Skyscrapers, Damping Systems, and Physics

Skyscrapers, Damping Systems, and Physics

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Skyscrapers are amazing! Architectural defeats. Wonders of the world. How are they able to withstand even the strongest of winds and earthquakes?

Today, engineers rely on damping systems to counteract nature's forces. There are many types of damping systems that engineers can now use for structures, automobiles, and even tennis rackets! This site focuses on damping systems in structures, mainly architectural variations of the tuned mass damper.

How Tuned Mass Dampers Work

A tuned mass damper (TMD) consists of a mass (m), a spring (k), and a damping device (c), which dissipates the energy created by the motion of the mass (usually in a form of heat). In this figure, M is the structure to which the damper would be attached.

From the laws of physics, we know that F = ma and a = F/m. This means that when an external force is applied to a system, such as wind pushing on a skyscraper, there has to be an accleration. Consequently, the people in the skyscraper would feel this acceleration. In order to make the occupants of the building feel more comfortable, tuned mass dampers are placed in structures where the horizontal deflections from the wind's force are felt the greatest, effectively making the building stand relatively still.

When the building begins to oscillate or sway, it sets the TMD into motion by means of the spring and, when the building is forced right, the TMD simultaneously forces it to the left.

Ideally, the frequencies and amplitudes of the TMD and the structure should nearly match so that EVERY time the wind pushes the building, the TMD creates an equal and opposite push on the building, keeping its horizontal displacement at or near zero. If their frequencies were significantly different, the TMD would create pushes that were out of sync with the pushes from the wind, and the building's motion would still be uncomfortable for the occupants. If their amplitudes were significantly different, the TMD would, for example, create pushes that were in sync with the pushes from the wind but not quite the same size and the building would still experience too much motion.

The effectiveness of a TMD is dependent on the mass ratio (of the TMD to the structure itself), the ratio of the frequency of the TMD to the frequency of the structure (which is ideally equal to one), and the damping ratio of the TMD (how well the damping device dissipates energy).

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*** Two bridges, spanning 46 and 38 meters long.***

*** A damping system was installed to avoid the possibility of exciting the bridges to resonance, which would have caused an amplitude large enough for pedestrians to feel.***

*** The bridge uses 6 TMDs, 3 on each bridge, and weighing1360 kg apiece.***

*** Like most TMDs, each of the 6 TMDs have springs and a viscous damper, through which vibration energy of the bridge is dissipated.***

One Wall Centre

Vancouver, British Columbia

***Tallest building in Vancouver, 48 stories high***

***Instead of a TMD, a tuned liqid column damper (TLCD) replaces the role of the mass, spring, and damping device of the TMD. In order to counteract the building's motion and keep it at rest, a TLCD uses large tanks of water or other liquid and a sluice gate. The geometry of the water tanks is designed to match the frequency of the structure so that it provides a near equal and opposite reaction to the motion of the building due to wind or other forces. The sluice gate is used to dissipate the energy created by the water's motion.***

Taipei Financial Center

Taipei, Taiwan

***This building is 508 meters tall.***

***As well as being a prominent architectural feature, a sphere suspended by flexible steel cables acts as the TMD and keeps the building relatively still.***

Trump World Tower

New York, New York

*** This building is 260 meters tall, rectangular, and nearly twice as long as it is wide, causing it to act like a cantilevered beam in the presence of wind or other forces (the people in the top floors would be swaying back and forth).***

*** To counteract this reaction, the TMD in this building is similar to a "stacked" pendulum, with the pendulum supported by massive hydraulic cylinders (similar to the hydraulic shocks on cars), which act as the damping device and through which energy is dissipated.***

Petronas Towers

Kuala Lumpur, Malaysia

*** The Petronas Towers are 452 meters tall, connected by

a steel skybridge 170 meters from the ground, on the 41st and 42nd floors.***

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