The function damping ratio in the response spectrum function definition is the damping ratio for which the response spectrum was generated.
As part of the Response Spectrum analysis case definition, one must also specify modal damping ratio for the structure:
During the analysis, the response-spectrum curve will automatically be adjusted from the function damping value to the actual damping present in the model. We are using the velocity formula of "N.M. Newmark and W.J. Hall, Earthquake Spectra and Design, Earthquake Engineering Research Institute, Berkeley, California, 1982" to adjust the response spectrum curve. This formula adjusts the response-spectrum curve as follows:
A2 = A1 * (2.31 - 0.41 * log(D2)) / (2.31 - 0.41 * log(D1))
where:
- A1 = acceleration corresponding to damping ratio D1,
- A2 = acceleration corresponding to damping ratio D2,
- 0.0 < D1 < 100,
- 0.0 < D2 < 100,
- and log = natural log (base e).
For example, if the input acceleration at a particular period A1 = 0.4 for function damping ratio of 0.05, the acceleration A2 used in the analysis for a modal damping ratio of 0.08 is
A2 = 0.4 * (2.31 - 0.41 * log(8)) / (2.31 - 0.41 * log(5)) = 0.4 * 1.457 / 1.650 = 0.353
In the above equation, D1 is the damping value (in percent) that was used to generate the response spectrum curve (i.e. Function damping ratio in the curve definition). On the other hand, D2 is modal damping (in percent) in the structure and is obtained by summing up the damping from the following three sources:
- Modal damping specified in the analysis case
- Composite modal damping from the materials
- Effective damping from the link/support elements
If D1 is not equal to D2 (and D1> 0) then the program will adjust the response spectrum curve per Newmark and Hall equation. If the function damping ratio is specified as zero, no adjustments are made to the response spectrum curve. The values are used "as-is".