An Evaluation of Scaling Methods for Earthquake Response Spectra
Nau, James Michael
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https://hdl.handle.net/2142/69908
Description
Title
An Evaluation of Scaling Methods for Earthquake Response Spectra
Author(s)
Nau, James Michael
Issue Date
1982
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Abstract
In current practice, design response spectra are scaled or normalized by the three peak ground motion values--displacement in the low, velocity in the intermediate, and acceleration in the high range of frequencies. In this study, alternative scaling factors are evaluated with the purpose of reducing the dispersion encountered in normalized spectral ordinates. The scaling factors fall into two major groups, one based on ground motion data, and the other, directly on response quantities. Within the group based on ground motion values are the integrals of the squared acceleration, velocity, and displacement, and those quantities derived therefrom, the root-square, mean-square, and root-mean-square motions. Included within the group based on response quantities are the spectrum intensity and the mean Fourier amplitude.
The foregoing scaling parameters have been evaluated statistically using a set of twelve representative earthquake recordings. Response spectra for elastic, elastoplastic, and bilinear hysteretic systems for wide ranges of damping and ductility have been used in the statistical study. The results show that a three parameter system of spectrum intensities, computed within low, medium, and high frequency regions, may afford a better means of scaling earthquake response spectra. Reductions in dispersion ranging from 20 percent in the velocity region to 45 percent in the displacement and acceleration regions may be realized if elastic spectra are normalized by the spectrum intensities rather than the peak ground motions. The spectrum intensities also afford reductions in scatter for normalized inelastic spectra, for low to moderate displacement ductilities.
As a prelude to the investigation regarding the dispersion characteristics of normalized spectra, an efficient algorithm was developed for the computation of inelastic response spectra. The method is based upon the exact solution of the equations of motion and permits the computation of dynamic response in a simple, arithmetic manner. Compared with Newmark's beta method, the procedure provides a two- to threefold savings in computation time.
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