Non-stationary seismic response of MDOF systems by wavelet transform

A wavelet-based formulation has been presented in this paper for the stochastic analysis of a linear multi-degree-of-freedom (MDOF) classically damped system subjected to earthquake ground motion. The ground motion has been modelled as a non-stationary process (both in amplitude and frequency) using wavelets. Closed-form expressions of the moments of the instantaneous Power Spectral Density Function (PSDF) of the response have been derived and used to predict the statistics of the response peak of any desired order. For illustration of the formulation, an example torsionally coupled multistoried building has been considered along with the twenty synthetically generated time-histories corresponding to an example ground motion process. © 1997 John Wiley & Sons, Ltd.     

非比例阻尼线性体系地震反应计算的振型分解反应谱法

以非比例阻尼线性体系地震反应计算实数形式的一般解答为基础,推导得到了非比例阻尼线性体系水平地震作用计算的多种形式,建立了非比例阻尼线性体系地震反应计算振型分解反应谱法的基本过程与步骤。最后,以一个五层剪切型结构为例,通过与各种常用直接积分方法计算结果的比较,证实了本文非比例阻尼线性体系地震反应计算实数形式的一般解答的高精度与可靠性。通过对多种形式地震作用所得地震效应的比较,证实了非比例阻尼线性体系地震反应振型分解反应谱方法的可靠性及可行性。     

Comparison of seismic force reduction factors used in U.S.A. and Japan

This paper compares the seismic force reduction factors used in the United States and Japan. Since these factors appear in a very different format in the two countries, for comparison purposes, a general expression relating the force reduction factor to the structural ductility and overstrength factors is first established. This study shows that (i) the seismic design limit state philosophy applied to moderate and severe earthquakes is treated differently in each country; (ii) the Japanese code requires the designer to check explicitly the serviceability limit state, while the American codes do not require the member's strength be checked for the serviceability limit state; (iii) the force reduction factors used in Japan for the ultimate limit state check are significantly smaller than those used in the United States, and (iv) the force reduction factors used in Japan are even smaller if structural overstrength is not explicitly checked by designers.     

剪切型结构的抗震强度折减系数研究

为了研究剪切型结构抗震强度需求的变化规律,本文基于单自由度体系的非线性时程分析,研究了不同场地条件下延性折减系数与位移延性系数和结构自振周期的关系;采用修正等效单自由度体系位移延性折减系数的方法,研究了剪切型多自由度体系的延性折减系数;以基于中国建筑抗震规范设计的代表不同抗震能力要求的RC框架结构为分析对象,通过静力弹塑性分析,研究了RC框架结构的体系超强能力。分析结果表明场地类别、位移延性水准和结构振动周期对单自由度体系的延性折减系数有显著的影响;多自由度体系的抗震延性折减系数明显比其相应的等效单自由度体系的抗震延性折减系数小;RC框架结构的超强系数一般随结构楼层数的增加而减小,随抗震设防烈度的增大而减小,内框架的超强系数比边框架的超强系数大。     

Estimation of strength reduction factors via normalized pseudo‐acceleration response spectrum

Estimation of design forces in ductility‐based earthquake‐resistant design continues to be carried out with the application of response modification factors on elastic design spectra, and it remains interesting to explore how best to estimate strength reduction factors (SRFs) for a design situation. This paper considers the relatively less explored alternative of modelling SRF spectrum via a given response spectrum. A new model is proposed to estimate the SRF spectrum in terms of a pseudo‐spectral acceleration (PSA) spectrum and ductility demand ratio with the help of two coefficients. The proposed model is illustrated for an elasto‐plastic oscillator, in case of 10 recorded accelerograms and three ductility ratios. The proposed model is convenient and is able to predict SRF spectrum reasonably well, particularly at periods up to 1.0 s. Coefficients of the proposed model may also be determined in case of a given design spectrum when there is uncertainty in SRF spectrum due to uncertainty in temporal characteristics of the ground motion. This is illustrated with the help of 474 accelerograms recorded in western U.S.A. and different scaled PSA spectra. It is shown that probabilistic estimates may be obtained in this situation for SRF spectrum by assuming the error residuals to be log normally distributed with period‐dependent parameters. Copyright © 2006 John Wiley & Sons, Ltd.     

