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Reinforced concrete structures are one of the most commonly used structures all over the world. However, the high nonlinear behaviour of this kind of structures still needs more research, e.g to shed light into the effects of nonlinear modelling and the structure characteristics. One of the most common methods to predict the nonlinear response of concrete structures is the simplified nonlinear spectra. The nonlinear spectra have been widely used in the seismic design and rehabilitation procedures e.g, ATC40 and FEMA 274. A set of closed-form formulas have been proposed in this manner to predict the strength reduction factor for a given period and ductility. The design and rehabilitation procedures can significantly simplified by using this kind of closed-form formulas. The aim of this paper is to evaluate the seismic behaviour of a set of 4620 single-degree-of-freedom (SDOF) oscillators, which was taken into account based on their period, damping and nonlinear backbone curve parameters. Eleven different periods, three damping ratios, five cracking states, seven ductility ratios, five hardening slopes and two collapse negative slopes were taken into account to cover a wide range of nonlinear behaviour of oscillators. The all combination of nonlinear characteristics with eleven periods and three damping ratios produces 4621 different oscillators to be investigated. The SDOF oscillators were analyzed for two sets of ground motion records which are representative of far and near field records. The far-field records contain 30 strike-slip records with moment magnitude of 6.5 to 6.9. The records are corresponding to the firm soil without any directivity effects. The near-field set contain 31 strike-slip records corresponding to four different earthquake events. They were all recorded within 16 kilometre of the earthquake epicentre. The incremental dynamic analysis was employed to calculate the system demand ductility in a wide range of earthquake intensity levels. The relationship between the strength reduction factor and the ductility factor was then derived for all considered SDOF systems. The results show that the natural period of vibration as well as the primary concrete cracking can significantly influence on the predicted strength reduction factors. The incremental dynamic analysis was employed to calculate the system demand ductility in a wide range of earthquake intensity levels. The relationship between the strength reduction factor and the ductility factor was then derived for all considered SDOF systems. The results show that the natural period of vibration as well as the primary concrete cracking can significantly influence on the predicted strength reduction factors. The incremental dynamic analysis was employed to calculate the system demand ductility in a wide range of earthquake intensity levels. The relationship between the strength reduction factor and the ductility factor was then derived for all considered SDOF systems. The results show that the natural period of vibration as well as the primary concrete cracking can significantly influence on the predicted strength reduction factors.

Keywords: Strength reduction factor, ductility, natural period of vibration, nonlinear spectrum, near field, Far field

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