equivalent linearization method

One of the important issues in performance-based earthquake engineering is the accurate estimation of the response statistics of nonlinear systems under seismic excitation. In this study, the near-field effects contained in the building design regulations against earthquakes (Standard No. 2800, fourth edition) are investigated on the nonlinear response of single degree of freedom systems with bilinear hysteretic restoring force characteristics. Near-field effects are presented in the Standard No. 2800 as spectral correction factor “N” in different seismicity regions. In this study, the site is located in a very high-seismicity zone and the ground type is considered as type II. Second- and third-order linearization methods are used to estimate the response of nonlinear systems. These methods are applied to derive equivalent linear properties. To achieve research goals, it is necessary to represent the input excitation as a quasi-stationary stochastic process compatible with target elastic design spectrum. In this regard, an effective numerical method in the field of random vibrations was used to determine the response spectrum compatible power spectra. After calculating the equivalent parameters related to linearization methods, random vibration theory and time history analysis approaches within the linear range were used to calculate the response of equivalent linear systems. In order to validate the results, the response values obtained from equivalent linearization methods for both approaches were compared with the results of nonlinear time history analysis (NTHA). For this purpose, 250 artificial non-stationary records compatible with two modes of the target spectrum were used to provide reasonable estimates of the peak response of the bilinear hysteretic systems. Artificial records were generated using simulation methods in the field of random vibrations by considering specified envelope functions and power spectral density. According to the results of this study, the second-order linearization method has insufficient accuracy in estimating the response of nonlinear systems under severe excitation. As the natural period of the systems increases, the discrepancy between the results of the equivalent linear system and the results of NTHA increases. Moreover, the good agreement between the third-order linearization results and the results of NTHA indicates the high efficiency of this method in estimating the response of nonlinear systems under the near field excitation.

Modern rocking self-centering frame is known as one of the most efficient seismic lateral resisting systems. Previous studies indicate that the analysis of this modern system is possible through nonlinear time history analysis (NTHA); however, its modeling and analysis are costly and time-consuming. To overcome this disadvantage, approximate analysis methods, including linearization analysis (ELA) method, are developed. For EAL method, the maximum inelastic displacement demand of a system is determined using elastic analysis of the equivalent single degree of freedom (SDOF) model. The method accuracy in estimating seismic demands depends on predefined parameters of equivalent damping ratio and secant stiffness for the equivalent system. This paper presents a new model for equivalent linear analysis of rocking self-centering systems under far-field ground motions. To this end, a set of rocking self-centering models with flag-shaped hysteretic behavior is simulated by OpenSees software. Exact and approximate estimations of inelastic displacement of the models are obtained using NTHA and ELA, respectively. Equivalent SDOF systems are first modeled with secant stiffness parameter and Jacobson's damping models. By using statistical analysis, the effect of the earthquake and modeling parameters on the analysis results is discussed based on various aspects. Findings indicated that the modeling parameters had the considerable effect on the equivalent linear model, while the seismic parameters had no significant effect. Moreover, it is shown that the Jacobson's damping parameter is not appropriate for ELA of rocking self-centering systems and leads to underestimating the maximum nonlinear displacement. In order to increase the accuracy of the proposed model, a new formula is proposed for optimal damping ratio by minimizing the error between the exact and approximate displacement demands obtained by NTHA and ELA, respectively. The assessment of efficiency for the proposed model showed that suggested formula could be used to estimate inelastic displacement of rocking self-centering systems.