Damping in Structures

Damping describes the energy dissipation present in vibrating systems, causing the vibration amplitudes to decay over time, or preventing them from increasing. In structures, it is typically described as measured as a damping ratio (% of critical damping), and denoted by the greek letter ζ.

Structural systems can be described as:

• Undamped.....................ζ = 0% of critical
• Underdamped...............ζ < 100% of critical
• Critically Damped........ζ = 100% of critical
• Overdamped..................ζ > 100% of critical

Sources of Inherent Damping in Buildings

Even in the absense of any special devices, typical building structures will have inherent energy dissipation capabilities. The source of this inherent damping can be broken down as follows:

How is Damping Measured and Represented?

Damping in structures is very difficult to "design" and predict. Instead, damping measurements of as-built structures has historically been undertaken to get a picture of approximate range of damping values.

A reliable method, where possible, is to perform a type of push test or similar on a structure and measure the natural vibration until it comes to rest. Although not possible on tall buildings, it can be reasonably practical to do on long-span bridges, control towers, transmission towers, chimney-like structures etc.

From the observed record, engineers can easily calculate the logarithimic damping - a measure favoured by wind engineers in Europe historically. It is also easy to convert this into a damping ratio.

The logarithmic decrement of damping can be calculated from the time history record as:

Log. decrement,

This can then be converted to a damping ratio by the following equation:

Damping ratio,

When the damping ratio is quite low as typical for normal buildings  (< 20% of critical), the approximation can be simplified to:

There are also other ways of measuring damping, such as from hysteresis curves, or from dynamic magnification curves. These shall be covered in future posts.

Estimating Damping

Commonly used damping ratios employed in design are as follows:

• Wind loading
  For normal building structures, this is about 1- to 2% damping of critical. The value you use depends on the main building material (concrete/steel/timber) and the return period loading being assessed (SLS or ULS). For very lightweight and slender structures like flagpoles or long-span bridges, this can be as low as 0.5%.
  
  
• Seismic loading
  Engineers in high seismic region usually adopt an equivalent viscous damping ratio of 3- to 5% damping. This is higher than for wind due to a higher expected hysteresis damping (from material cracking and internal friction).
  
  
• Floor Vibration
  These are often taken conservatively as around 2.0% damping of critical. However, if there is a lot of fit out, and especially if there are partitions, the value can be as high as 5.0% of critical.

Note that in all the cases represented above, a constant damping ratio is assumed for all modes of vibration, which can sometimes be a slightly conservative simplification. Higher order modes may exhibit higher levels of damping. Some designers prefer to use Rayleigh damping (mass and stiffness proportional damping) to calculate damping ratios for all individual vibration modes.

Supplementary Damping

Where the dynamic response of a structure is excessive or undesirable, designers can seek to provide supplementary damping in order to significantly enhance the structures own inherent energy dissipation. These usually take the form of distributed damping, or mass dampers.