Non-stationary spectral moments of base excited MDOF systems

The paper deals with the evaluation of non-stationary spectral moments of multi-degree-of-freedom (MDOF) line systems subjected to seismic excitations. The spectral moments of the response are evaluated in incremental form solution by means of an unconditionally stable step-by-step procedure. As an application, the statistics of the largest peak of the response are also evaluated.     

The non‐stationary cross‐correlation coefficients in the seismic analysis of MDOF structural systems

A method concerning the evaluation, in a very compact form, of the non‐stationary modal cross‐correlation coefficients of MDOF structural systems subjected to seismic excitations is presented. It is available both in the case when the excitation is considered as a white‐noise process and when it is considered as a filtered process. The evaluation of these coefficients is required when a transient seismic analysis is performed by the use of the modal response spectrum approach. This is necessary when the strong‐motion phase of the earthquake is significantly short with respect to the fundamental period of the structure. Copyright © 2003 John Wiley & Sons, Ltd.     

结构抗震设计中的强度折减系数研究

借助于单自由度弹塑性动力时程分析程序，对延性结构的强度折减系数进行了研究，在统计平均和回归分析的基础上，建立了平均强度折系数的函数形式，本文所建立的平强度折减系数函数，从理论上明确了结构具有延性对弹性地震力的折减关系，研究成果可供结构抗震设计规范采纳应用。     

Effect of structural characteristics distribution on strength demand and ductility reduction factor of MDOF systems considering soil-structure interaction

It is known that structural stiffness and strength distributions have an important role in the seismic response of buildings.The effect of using different code-specified lateral load patterns on the seismic performance of fixed-base buildings has been investigated by researchers during the past two decades.However,no investigation has yet been carried out for the case of soil-structure systems.In the present study,through intensive parametric analyses of 21,600 linear and nonlinear MDOF systems and considering five different shear strength and stiffness distribution patterns,including three code-specified patterns as well as uniform and concentric patterns subjected to a group of earthquakes recorded on alluvium and soft soils,the effect of structural characteristics distribution on the strength demand and ductility reduction factor of MDOF fixed-base and soil-structure systems are parametrically investigated.The results of this study show that depending on the level of inelasticity,soil flexibility and number of degrees-of-freedoms(DOFs),structural characteristics distribution can significantly affect the strength demand and ductility reduction factor of MDOF systems.It is also found that at high levels of inelasticity,the ductility reduction factor of low-rise MDOF soil-structure systems could be significantly less than that of fixed-base structures and the reduction is less pronounced as the number of stories increases.     

Site-dependent strength reduction factors for soil-structure systems

The effect of soil conditions on strength reduction factors (SRFs) is investigated. Both site effect and soil-structure interaction (SSI) effect are considered in the study with special emphasis on the latter effect. The structure is modeled as an elasto-plastic single degree of freedom (SDOF) system, whereas the underlying soil is considered as a homogeneous half-space. The half-space is also replaced by a simplified 3DOF system, based on the concept of Cone Models. The whole 4DOF model is then analyzed under a total of 54 strong motions recorded on different soil types. A parametric study is done for a wide range of non-dimensional parameters, which completely define the problem. It is concluded that SSI reduces the SRF values, especially for the case of buildings located on soft soil. Consequently, using the fixed-base SRFs for soil-structure systems lead to non-conservative design forces. Simplified expressions are proposed to estimate SRF for soil-structure systems.     

