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Earthquakes and Structures
  Volume 12, Number 4, April 2017, pages 397-407

Seismic structural demands and inelastic deformation ratios: a theoretical approach
Benazouz Chikh, Ahmed Mebarki, Nacer Laouami, Moussa Leblouba, Youcef Mehani, Mohamed Hadid, Abderrahmane Kibboua and Djilali Benouar

    To estimate the structural seismic demand, some methods are based on an equivalent linear system such as the Capacity Spectrum Method, the N2 method and the Equivalent Linearization method. Another category, widely investigated, is based on displacement correction such as the Displacement Coefficient Method and the Coefficient Method. Its basic concept consists in converting the elastic linear displacement of an equivalent Single Degree of Freedom system (SDOF) into a corresponding inelastic displacement. It relies on adequate modifying or reduction coefficient such as the inelastic deformation ratio which is usually developed for systems with known ductility factors (C_µ) and (C_R) for known yield-strength reduction factor. The present paper proposes a rational approach which estimates this inelastic deformation ratio for SDOF bilinear systems by rigorous nonlinear analysis. It proposes a new inelastic deformation ratio which unifies and combines both C_µ and C_R effects. It is defined by the ratio between the inelastic and elastic maximum lateral displacement demands. Three options are investigated in order to express the inelastic response spectra in terms of: ductility demand, yield strength reduction factor, and inelastic deformation ratio which depends on the period, the post-to-preyield stiffness ratio, the yield strength and the peak ground acceleration. This new inelastic deformation ratio (C_n) is describes the response spectra and is related to the capacity curve (pushover curve): normalized yield strength coefficient (n), post-to-preyield stiffness ratio (α), natural period (T), peak ductility factor (µ), and the yield strength reduction factor (R_y). For illustrative purposes, instantaneous ductility demand and yield strength reduction factor for a SDOF system subject to various recorded motions (El-Centro 1940 (N/S), Boumerdes: Algeria 2003). The method accuracy is investigated and compared to classical formulations, for various hysteretic models and values of the normalized yield strength coefficient (n), post-to-preyield stiffness ratio (α), and natural period (T). Though the ductility demand and yield strength reduction factor differ greatly for some given T and n ranges, they remain take close when n>1, whereas they are equal to 1 for periods T>1s.
Key Words
    deformation ratio; yield strength; reduction factors; ductility; inelastic spectra; Pushover; normalized yield strength coefficient; seismic design
Benazouz Chikh, Nacer Laouami, Youcef Mehani, Abderrahmane Kibboua: National Earthquake Engineering Research Center, CGS, Rue Kaddour Rahim, BP 252 Hussein-Dey, Algiers, Algeria

Ahmed Mebarki: University Paris-Est, Laboratoire Modelisation et Simulation Multi Echelle (MSME), UMR 8208 CNRS, 5 Bd Descartes, 77454 Marne-La-Vallee, France

Moussa Leblouba: Department of Civil & Environmental Engineering, College of Engineering, University of Sharjah, P.O. Box 27272 Sharjah, United Arab Emirates

Mohamed Hadid: National School of Built and Ground Works Engineering (ENSTP), 01 Rue SidiGaridi, Vieux Kouba 16003, Algiers, Algeria

Djilali Benouar: University of Sciences& Technology Houari Boumediene (USTHB), Faculty of Civil Engineering, BP 32, 16111 El-Alia / Bab Ezzouar, Algiers, Algeria

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