基于小波方法的多自由度体系地震动输入能量研究

对多自由度体系应用小波分解的地震激励,将地震动总输入能量表示为不同频段地震动输入能量的叠加.与单自由度体系相比,多自由度体系应用小波分解会产生较大的误差,这并不影响研究小波分解后各频段对单一固有振型输入能量的贡献.这样可以从频率的角度分析多自由度体系的地震动输入能量.     

On the estimation of hysteretic energy demands for SDOF systems

Based on a statistical study of the dynamic response of single degree of freedom (SDOF) systems subjected to earthquake ground motions, a rule to estimate hysteretic energy demands is proposed. Expressions for elastic–perfectly plastic, stiffness degrading and pinching SDOF systems were obtained. The proposed rule does not explicitly depend on the period of the system; instead, it depends on the elastic pseudo‐acceleration and elastic velocity spectra. It is shown that the proposed rule can be applied to compute hysteretic energy demands for systems located at different soil conditions. In addition, information about scatter and bias of the proposed rule is also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

Near‐fault ground motions,and the response of elastic and inelastic single‐degree‐of‐freedom (SDOF) systems

In order to investigate the response of structures to near‐fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long‐period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single‐degree‐of‐freedom (SDOF) system to near‐fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model is performed to gain insight regarding the near‐fault ground motion characteristics that significantly affect the elastic and inelastic structural performance. A parameter of the mathematical representation of near‐fault motions, referred to as ‘pulse duration’ (T_P), emerges as a key parameter of the problem under investigation. Specifically, T_P is employed to normalize the elastic and inelastic response spectra of actual near‐fault strong ground motion records. Such normalization makes feasible the specification of design spectra and reduction factors appropriate for near‐fault ground motions. The ‘pulse duration’ (T_P) is related to an important parameter of the rupture process referred to as ‘rise time’ (τ) which is controlled by the dimension of the sub‐events that compose the mainshock. Copyright © 2004 John Wiley & Sons, Ltd.     

Wavelet‐based characterization of design ground motions

With the recent emergence of wavelet‐based procedures for stochastic analyses of linear and non‐linear structural systems subjected to earthquake ground motions, it has become necessary that seismic ground motion processes are characterized through statistical functionals of wavelet coefficients. While direct characterization in terms of earthquake and site parameters may have to wait for a few more years due to the complexity of the problem, this study attempts such characterization through commonly available Fourier and response spectra for design earthquake motions. Two approaches have been proposed for obtaining the spectrum‐compatible wavelet functionals, one for input Fourier spectrum and another for input response spectrum, such that the total number of input data points are 30–35% of those required for a time‐history analysis. The proposed methods provide for simulating ‘desired non‐stationary characteristics’ consistent with those in a recorded accelerogram. Numerical studies have been performed to illustrate the proposed approaches. Further, the wavelet functionals compatible with a USNRC spectrum in the case of 35 recorded motions of similar strong motion durations have been used to obtain the strength reduction factor spectra for elasto‐plastic oscillators and to show that about ±20% variation may be assumed from mean to 5 and 95% confidence levels due to uncertainty in the non‐stationary characteristics of the ground motion process. Copyright © 2002 John Wiley & Sons, Ltd.     

Seismic response of self‐centring hysteretic SDOF systems

The seismic response of single‐degree‐of‐freedom (SDOF) systems incorporating flag‐shaped hysteretic structural behaviour, with self‐centring capability, is investigated numerically. For a SDOF system with a given initial period and strength level, the flag‐shaped hysteretic behaviour is fully defined by a post‐yielding stiffness parameter and an energy‐dissipation parameter. A comprehensive parametric study was conducted to determine the influence of these parameters on SDOF structural response, in terms of displacement ductility, absolute acceleration and absorbed energy. This parametric study was conducted using an ensemble of 20 historical earthquake records corresponding to ordinary ground motions having a probability of exceedence of 10% in 50 years, in California. The responses of the flag‐shaped hysteretic SDOF systems are compared against the responses of similar bilinear elasto‐plastic hysteretic SDOF systems. In this study the elasto‐plastic hysteretic SDOF systems are assigned parameters representative of steel moment resisting frames (MRFs) with post‐Northridge welded beam‐to‐column connections. In turn, the flag‐shaped hysteretic SDOF systems are representative of steel MRFs with newly proposed post‐tensioned energy‐dissipating connections. Building structures with initial periods ranging from 0.1 to 2.0s and having various strength levels are considered. It is shown that a flag‐shaped hysteretic SDOF system of equal or lesser strength can always be found to match or better the response of an elasto‐plastic hysteretic SDOF system in terms of displacement ductility and without incurring any residual drift from the seismic event. Copyright © 2002 John Wiley & Sons, Ltd.     