抗震规范应用强度折减系数的现状及分析

世界上大多数的抗震规范都采用了基于强度的设计方法,强度折减系数是基于强度的抗震设计中确定设计地震力的关键因素,提高强度折减系数的可靠性已经被认为是提高现有抗震规范可靠性的有效途径。本文主要介绍了抗震研究处于世界先进水平的美国(UBC97)、欧洲(EC8)、日本、墨西哥、加拿大、中国等国家抗震规范中强度折减系数取值的有关规定,然后给出了各国学者关于规范规定的强度折减系数的一些重要讨论和分析,最后指出了世界各国应用强度折减系数过程中存在的不足,指出了需进一步研究的问题。     

近断层地震动和单自由度体系地震反应的分形特征分析

从分形几何的新视角出发,分析近断层地震动的不规则性和复杂性.利用盒维数法计算了来自台湾集集地震和美国北岭地震的30条近断层地震动加速度时程的分形维数.计算结果表明,这些地震动加速度时程具有统计分形特征.近断层地震动运动特征对其分维数影响明显,滑冲效应脉冲地震动的分维数平均值最小,向前方向性效应脉冲地震动的分维数平均值居中,无脉冲地震动的分维数平均值最大,其波形不规则程度也最高.而且,地震动时程的分维数反映了其频谱特性,可作为频谱周期的表征参数.地震动的分维数D与特征周期Tc具有较强的负相关关系.最后,对于近断层地震动作用下单自由度(SDOF)体系的弹性和非弹性动力反应时程,应用盒维数法计算了其分形维数,考察了其分形性质.     

Optimal design of SDOF envelope systems for the responses of MDOF dynamic systems

The concept of envelope system for a given dynamic system is proposed in this paper which refers to those systems whose module of transfer function in the whole range of frequency domain is always bigger than that of a given system. This concept opens a new way to study the problems of robust design and modelling for dynamic systems. The condition that an envelope system has to satisfy is rendered as the determination of the positiveness of a real polynomial function and Sturm's sequence method is used to establish an easily implemented criterion for evaluating the positiveness of the polynomial in terms of its coefficients. The optimization for the envelope system is expressed as the minimization of the 2-norm of its transfer function and simplex method is employed to search for the optimal solution. Two dynamic systems are used to illustrate the optimal design for the envelope systems of some of their responses. © 1998 John Wiley & Sons, Ltd.     

Spectra of seismic waves of Matsushiro micro-earthquakes

Summary The spectra of Matsushiro micro-earthquakes were studied using a spectrum analyser and discussed in relation to their magnitude and the epicentral distance. It was found that the spectra of seismic waves by Matsushiro micro-earthquakes did not depend upon the epicentral distance since the sonagrams showed a peak around 5 cps at Matsushiro as well as Suzaka. The spectrum also failed to show any distinct peak for micro-earthquakes of magnitude lower than 1.0 due to the decrease of signal to noise ratio.     

中国地震科学台阵两期观测资料近场记录揭示的南北地震带地壳剪切波分裂特征

利用中国地震科学台阵第一期（2011-01—2014-06）及部分中国地震科学台阵第二期（2013-02—2015-12）的流动地震台阵记录到的小震波形资料,运用剪切波分裂系统分析（SAM）方法,分析南北地震带的地壳各向异性,对剪切波分裂参数所反映的区域应力环境及构造特征,以及区域内主压应力方向与断裂分布的关系展开讨论.研究结果表明,南北地震带快剪切波偏振方向自北向南由NE向逐渐转变为NNW向,与南北地震带区域主压应力的方向变化具有一致性.区域内分布的大量NE及WNW或NW向断裂构造同样对快波偏振方向有比较大的影响,位于走滑断裂附近的台站,其快波方向与断裂走向大致平行,部分位于走滑断裂附近的台站其快波方向几乎垂直于断裂走向,而与构造应力场方向一致性较好.个别台站表现出复杂快波优势方向特征,反映出研究区内构造环境的复杂性.慢波时间延迟结果显示,南北地震带南段的平均时间延迟高于北段,反映了受印度板块和欧亚板块的碰撞挤压作用,南段地壳介质各向异性程度更大,构造变形更加剧烈.对比南北地震带上地幔各向异性特征,推测在川滇菱形块体内部可能存在复杂的壳幔耦合现象,地壳剪切波分裂除了反映区域应力特征,还可以揭示出区域构造信息.

