IACSIT International Journal of Engineering and Technology, Vol. 5, No. 6, December 2013 694 DOI: 10.7763/IJET.2013.V5.644 Abstract—This paper examines the spectrum of inelastic displacement ratio (IDR) for structures subjected to near-fault earthquakes. IDR can be defined as the ratio of the maximum inelastic to the maximum elastic displacement of a structure and allows the computation of its maximum inelastic displacement directly from the corresponding elastic counterpart. Extensive parametric analyses are carried out to obtain empirical expressions for this ratio, in terms of the period of vibration and ductility demands. Index Terms—Inelastic displacement ratio spectrum, seismic analysis, ductility demands, near-fault earthquakes. I. INTRODUCTION This study develops a simple and efficient method for the evaluation of inelastic displacement ratio (IDR) spectrum. Knowledge of IDR, i.e. the ratio of the maximum inelastic to the maximum elastic displacement of a structure, allows the computation of its maximum inelastic displacement directly from the corresponding elastic counterpart. Veletsos [1], Veletsos and Newmark [2] and Clough [3] found that in the low-frequency range of the spectrum, the maximum displacement of an inelastic system may be considered the same as the maximum displacement of the associated elastic system, according to the so-called 'equal-displacement rule'. Nonetheless, Miranda [4] and Chopra and Chintanapakdee [5] observed that IDR can differ considerably from unity in the moderately high to high frequency regions of spectrum. Furthermore, Hatzigeorgiou and Beskos [6] found that repeated earthquakes significantly affect the inelastic displacement ratio. It is worth noticing that most of the seismic codes assumed far-fault earthquakes to describe the seismic loads. However, an earthquake that recorded closely to its fault at a station located toward the direction of the fault rupture is qualitatively quite different from the usual far-fault seismic records [7]. The categorization and analytical representation of near-fault earthquakes as well as the study of their effects on the seismic behavior of structures are very important research topics today. On e can mention here the works of Makris [8], Makris and Chung [9], Zhai et al., [10], Ruiz-Garcia [11] and Iervolino et al. [12]. Although the development that has been accomplished so far, there is still a clear need to understand the behavior of structures subjected to near-source seismic ground motions. Thus, this study Manuscript received May 15, 2013; revised July 1, 2013. The authors are with the Department of Environmental Engineering, Democritus University of Thrace, GR 67100 Greece (e-mail: gaylkabo@env.duth.gr, gchatzig@env.duth.gr). focuses on the evaluation of inelastic displacement ratio (IDR) spectrum of structures subjected to near-fault earthquakes. Without loss of generality, elastic - perfectly plastic models are adopted. These models are simple and can adequately describe steel or reinforced concrete structures with primarily flexural behavior. The influence of period of vibration and ductility demands are taken into account in constructing expressions for the IDR through extensive parametric studies and nonlinear regression analysis. A statistical investigation of 72,000 inelastic time-history analyses are carried out to study 200 SDOF models with 6 levels of ductility demands, excited by 60 earthquake accelerogram records from around the world, under various types of faults mechanisms such as strike-slip, reverse or oblique-reverse. II. DESCRIPTION OF MODEL An elastic – perfectly plastic SDOF system with viscous damping is used to model the structure, as shown in Fig. 1. The dynamic equilibrium equation of this system is given by g T ma u k u c u m - = + + $ $ $ (1) where m is the mass, u the relative displacement, c the damping coefficient, k T the tangent stiffness, a g the acceleration of the ground motion while upper dots stand for time derivatives. Fig. 1. Elastic - perfectly plastic model of a SDOF. Using structural dynamics theory [6], these systems are defined here by their elastic vibration period T, ranging from 0.02 sec to 4.0 sec, and viscous damping ratio, ξ , assumed to be 5%. The yield force f y can be expressed in terms of the yield displacement u y and the elastic stiffness k el as f y =k el ⋅u y (2) While the ductility μ is defined in terms of the maximum displacement u max and the yield displacement u y , as Inelastic Displacement Ratio Spectrum for Near-Fault Ground Motions Gaylord Kabongo-Booto and George D. Hatzigeorgiou