Non‐stationary seismic response of tanks with soil interaction by wavelets

A wavelet‐based random vibration theory has been developed for the non‐stationary seismic response of liquid storage tanks including soil interaction. The ground motion process has been characterized via estimates of statistical functionals of wavelet coefficients obtained from a single time history of ground accelerations. The tank–liquid–soil system has been modelled as a two‐degree‐of‐freedom (2‐DOF) system. The wavelet domain equations have been formulated and the wavelet coefficients of the required response state are obtained by solving two linear simultaneous algebraic equations. The explicit expression for the instantaneous power spectral density function (PSDF) in terms of the functionals of the input wavelet coefficients has been obtained. The moments of this PSDF are used to estimate the expected pseudo‐spectral acceleration (PSA) response of the tank. Parametric variations are carried out to study the effects of tank height, foundation natural frequency, shear wave velocity of soil and ratio of the mass of tank (including liquid) to the mass of foundation on the PSA responses of tanks. Copyright © 2001 John Wiley & Sons, Ltd.     

Simplification of strong ground motion considering inelastic responses of structures

Simplification of strong ground motions to 1 cycle sine waves was investigated from the elastic and inelastic earthquake response analyses and response analyses under sine wave input using single‐degree‐of‐freedom systems. Strong ground motions could be simplified to 1 cycle sine waves if large plastic deformations, with ductility factor more than 2, were assumed. This is because the approximate maximum responses from input sine waves are determined by the initial response cycle, due to period elongation and plastic energy dissipation of the systems. A sine wave whose acceleration amplitude is the peak ground acceleration (PGA) and whose period is that of an equivalent 1 cycle sine wave is proposed. The period of an equivalent sine wave is easily obtained from the elastic response acceleration spectrum of a seismic record. This means that the inelastic responses are approximately determined by the PGA and an equivalent 1 cycle sine wave period. Therefore, an equivalent 1 cycle sine wave period provides a single index to express the frequency characteristics of a strong ground motion. Copyright © 2000 John Wiley & Sons, Ltd.     

Quantification of ground-motion parameters and response spectra in the near-fault region

This study focuses on the characteristics of near-fault ground motions in the forward-direction and structural response associated with them. These ground motions are narrow-banded in nature and are characterized by a predominant period at which structures excited by them are severely affected. In this work, predominant period is defined as the undamped natural period of a single-degree-of-freedom (SDOF) oscillator at which its 5% damped linear elastic pseudo-spectral velocity (PSV) contains a clear and dominant peak. It is found that a linear relationship exists between predominant period and seismic moment. An empirical equation describing this relationship is presented by using a large set of accelerograms. Attenuation equations are developed to estimate peak ground velocity (PGV) as a function of earthquake magnitude and source-to-site distance. In addition, a predictive equation for spectral shapes of PSV (i.e., PSV normalized by PGV) is presented as a continuous function of the undamped natural period of SDOF oscillators. The model is independent of PGV, and can be used in conjunction with any available PGV attenuation relation applicable to near-fault ground motion exhibiting forward-directivity effects. Furthermore, viscous damping of the SDOF is included in the model as a continuous parameter, eliminating the use of so-called damping correction factors. Finally, simple equations relating force reduction factors and displacement ductility of elasto-plastic SDOF systems are presented.     

