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This paper investigates the non-linear seismic behavior of structures such as slender unreinforced masonry shear walls or precast post-tensioned reinforced concrete elements, which have little hysteretic energy dissipation capacity. Even if this type of seismic response may be associated with significant deformation capacity, it is usually not considered as an efficient mechanism to withstand strong earthquakes. The objective of the investigations is to propose values of strength reduction factors for seismic analysis of such structures.The first part of the study is focused on non-linear single-degree of freedom (SDOF) systems. A parametric study is performed by computing the displacement ductility demand of non-linear SDOF systems for a set of 164 recorded ground motions selected from the European Strong Motion Database. The parameters investigated are the natural frequency, the strength reduction factor, the post-yield stiffness ratio, the hysteretic energy dissipation capacity and the hysteretic behavior model (four different hysteretic models: bilinear selfcentring, with limited or without energy dissipation capacity, modified Takeda and Elastoplastic). Results confirm that the natural frequency has little influence on the displacement ductility demand if it is below a frequency limit and vice versa. The frequency limit is found to be around 2 Hz for all hysteretic models. Moreover, they show that the other parameters, especially the hysteretic behavior model, have little influence on the displacement ductility demand. New relationships between the displacement ductility demand and the strength reduction factor for structures having little hysteretic energy dissipation capacity are proposed. These relationships are an improvement of the equal displacement rule for the considered hysteretic models. In the second part of the investigation, the parametric study is extended to multi-degree of freedom (MDOF) systems. The investigation shows that the results obtained for SDOF systems are also valid for MDOF systems. However, the SDOF system overestimates the displacement ductility demand in comparison to the corresponding MDOF system by approximately 15%.

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This paper reports the main results of an extensive parametric study using numerical simulations and computing displacement ductility demand of nonlinear single-degree of freedom (SDOF) systems and multi-degree of freedom (MDOF) systems for a set of 164 registered ground motions. The objective of this study is to propose values of strength reduction factors for rocking behavior for seismic analysis. In the first part focused on SDOF systems, non-linear seismic responses obtained with a hysteretic model simulating rocking are statistically compared with the ones related to established hysteretic models for ductile structures. Similar to established hysteretic models, results confirm that the frequency has little influence on the ductility demand if it is below 2 Hz and a substantial influence if it is above 2 Hz. Moreover, they show that the other parameters, especially the hysteretic behavior model, have only little influence on the displacement ductility demand. Surprisingly, displacement ductility demand is found to be practically independent of the additional viscous damping ratio. Finally, a relationship between displacement ductility demand and strength reduction factor for rocking systems is proposed. The second part shows that the results obtained for SDOF systems are also valid for MDOF systems.