     

几条地震波的归一化时-频反应谱分析

时-频反应谱是地震动幅值、频谱和持时三要素构成的空间三维谱.基于此,本文提出归一化时-频反应谱定义与计算方法,计算三条典型地震波的归一化时-频反应谱,对比分析表明:不同地震记录的时-频反应谱的幅值在时间和周期两个轴上的分布差别很大,具有不同时-频反应谱的地震波可能对结构地震响应产生不同影响;对12层钢筋混凝土框架结构模型进行弹塑性时程分析,通过结构地震反应、结构损伤曲线与输入地震动的归一化时-频反应谱对比,发现结构最大反应并不一定是造成结构倒塌的直接原因,用结构弹性阶段反应最大值进行抗震设计存在一定局限性,从而证明归一化时-频反应谱可有效用来分析地震动特性和结构破坏机理.     

Strength reduction factors for seismic analyses of buildings exposed to near-fault ground motions

To estimate the near-fault inelastic response spectra, the accuracy of six existing strength reduction factors (R) proposed by different investigators were evaluated by using a suite of near-fault earthquake records with directivity-induced pulses. In the evaluation, the force-deformation relationship is modelled by elastic-perfectly plastic, bilinear and stiffness degrading models, and two site conditions, rock and soil, are considered. The R-value ratio (ratio of the R value obtained from the existing R-expressions (or the R-μ-T relationships) to that from inelastic analyses) is used as a measurement parameter. Results show that the R-expressions proposed by Ordaz & Perez-Rocha are the most suitable for near-fault ground motions, followed by the Newmark & Hall and the Berrill et al. relationships. Based on an analysis using the near-fault ground motion dataset, new expressions of R that consider the effects of site conditions are presented and verifi ed.     

An alternative construction of normalized seismic design spectra for near-fault regions

This paper presents a methodology for constructing seismic design spectra in near-fault regions.By analyzing the characteristics of near-fault pulse-type ground motions,an equivalent pulse model is proposed,which can well represent the characteristics of the near-fault forward-directivity and fling-step pulse-type ground motions.The normalized horizontal seismic design spectra for near-fault regions are presented using recorded near-fault pulse-type ground motions and equivalent pulse-type ground motions,which are derived based on the equivalent pulse model coupled with ground motion parameter attenuation relations.The normalized vertical seismic design spectra for near-fault regions are obtained by scaling the corresponding horizontal spectra with the vertical-to-horizontal acceleration spectral ratios of near-fault pulse-type ground motions.The proposed seismic design spectra appear to have relatively small dispersion in a statistical sense.The seismic design spectra for both horizontal and vertical directions can provide alternative spectral shapes for seismic design codes.     

Probabilistic analysis of peak response of MDOF systems with uncertain PSD function

The use of uniform hazard spectra which have the same probability of exceedance at different frequencies has been proposed for the future version of the National Building Code of Canada. Commonly used combination rules to estimate the peak responses of multi‐degree‐of‐freedom (MDOF) systems are the square root of sum of squares rule and the complete quadratic combination rule. However, the probability that the peak response of a MDOF system exceeds the one estimated by using these rules with the peak modal responses from the uniform hazard spectra cannot be inferred directly. The assessment of the probability of exceedance of the peak response of MDOF systems is presented by considering that the uncertainty in seismic excitation due to all potential earthquakes can be lumped in the power spectral density function of the ground acceleration with uncertain model parameters. This probability is evaluated based on the random vibration of linear systems and the first‐order reliability method. It is found that the under‐ or over‐estimations are less than about 5 or 10% if the modal contributions are not within 10–90% of, or not within 20–80% of, the absolute sum of the effective modal peak responses, respectively. Otherwise, severe under‐ or over‐estimation could result. Copyright © 2002 John Wiley & Sons, Ltd.