Analyzing the effect of moving resonance on seismic response of structures using wavelet transforms

There is a complex interaction between the seismic response (i.e., peak displacements) of a nonlinear structure and the characteristics of a ground motion. One ground motion characteristic that contributes to record‐to‐record variability is spectral nonstationarity, or the variation of signal's frequency content with time. When the predominant natural periods of a nonlinear structure elongate in such a way as to match with the predominant frequency content in the ground motion, a phenomenon called moving resonance occurs. The effect of moving resonance on the response of nonlinear structures is investigated. Continuous complex wavelet transforms are used to examine the spectral nonstationarity of ground motion acceleration histories and associated structural displacement histories to identify the occurrences of moving resonance. A three‐dimensional displacement response spectrum is used to determine which combinations of initial period and strength create the largest displacements and thus are candidate configurations for experiencing moving resonance. A method is then proposed for quantifying the effect of moving resonance on structural response. The method utilizes discrete wavelet transforms to decompose a ground motion into component signals with limited frequency band and examines the structural response due to each individual component. A discussion is provided as to how these tools can be used to identify ground motion characteristics that may be conducive to moving resonance. Copyright © 2013 John Wiley & Sons, Ltd.     

Ductility‐dependent intensity measure that accounts for ground‐motion spectral shape and duration

The calculated nonlinear structural responses of a building can vary greatly, even if recorded ground motions are scaled to the same spectral acceleration at a building's fundamental period. To reduce the variation in structural response at a particular ground‐motion intensity, this paper proposes an intensity measure (IM_comb) that accounts for the combined effects of spectral acceleration, ground‐motion duration, and response spectrum shape. The intensity measure includes a new measure of spectral shape that integrates the spectrum over a period range that depends on the structure's ductility. The new IM is efficient, sufficient, scalable, transparent, and versatile. These features make it suitable for evaluating the intensities of measured and simulated ground motions. The efficiency and sufficiency of the new IM is demonstrated for the following: (i) elastic‐perfectly plastic single‐degree‐of‐freedom (SDOF) oscillators with a variety of ductility demands and periods; (ii) ductile and brittle deteriorating SDOF systems with a variety of periods; and (iii) collapse analysis for 30 previously designed frames. The efficiency is attributable to the inclusion of duration and to the ductility dependence of the spectral shape measure. For each of these systems, the transparency of the intensity measure made it possible to identify the sensitivity of structural response to the various characteristics of the ground motion. Spectral shape affected all structures, but in particular, ductile structures. Duration only affected structures with cyclic deterioration. Copyright © 2015 John Wiley & Sons, Ltd.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

单自由度自复位体系设计能量谱研究

本文对具有旗帜型滞回模型的单自由度自复位体系提出了设计能量谱的构造方法,包括设计输入能量谱和设计滞回耗能比谱。首先按中国规范场地类别选取360条实际强震记录进行时程分析,对影响单自由度自复位体系输入能量谱和滞回耗能比谱的参数,包括地震波类型、滞回模型、阻尼比、延性系数等进行研究。在此基础上分别建议了设计输入能量谱和设计滞回耗能比谱及其曲线参数的确定方法,并与实际强震记录计算结果进行比较。结果表明结构滞回模型对能量谱影响明显;阻尼比和延性系数对输入能量谱的影响在整个周期范围内有显著差异,但均有明显的削峰作用。建议的两种设计能量谱综合考虑了结构参数、地震波参数和中国场地类别的影响,可以较好的拟合实际情况,并对弹塑性单自由度自复位体系在地震作用下的耗能需求做出较准确的估计。     

Influence of time‐varying frequency content in earthquake ground motions on seismic response of linear elastic systems

Earthquake ground motion records are nonstationary in both amplitude and frequency content. However, the latter nonstationarity is typically neglected mainly for the sake of mathematical simplicity. To study the stochastic effects of the time‐varying frequency content of earthquake ground motions on the seismic response of structural systems, a pair of closely related stochastic ground motion models is adopted here. The first model (referred to as ground motion model I) corresponds to a fully nonstationary stochastic earthquake ground motion model previously developed by the authors. The second model (referred to as ground motion model II) is nonstationary in amplitude only and is derived from the first model. Ground motion models I and II have the same mean‐square function and global frequency content but different features of time variation in the frequency content, in that no time variation of the frequency content exists in ground motion model II. New explicit closed‐form solutions are derived for the response of linear elastic SDOF and MDOF systems subjected to stochastic ground motion model II. New analytical solutions for the evolutionary cross‐correlation and cross‐PSD functions between the ground motion input and the structural response are also derived for linear systems subjected to ground motion model I. Comparative analytical results are presented to quantify the effects of the time‐varying frequency content of earthquake ground motions on the structural response of linear elastic systems. It is found that the time‐varying frequency content in the seismic input can have significant effects on the stochastic properties of system response. Copyright © 2016 John Wiley & Sons, Ltd.     

