American Society of Civil Engineers

Dimensional Response Analysis of Bilinear Systems Subjected to Non-pulselike Earthquake Ground Motions

by Theodore L. Karavasilis, (Dept. Lecturer in Civil Engineering, Dept. of Engineering Science, Univ. of Oxford, Oxford OX1 3PJ, UK. E-mail:, Choung-Yeol Seo, (Research Associate, ATLSS Center, Dept. of Civil and Environmental Engineering, Lehigh Univ., Bethlehem, PA 18015. E-mail:, and Nicos Makris, (corresponding author), M.ASCE, (Professor of Structural Engineering and Applied Mechanics, Dept. of Civil Engineering, Univ. of Patras, 26500 Patras, Greece E-mail:

Journal of Structural Engineering, Vol. 137, No. 5, May 2011, pp. 600-606, (doi:

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Document type: Journal Paper
Abstract: The maximum inelastic response of bilinear single-degree-of-freedom (SDOF) systems when subjected to ground motions without distinguishable pulses is revisited with dimensional analysis by identifying timescales and length scales in the time histories of recorded ground motions. The characteristic length scale is used to normalize the peak inelastic displacement of the bilinear system. The paper adopts the mean period of the Fourier transform of the ground motion as an appropriate timescale and examines two different length scales that result from the peak ground acceleration and the peak ground velocity. When the normalized peak inelastic displacement is presented as a function of the normalized strength and normalized yield displacement, the response becomes self-similar, and a clear pattern emerges. Accordingly, the paper proposes two alternative predictive master curves for the response that solely involve the strength and yield displacement of the bilinear SDOF system in association with either the peak ground acceleration or the peak ground velocity, together with the mean period of the Fourier transform of the ground motion. The regression coefficients that control the shape of the predictive master curves are based on 484 ground motions recorded at rock and stiff soil sites and are applicable to bilinear SDOF systems with a postyield stiffness ratio equal to 2% and an inherent viscous damping ratio equal to 5%.

ASCE Subject Headings:
Dimensional analysis
Seismic effects

Author Keywords:
Dimensional analysis
Inelastic displacement
Ground acceleration
Ground velocity
Mean period