Response spectrum
A response spectrum is a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of
If the input used in calculating a response spectrum is steady-state periodic, then the steady-state result is recorded. Damping must be present, or else the response will be infinite. For transient input (such as seismic ground motion), the peak response is reported. Some level of damping is generally assumed, but a value will be obtained even with no damping.
Response spectra can also be used in assessing the response of linear systems with multiple modes of oscillation (multi-degree of freedom systems), although they are only accurate for low levels of damping. Modal analysis is performed to identify the modes, and the response in that mode can be picked from the response spectrum. These peak responses are then combined to estimate a total response. A typical combination method is the square root of the sum of the squares (SRSS) if the modal frequencies are not close. The result is typically different from that which would be calculated directly from an input, since phase information is lost in the process of generating the response spectrum.
The main limitation of response spectra is that they are only universally applicable for
Seismic response spectra
Response spectra are very useful tools of
As mentioned earlier, the ground response spectrum is the response plot done at the free surface of the earth. Significant seismic damage may occur if the building response is 'in tune' with components of the ground motion (resonance), which may be identified from the response spectrum. This was observed in the 1985 Mexico City Earthquake[1] where the oscillation of the deep-soil lake bed was similar to the natural frequency of mid-rise concrete buildings, causing significant damage. Shorter (stiffer) and taller (more flexible) buildings suffered less damage.
In 1941 at Caltech, George W. Housner began to publish calculations of response spectra from accelerographs.[1] In the 1982 EERI Monograph on "Earthquake Design and Spectra",[2] Newmark and Hall describe how they developed an "idealized" seismic response spectrum based on a range of response spectra generated for available earthquake records. This was then further developed into a design response spectrum for use in structural design, and this basic form (with some modifications) is now the basis for structural design in seismic regions throughout the world (typically plotted against structural "period", the inverse of frequency). A nominal level of damping is assumed (5% of critical damping).
For "regular" low-rise buildings, the structural response to earthquakes is characterized by the fundamental mode (a "waving" back-and-forth), and most building codes permit design forces to be calculated from the design spectrum on the basis of that frequency, but for more complex structures, combination of the results for many modes (calculated through modal analysis) is often required. In extreme cases, where structures are either too irregular, too tall or of significance to a community in disaster response, the response spectrum approach is no longer appropriate, and more complex analysis is required, such as
See also
References
- ^ "Earthquake Hazards Program: Michoacan, Mexico 1985 September 19 13:17:47 UTC, Magnitude 8.0". Archived from the original on 6 February 2007.
Other sources
- Report on 1985 Mexico City Earthquake] from "EQ Facts & Lists: Large Historical Earthquakes", USGS. (https://web.archive.org/web/20070206063939/http://neic.usgs.gov/neis/eq_depot/world/1985_09_19.html )
- ^ "Historic Developments in the Evolution of Earthquake Engineering", illustrated essays by Robert Reitherman, CUREE, 1997, p10.
- ^ Newmark, N. M., and Hall, W. J. 1982. “Earthquake Spectra and Design,” Engineering Monographs on Earthquake Criteria, Structural Design, and Strong Motion Records, Vol 3, Earthquake Engineering Research Institute, Oakland, CA.
External links
- "Illustration of Newmark-Hall Approach to Developing Design Response Spectra" – Appendix B of "Engineering and Design – Response Spectra and Seismic Analysis for Concrete Hydraulic Structures (EM 1110-2-6050)", US Army Corps of Engineers