Scaling of ductility and damage‐based strength reduction factors for horizontal motions

The conventional approach of obtaining the inelastic response spectra for the aseismic design of structures involves the reduction of elastic spectra via response modification factors. A response modification factor is usually taken as a product of (i) strength factor, R_S, (ii) ductility factor, R_μ, and (iii) redundancy factor, R_R. Ductility factor, also known as strength reduction factor (SRF), is considered to primarily depend on the initial time period of the single‐degree‐of‐freedom (SDOF) oscillator and the displacement ductility demand ratio for the ground motion. This study proposes a preliminary scaling model for estimating the SRFs of horizontal ground motions in terms of earthquake magnitude, strong motion duration and predominant period of the ground motion, geological site conditions, and ductility demand ratio, with a given level of confidence. The earlier models have not considered the simultaneous dependence of the SRFs on various governing parameters. Since the ductility demand ratio is not a complete measure of the cumulative damage in the structure during the earthquake‐induced vibrations, the existing definition of the SRF is sought to be modified with the introduction of damage‐based SRF (in place of ductility‐based SRF). A parallel scaling model has been proposed for estimating the damage‐based SRFs. This model considers damage and ductility supply ratio as parameters instead of ductility demand ratio. Through a parametric study on ductility‐based SRFs, it has been shown that the hitherto assumed insensitivity of earthquake magnitude and strong motion duration may not be always justified and that the initial time period of the oscillator plays an important role in the dependence of SRF on these parameters. Further, the damage‐based SRFs are found to show similar parametric dependence as observed in the case of the ductility‐based SRFs. Copyright © 2000 John Wiley & Sons, Ltd.     

Inelastic displacement demands in steel structures and their relationship with earthquake frequency content parameters

This paper deals with the estimation of peak inelastic displacements of SDOF systems, representative of typical steel structures, under constant relative strength scenarios. Mean inelastic deformation demands on bilinear systems (simulating moment resisting frames) are considered as the basis for comparative purposes. Additional SDOF models representing partially‐restrained and concentrically‐braced (CB) frames are introduced and employed to assess the influence of different force‐displacement relationships on peak inelastic displacement ratios. The studies presented in this paper illustrate that the ratio between the overall yield strength and the strength during pinching intervals is the main factor governing the inelastic deformations of partially‐restrained models and leading to significant differences when compared with predictions based on bilinear structures, especially in the short‐period range. It is also shown that the response of CB systems can differ significantly from other pinching models when subjected to low or moderate levels of seismic demand, highlighting the necessity of employing dedicated models for studying the response of CB structures. Particular attention is also given to the influence of a number of scalar parameters that characterise the frequency content of the ground motion on the estimated peak displacement ratios. The relative merits of using the average spectral period T_aver, mean period T_m, predominant period T_g, characteristic period T_c and smoothed spectral predominant period T_o of the earthquake ground motion, are assessed. This paper demonstrates that the predominant period, defined as the period at which the input energy is maximum throughout the period range, is the most suitable frequency content scalar parameter for reducing the variability in displacement estimations. Finally, noniterative equivalent linearisation expressions based on the secant period and equivalent damping ratios are presented and verified for the prediction of peak deformation demands in steel structures. Copyright © 2011 John Wiley & Sons, Ltd.     

Wavelet‐based non‐stationary response analysis of a friction base‐isolated structure

A wavelet‐based stochastic formulation has been presented in this paper for the seismic analysis of a base‐isolated structural system which is modelled as a two‐degree‐of‐freedom (2‐DOF) system. The ground motion has been modelled as a non‐stationary process (both in amplitude and frequency) by using modified Littlewood–Paley basis wavelets. The proposed formulation is based on replacing the non‐linear system by an equivalent linear system with time‐dependent damping properties. The expressions of the instantaneous damping and the power spectral density function (PSDF) of the superstructure response have been obtained in terms of the functionals of input wavelet coefficients. The proposed formulation has been validated by simulating a ground motion process. The effect of the frequency non‐stationarity on the non‐linear response has also been studied in detail, and it has been clearly shown how ignoring the frequency non‐stationarity in the ground motion leads to inaccurate non‐linear response calculations. Copyright © 2000 John Wiley & Sons, Ltd.     

