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

Abstract

The maximum inelastic response of bilinear single-degree-of-freedom systems when subjected to ground motions without distinguishable pulses is revisited with dimensional analysis by identifying time scales 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 time scale and examines two different length scales which 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 which involve solely 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 post-yield stiffness ratio equal to 2% and inherent viscous damping ratio equal to 5%.

Estimation of peak displacements in steel structures through dimensional analysis and the efficiency of alternative ground-motion time and length scales

“…These studies employed the mean period from the Fourier transform of the acceleration series (T m ) together with peak acceleration and velocity values as characteristic ground-motion parameters. Although the estimated inelastic response quantities were found to be in superior agreement with the results of nonlinear response history analysis than previously published estimations, the necessity of further work towards the identification of more effective time and length scales in non-coherent recordings was recognised [18]. Furthermore, a systematic comparison of the relative merits of the use of one time or length scale over others in the context of dimensional response analysis has not yet been carried out, particularly for Partially-Restrained (PR) and Concentrically-Braced (CB) structures.…”

“…In effect, Equation 10 was initially proposed by Makris and Psychogios [24] to define the response of structures under pulselike records and latter employed by Karavasilis et al [18] to characterize the response of bilinear oscillators under non-pulselike ground-motions.…”

“…The peak displacement in both cases has been normalized by L g = P GA/ω 2 g and T g = T m as proposed by Karavasilis et al for non-pulselike records [18].…”

“…By contrast, the determination of adequate time and length scales from non-coherent earthquake ground-motion series is less well defined and there is a dearth of information regarding their relative merits. Dimitrakopoulos et al [9] and Karavasilis et al [18] explored the possibility of extending the application of dimensional analysis to the study of elastoplastic and bilinear systems under excitations without distinguishable pulses. These studies employed the mean period from the Fourier transform of the acceleration series (T m ) together with peak acceleration and velocity values as characteristic ground-motion parameters.…”

Optimal Friction Coefficients for Isolated Structures Depending on the Soil Condition

“…Eqn. (4) also reveals that the non-dimensional parameters ( terms) [36]- [37] that control the system non-dimensional response to the seismic input ( ) are:…”