Hysteretic energy prediction method for mainshock-aftershock sequences     

Changhai Zhai  Duofa Ji  Weiping Wen  Cuihua Li  Weidong Lei  Lili Xie 《地震工程与工程振动(英文版)》2018,17(2):277-291

Structures located in seismically active regions may be subjected to mainshock-aftershock (MSAS) sequences. Strong aftershocks significantly affect the hysteretic energy demand of structures. The hysteretic energy, E_H,seq, is normalized by mass m and expressed in terms of the equivalent velocity, V_D,seq, to quantitatively investigate aftershock effects on the hysteretic energy of structures. The equivalent velocity, V_D,seq, is computed by analyzing the response time-history of an inelastic single-degree-of-freedom (SDOF) system with a varying vibration period subjected to 309 MSAS sequences. The present study selected two kinds of MSAS sequences, with one aftershock and two aftershocks, respectively. The aftershocks are scaled to maintain different relative intensities. The variation of the equivalent velocity, V_D,seq, is studied for consideration of the ductility values, site conditions, relative intensities, number of aftershocks, hysteretic models, and damping ratios. The MSAS sequence with one aftershock exhibited a 10% to 30% hysteretic energy increase, whereas the MSAS sequence with two aftershocks presented a 20% to 40% hysteretic energy increase. Finally, a hysteretic energy prediction equation is proposed as a function of the vibration period, ductility value, and damping ratio to estimate hysteretic energy for mainshock-aftershock sequences.  相似文献   

A statistical approach to determine 2D optimal equivalent linear parameters with application to earthquake engineering     

Liang Su  Nan Xiao  Yi Wang 《地震工程与工程振动(英文版)》2012,11(3):415-425

The equivalent linearization method approximates the maximum displacement response of nonlinear structures through the corresponding equivalent linear system.By using the particle swarm optimization technique,a new statistical approach is developed to determine the key parameters of such an equivalent linear system over a 2D space of period and damping ratio.The new optimization criterion realizes the consideration of the structural safety margin in the equivalent linearization method when applied to the performance-based seismic design/evaluation of engineering structures.As an application,equations for equivalent system parameters of both bilinear hysteretic and stiffness degrading single-degree-offreedom systems are deduced with the assumption of a constant ductility ratio.Error analyses are also performed to validate the proposed approach.  相似文献   

An improved capacity spectrum method for ATC‐40     

Yu‐Yuan Lin  Kuo‐Chun Chang 《地震工程与结构动力学》2003,32(13):2013-2025

In order to account for the non‐linear behavior of structures via non‐linear static procedure, the capacity spectrum method has been adopted by ATC‐40 for evaluation and retrofit of reinforced concrete buildings. For elastic‐perfectly‐plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo‐acceleration response spectrum (PS_a) is used to create the demand diagram. It is found that the ATC‐40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S0._a) instead of the PS_a to establish the demand diagram. The step‐by‐step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake‐induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC‐40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (μ) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when μ>4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

Non‐iterative equivalent linearization of inelastic SDOF systems for earthquakes in Japan and California     

Katsuichiro Goda  Gail M. Atkinson 《地震工程与结构动力学》2010,39(11):1219-1238

The seismic performance of existing structures can be assessed based on nonlinear static procedures, such as the Capacity Spectrum Method. This method essentially approximates peak responses of an inelastic single‐degree‐of‐freedom (SDOF) system using peak responses of an equivalent linear SDOF model. In this study, the equivalent linear models of inelastic SDOF systems are developed based on the constant strength approach, which does not require iteration for assessing the seismic performance of existing structures. To investigate the effects of earthquake type and seismic region on the equivalent linear models, four ground‐motion data sets—Japanese crustal/interface/inslab records and California crustal records—are compiled and used for nonlinear dynamic analysis. The analysis results indicate that: (1) the optimal equivalent linear model parameters (i.e. equivalent vibration period ratio and damping ratio) decrease with the natural vibration period, whereas they increase with the strength reduction factor; (2) the impacts of earthquake type and seismic region on the equivalent linear model parameters are not significant except for short vibration periods; and (3) the degradation and pinching effects affect the equivalent linear model parameters. We develop prediction equations for the optimal equivalent linear model parameters based on nonlinear least‐squares fitting, which improve and extend the current nonlinear static procedure for existing structures with degradation and pinching behavior. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

Equivalent viscous damping for steel concentrically braced frame structures   总被引：1，自引：1，他引：0  

K. K. Wijesundara  R. Nascimbene  T. J. Sullivan 《Bulletin of Earthquake Engineering》2011,9(5):1535-1558

The direct displacement based seismic design procedure utilises equivalent viscous damping expressions to represent the effect of energy dissipation of a structural system. Various expressions for the equivalent viscous damping of different structural systems are available in the literature, but the structural systems examined in the past have not included concentrically braced frame structures. Thus, this study describes the development of an equivalent viscous damping equation for concentrically braced frame structures based on the hysteretic response of 15 different single storey models. Initially, equivalent viscous damping is calculated based on the area based approach and then corrected for the earthquake excitation. An iterative procedure is adopted to calibrate the equivalent viscous damping expression to the results of inelastic time history analyses using a number of spectrum-compatible real accelerograms. From the results of this research, a new damping expression is developed as a function of the ductility and the non dimensional slenderness ratio.  相似文献   

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity   总被引：1，自引：0，他引：1  

Pierino Lestuzzi  Youssef Belmouden  Martin Trueb 《Bulletin of Earthquake Engineering》2007,5(4):549-569

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 self-centring, 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%.  相似文献   

Estimating the “effective period” of bilinear systems with linearization methods,wavelet and time-domain analyses: From inelastic displacements to modal identification     

《Soil Dynamics and Earthquake Engineering》2013

This paper revisits and compares estimations of the effective period of bilinear systems as they result from various published equivalent linearization methods and signal processing techniques ranging from wavelet analysis to time domain identification. This work has been mainly motivated from the modal identification studies which attempt to extract vibration periods and damping coefficients of structures that may undergo inelastic deformations. Accordingly, this study concentrates on the response of bilinear systems that exhibit low to moderate ductility values (bilinear isolation systems are excluded) and concludes that depending on the estimation method used, the values of the “effective period” are widely scattered and they lie anywhere between the period-values that correspond to the first and the second slope of the bilinear system. More specifically, this paper shows that the “effective period” estimated from the need to match the spectral displacement of the equivalent linear system with the peak deformation of the nonlinear system may depart appreciably from the time needed for the nonlinear system to complete one cycle of vibration. Given this wide scattering the paper shows that for this low to moderate ductility values (say μ<10) the concept of the “effective period” has limited technical value and shall be used with caution and only within the limitations of the specific application.  相似文献