Procedure to predict the storey where plastic drift dominates in two‐storey building under strong ground motion

A procedure is presented to predict the storey where plastic drift dominates in two‐storey buildings under strong ground motion. The procedure utilizes the yield strength and the mass of each storey as well as the peak ground acceleration. The procedure is based on two different assumptions: (1) the seismic force distribution is of inverted triangular form and (2) the rigid‐plastic model represents the system. The first and the second assumptions, respectively, lead to lower and upper estimates of the base shear coefficient under which the drift of the first storey exceeds that of the second storey. The efficiency of the procedure is verified by dynamic response analyses using elasto‐plastic model. Copyright © 2008 John Wiley & Sons, Ltd.     

The effects of repeated earthquake ground motions on the non‐linear response of SDOF systems

In many parts of the world, the repetition of medium–strong intensity earthquake ground motions at brief intervals of time has been observed. The new design philosophies for buildings in seismic areas are based on multi‐level design approaches, which take into account more than a single damageability limit state. According to these approaches, a sequence of seismic actions may produce important consequences on the structural safety. In this paper, the effects of repeated earthquake ground motions on the response of single‐degree‐of‐freedom systems (SDOF) with non‐linear behaviour are analysed. A comparison is performed with the effect of a single seismic event on the originally non‐damaged system for different hysteretic models in terms of pseudo‐acceleration response spectra, behaviour factor q and damage parameters. The elastic–perfect plastic system is the most vulnerable one under repeated earthquake ground motions and is characterized by a strong reduction of the q‐factor. A moment resisting steel frame is analysed as well, showing a reduction of the q‐factor under repeated earthquake ground motions even larger than that of an equivalent SDOF system. Copyright © 2002 John Wiley & Sons, Ltd.     

A nonlinear SDOF model for the simplified evaluation of the displacement demand of low-rise URM buildings

The determination of displacement demands for masonry buildings subjected to seismic action is a key issue in the performance-based assessment and design of such structures. A technique for the definition of single-degree-of-freedom (SDOF) nonlinear systems that approximates the global behaviour of multi-degree-of-freedom (MDOF) 3D structural models has been developed in order to provide useful information on the dependency of displacement demand on different seismic intensity measures. The definition of SDOF system properties is based on the dynamic equivalence of the elastic properties (vibration period and viscous damping) and on the comparability with nonlinear hysteretic behaviour obtained by cyclic pushover analysis on MDOF models. The MDOF systems are based on a nonlinear macroelement model that is able to reproduce the in-plane shear and flexural cyclic behaviour of pier and spandrel elements. For the complete MDOF models an equivalent frame modelling technique was used. The equivalent SDOF system was modelled using a suitable nonlinear spring comprised of two macroelements in parallel. This allows for a simple calibration of the hysteretic response of the SDOF by suitably proportioning the contributions of flexure-dominated and shear-dominated responses. The comparison of results in terms of maximum displacements obtained for the SDOF and MDOF systems demonstrates the feasibility and reliability of the proposed approach. The comparisons between MDOF and equivalent SDOF systems, carried out for several building prototypes, were based on the results of time-history analyses performed with a large database of natural records covering a wide range of magnitude, distance and local soil conditions. The use of unscaled natural accelerograms allowed the displacement demand to be expressed as a function of different ground motion parameters allowing for the study of their relative influence on the displacement demand for masonry structures.     

基于SDOF体系和高层结构的地震动强度指标研究

合理的地震动强度指标是预测和评价结构抗震响应的重要基础。选取24个周期点的单自由度体系和一个高层框架核心筒长周期结构,基于不同震源机制的100条地震动记录时程分析结果,研究16种地震动强度指标与结构地震响应的相关性,并提出考虑高阶振型影响的改进反应谱相关型地震动强度指标。研究表明：（1）不同地震动强度指标与结构地震响应的相关性差别较大,随着单自由度体系自振周期的增大,地震动强度指标与单自由度体系地震响应的相关性大致呈减小的趋势;（2）对于高层长周期结构,综合对比分析各地震动强度指标分别与顶点最大位移、最大基底剪力、最大层间位移的相关性,从工程实用角度出发,推荐地面运动峰值速度为最佳地震动强度指标;（3）由于高层长周期结构受高阶振型影响显著,采用含有高阶振型因素的反应谱强度指标可提高与结构地震响应的相关性。