Arup fixed the wobble in the Millennium Bridge, it has applied the lessons learned from that debacle to a much bigger problem: wobbly towers.

A combination of the vibrations inherent in tall structures and the high winds that often buffet the upper floors can create a distinct wobble at the top of them. This can be at best nausea-inducing and at worst terrifying, putting off anybody from wanting to live or work in them.

But the usual way of counteracting such vibration is problematic: beefing up the building with lots of extra structure makes it stiffer and heavier, but takes up a lot of room and is very expensive. To cut vibration by half means either increasing the building’s mass or its stiffness by a factor of four.

A more effective, less expensive solution was clearly required.

Putting a damper on proceedings

There has traditionally been another solution, which is to use dampers to reduce the vibration. The usual option is tuned-mass dampers – large weights positioned at the top of a building. However, engineers are reluctant to rely on these, for four reasons:

• There is an issue with reliability. Typically, there is just one damper to take care of movement for each direction the building will move in. “If something jams or it fails, it won’t work,” says Michael Willford, the Arup structural engineer who came up with the Millennium Bridge solution.

• The position of the dampers inadvertently makes it a more costly option. “That’s hundreds of tonnes of mass at the top, right where the prime real estate is,” says Willford.

• As the name implies, tuned mass dampers are tuned to respond to the frequency of a building’s natural vibration. However, this can change over time. Concrete progressively gains strength over many years, changing the building’s natural frequency and rendering the damping less effective.

• Perhaps most importantly, dampers have a damping factor of just 3% to 4%, which in many instances isn’t enough to take care of vibration without a strengthened structure.

All of which means that damping usually only supplements a heavier, more costly structure. Until now, that is.

The lessons of the bridge

According to Willford, Arup has found a better option: the viscous dampers used on the Millennium Bridge. A viscous damper works by forcing a plunger through a tube filled with oil – this absorbs the energy that otherwise will cause a building to oscillate (see graphic).

Viscous dampers have a damping factor of 6-10%. This takes care of vibration well enough to keep occupants comfortable – it’s equivalent to making the building 44% stiffer.

Willford also says 10% damping means consultants don’t have to worry about designing structures for resonance. Mechanical resonance occurs when the wind frequency matches the building’s natural frequency, leading the vibration to become stronger and stronger. This is what caused Washington State’s one-mile-long Tacoma Narrows Bridge to collapse in 1940.

The other key element is dependability.

A building damped in this fashion would contain 20 to 30 dampers, which means there is plenty of back-up. “Even if 50% of the damping failed, the damping effect would work almost as effectively,” says Willford.

He adds that viscous dampers cope well with changes in the building’s frequency, so can be relied on for the life of the structure.

The Arup solution works by inserting the viscous dampers between key structural elements, which move relative to each other to damp out the vibration (see below). “It means we can reduce the structure and foundation size; it’s faster to build – which means lower costs – there’s more net floor area; it’s more sustainable as there is less material needed, and there’s more valuable space at the top,” says Willford.

Arup is using the system on the 60-storey residential St Francis tower in Mandaluyong City, the Philippines, set for completion next year. Willford says the building has an acceleration value of 75 milli-G when key structural elements are locked together, and just 24 milli-G when viscous dampers are inserted between those elements.

Willford claims the amount of concrete needed for the tower has been cut by 30% and the density of steel reinforcement has been reduced from 300kg per m3 to 200kg. This adds up to a saving of $5m (£2.57m).

If the system is as successful as Arup hopes, the £5m cost of fixing the Millennium Bridge’s wobble could turn out to have been a very good investment indeed.

How dampers work

Viscous dampers
These consist of an oil-filled tube 1, which is connected to one structural element 2. A plunger 3 that can move in and out of the tube is connected to the other structural element 4. Building movement causes the plunger to move and damping is provided by oil being forced through tiny holes in a disc attached to the end of the plunger 5. This mechanical energy is dissipated as heat.

Tuned mass damper
A tuned mass damper is a large weight fixed at the top of a structure, which moves in opposition to the building’s movement. Its weight has to be adjusted to match the natural frequency of the structure. Tuned mass dampers are present at the top of many tall structures, including the Spire of Dublin. These were also used on the Millennium Bridge in combination with viscous dampers.

Active control
This is a variant on the tuned mass damper. “Acceleratometers” monitor the building’s movement and a large weight is moved by motors to produce an opposite force equivalent to that produced by the wind. An active control system has been used at the top of the new Heathrow control tower.

Tuned slosh damper
Another variant on the tuned mass damper, these damp out horizontal motion. The mass is provided by water, which sloshes around in a tank to damp out vibration. Good for bridges, it has been used on the new London Gatwick air passenger bridge.

Visco elastic damper
An elastic material capable of absorbing high levels of energy is sandwiched between structural components. Used to damp movement on the ramp at London’s City Hall.

Impact damper
Useful when there isn’t room for a tuned mass damper. A large metal ball rolls around in a square box. When movement gets up to a predetermined point, it kicks in; the energy from the impact against the side of the box damps out the structural movement. This was used for the Washington Airforce Memorial.

How the Arup system works

The Arup damping solution can be used in three ways. All rely on a degree of relative movement between the structural elements, which is damped out by the viscous dampers. Typically, dampers will be fixed every 25 floors.

The first solution, as seen on the St Francis tower, uses structural outriggers fixed to the core. These are more than one storey deep and incorporate plant rooms. The outrigger extends to the structural columns at the building perimeter and is connected to these by three viscous dampers.

The second variation is used on shear walls, which are typically used to resist lateral loads in tall residential buildings. The wall is the full width of the building but is split vertically and the two halves are connected with dampers.

The final variation is used for buildings where the main loads are transferred down columns at the building perimeter. A special column is used, which is split into two. The dampers span the two elements.