Response spectrum or response spectrum — a graph of the peak or steady-state response (bias, velocity, or acceleration) of a series of oscillators of different natural frequencies that are driven by a disturbance. The resulting graph can be used to capture the response of any linear system, taking into account its own oscillation frequency. One such application is to assess the peak response of buildings to an earthquake. Science can use some values from the spectrum of the earth's response (calculated from records of surface movement of soil from a seismograph) to correlate with seismic damage.
If the input used to calculate the response spectrum is stationary, then the stationary result is fixed. Damping must be present, otherwise the answer will be infinite. For non-stationary input signals (such as motion in seismic soil), a peak response is reported. A certain level of attenuation is usually assumed, but a value can be obtained even without attenuation.
Response spectra can also be used to evaluate the response of linear systems with several modes of oscillation (systems with several degrees of freedom), although they are accurate only for low attenuation levels. Modal analysis is performed to identify the modes, and the answer in this mode can be selected from the response spectrum. These peak responses are then combined to assess the overall response. A typical combination method is the square root of the sum of squares (SRSS) if the modal frequencies are not close. The result, as a rule, differs from the result, which will be calculated directly from the input signal, since the phase information is lost in the process of generating the response spectrum.
The main limitation when using response spectra is that they are universally applicable to linear systems. Response spectra can be generated for nonlinear systems, but are applicable only to systems with the same nonlinearity, although attempts have been made to develop spectra of a nonlinear seismic structure with wider structural applications. The results of this cannot be combined directly for a multi-mode response.
Content
- 1 Spectra of seismic response
- 2 History
- 3 notes
- 4 Literature
Seismic Response Spectra
Response spectra are very useful engineering tools for analyzing the characteristics of structures and equipment during earthquakes, since many behave mostly like simple oscillators (one degree of freedom). Thus, if you can find out the frequency of the structure, then the peak response of the building can be estimated by calculating the value from the spectrum of the earth's response for the corresponding frequency. In most building codes of states in seismic areas, this value serves as the basis for calculating the forces that the building must withstand.
In California in 1941, George W. Hausner began to publish calculations of the response spectra from an accelerograph. In 1982, in the design and earthquake spectra monograph, Newmark and Hall described how they developed the “idealized” seismic response spectrum based on the response spectrum generated for existing earthquake records. This was then developed into a spectrum of project response for use in structural design, and this basic form (with some modifications) is now the basis for structural design in seismic areas around the world (usually built in relation to the structural “period”, reverse frequency). The nominal attenuation level is assumed (5% of critical attenuation).
For "ordinary" low-rise buildings, the structural reaction to earthquakes is characterized by a fundamental mode ("swinging" back and forth), and most building codes allow you to design forces calculated on the basis of the response spectrum and this frequency, but for more complex structures, a combination of results for many modes (calculated using modal analysis). In extreme cases, when the structures are too irregular, too high, or important for society in responding to natural disasters, the approach using the response spectrum is no longer suitable, and more complex analysis, such as non-linear Seismic Resistance Analysis, is required.
History
The response spectrum theory was developed between 1932 and 1942 by Maurice Bio [1] .
Notes
- ↑ Biot, MA Analytical and experimental methods in engineering seismology (English) // Proceedings American Society of Civil Engineers 68: 365-409. : journal. - 1942.
Literature
- Report on 1985 Mexico City Earthquake from "EQ Facts & Lists: Large Historical Earthquakes", USGS.
- ↑ “Historic Developments in the Evolution of Earthquake Engineering” , illustrated essays by Robert Reitherman, CUREE, 1997, p10.
- ↑ Newmark, NM, and Hall, WJ 1982. "Earthquake Spectra and Design," Engineering Monographs on Earthquake Criteria, Structural Design, and Strong Motion Records, Vol 3, Earthquake Engineering Research Institute , Oakland, CA.
- "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
- Software Applicability ANSYS, Inc. when calculating structures for seismic effects