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Third-order statistical linearization-based approach to derive equivalent linear properties of bilinear hysteretic systems for seismic response spectrum analysis

Spanos, P. D. and Giaralis, A. (2013). Third-order statistical linearization-based approach to derive equivalent linear properties of bilinear hysteretic systems for seismic response spectrum analysis. Structural Safety, 44, pp. 59-69. doi: 10.1016/j.strusafe.2012.12.001


A novel statistical linearization based approach is proposed to derive effective linear properties (ELPs), namely damping ratio and natural frequency, for bilinear hysteretic SDOF systems subject to seismic excitation specified by an elastic response/design spectrum. First, an efficient numerical scheme is used to derive a power spectrum satisfying a certain statistical compatibility criterion with the given response spectrum. Next, the thus derived power spectrum is used in conjunction with a frequency domain higher-order statistical linearization formulation to replace the bilinear hysteretic system by a third order linear system by minimizing an appropriate error function in the least square sense. Then, this third order linear system is used to derive a second order linear oscillator possessing a set of ELPs by enforcing equality of certain response statistics of the two linear systems. The thus derived ELPs, are utilized to estimate the peak response of the considered nonlinear system in the context of linear response spectrum-based dynamic analysis. In this manner the need for numerical integration of the nonlinearequation of motion is circumvented. Numerical results pertaining to the European EC8 uniform hazard elastic response spectrum are presented to demonstrate the applicability and the usefulness of the proposed approach. These are further supported by Monte Carlo analyses involving an ensemble of 250 non-stationary artificial EC8 spectrum compatible accelerograms. It is believed that the proposed approach can be an effective tool in the preliminary aseismic design stages of yielding structures following either a force-based or a displacement-based methodology.

Publication Type: Article
Additional Information: NOTICE: this is the author’s version of a work that was accepted for publication in Structural Safety. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Structural Safety Volume 44, September 2013, Pages 59–69,
Publisher Keywords: statistical linearization, seismic design spectrum, inelastic response spectrum, power spectrum, bilinear hysteretic systems, equivalent linear properties
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Mathematics, Computer Science & Engineering > Engineering
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