Midbroken reinforced concrete shear frames due to earthquakes. A hysteretic model to quantify damage at the storey level

A nonlinear hysteretic model for the response and local damage analyses of reinforced concrete shear frames subject to earthquake excitation is proposed, and, the model is applied to analyse midbroken reinforced concrete (RC) structures due to earthquake loads. Each storey of the shear frame is represented by a Clough and Johnston hysteretic oscillator with degrading elastic fraction of the restoring force. The local damage is numerically quantified in the domain [0,1] using the maximum softening damage indicators which are defined in closed form based on the variation of the eigenfrequency of the local oscillators due to the local stiffness and strength deterioration. The proposed method of response and damage analyses is illustrated using a sample 5 storey shear frame with a weak third storey in stiffness and/or strength subject to sinusoidal and simulated earthquake excitations for which the horizontal component of the ground motion is modeled as a stationary Gaussian stochastic process with Kanai-Tajimi spectrum, multiplied by an envelope function.     

Random vibration of nonlinear structures with stiffness and strength deterioration by modified tail equivalent linearization method

In this research the tail equivalent linearization method(TELM) has been extended to study structures with degrading materials. The responses of such structures to excitations are non-stationary, even if the excitations are stationary. Non-stationary behavior of the system cannot be considered by conventional TELM. Applying the conventional TELM, the only distinction in the design point excitation for two stationary excitations with different durations is in the addition of a zero value part at the beginning of the design point of the longer excitation. This means that the failure probability is the same for the non-stationary systems under excitations with different durations. Therefore, this solution cannot be correct. In this study, in using TELM for systems with degrading materials, hysteretic energy is replaced by average hysteretic energy, calculated by averaging the obtained hysteretic energy of the structure subjected to a few random sample load realization. In this way, the degradation parameters under design point coincide with those under sample load realizations. Since the average of the hysteretic energy is converges very fast, the modified TELM only requires about tens to hundreds solutions of the response in addition to the ordinary calculations of conventional TELM.     

Statistical insight into constant-ductility design using a non-stationary earthquake ground motion model

A recently developed earthquake ground motion model non-stationary in both intensity and frequency content is validated at the inelastic Single-Degree-Of-Freedom (SDOF) structural response level. For the purpose of this study, the earthquake model is calibrated for two actual earthquake records. The objective of a constant (or target) displacement ductility used in conventional earthquake-resistant design is examined from the statistical viewpoint using this non-stationary earthquake model. The non-linear hysteretic structural behaviour is modelled using several idealized hysteretic SDOF structural models. Ensemble-average inelastic response spectra corresponding to various inelastic SDOF response (or damage) parameters and conditioned on a constant displacement ductility response are derived from the two identified stochastic ground motion models. The effects of the type of hysteretic behaviour, the structural parameters, the target displacement ductility factor, and the ground motion model on the statistics of the inelastic response parameters are thoroughly investigated. The results of this parametric study shed further light on the proper interpretation and use of inelastic response or damage parameters in earthquake-resistant design in order to achieve the desirable objective of ‘constant-damage design’. © 1997 by John Wiley & Sons, Ltd.     

隔震减震主次结构体系非线性随机地震反应分析

为研究隔震、减震装置非线性恢复力特性对2自由度主次结构体系均方根位移反应的影响规律,以隔震、减震装置微分型恢复力模式的滞回参数为变量,地震地面运动模拟成高斯白噪声过程,利用等效线性化方法得到主体结构和二次结构均方根位移反应的表达式.分析表明,主体结构隔震装置非线性恢复力特征对主、次结构的均方根位移反应的影响占主导地位;隔震、减震装置的恢复力特征产生适度非线性有利于减小主、次结构的均方根位移反应.     

大型渡槽结构非线性地震响应分析

运用渡槽薄壁结构弹塑性动力分析模型,开展了渡槽非线性地震响应分析计算。该渡槽薄壁结构弹塑性动力分析模型集渡槽薄壁结构线弹性模型和非线性多弹簧模型为一体,应用多弹簧等效关系模拟结构塑性铰区的非线性滞回特性。经结构线弹性和非线性地震响应比较,结果表明两者存在差异,开展大型渡槽结构非线性地震响应分析是很有必要的。     

多点激励下圆柱面巨型网格结构地震响应分析

空间相关性对大跨度空间结构的影响不容忽视。本文采用动力时程分析方法对圆柱面巨型网格结构进行了多点激励下的地震响应分析,并与一致激励下的结构地震响应进行对比,探讨了主体结构单独承载和子结构参与协同承载这2种情况下,不同行波激励对结构关键节点和杆件响应的影响及其变化特点;通过比较分析结构在多点激励和一致激励下的响应差异,得出圆柱面巨型网格结构在地震输入时需考虑多点激励的结论,可供该类结构的抗震设计参考。     

基于滞回曲线以及结构动力方程的混凝土结构抗震稳定性分析

为准确全面地量化分析研究土木工程建筑中混凝土结构抗震稳定性,提出基于滞回曲线以及结构动力方程的混凝土结构抗震稳定性分析方法。首先采用滞回曲线描述混凝土结构在地震作用下的损伤情况,对滞回曲线模型拐点进行有效操作,确保动力方程对混凝土结构抗震稳定性进行有效分析。其次采用基于混凝土结构动力方程的抗震稳定性分析方法,对地震地面运动模型以及结构分析模型来分析混凝土结构的随机地震反应情况,得到混凝土结构随机反应的汇总量,在此基础上通过双参数的结构破坏模型,基于结构稳定性原理,获取运算混凝土结构抗震稳定性的概率表达式,再基于该表达式分析混凝土结构的抗震稳定性情况。实验结果说明,所提方法能够对土木工程建筑中不同类型混凝土构件抗震稳定性进行有效分析,分析结果准确且全面。     

Experimental and theoretical study on softening and pinching effects of bridge column

The goal of this study is to provide a better understanding on the behavior of pinching and softening effects for bridge column under earthquake loading. In the first part, a nonlinear cyclic loading test on a well-designed ductile RC bridge column was carried out experimentally. The hysteretic behavior of the bridge column was generated. In the second part, finite element analyses were used to predict the response under earthquake excitation. The hysteretic behavior obtained by experiment will be used as an input in material modeling for finite element programs. Discussions were made by using different computer codes to simulate the effects of pinching and softening of bridge column subjected to earthquake loading. Due to the inadequate functions of the element modeling, the theoretical system may underestimate the structural response under strong earthquake loading particularly on the prediction of softening and pinching effects.     

滞变—摩擦基底隔震系统的随机地震反应分析

本建立了滞变－摩擦基底隔震系统在地震作用下的运动微分方程，并将地震地面运动模拟成均值为零的两次过滤Ｇａｕｓｓ白噪声过程。使用等效线性化方法求解了这种隔震系统的地震反应统计特征，并分析了这种隔震系统参数的变化对其反应统计特征的影响。     

Site-dependent critical design spectra

A new type of seismic response spectrum is presented. It is based on the concept of a ‘ critical excitation’ which is defined here as an excitation among a certain class of excitations that will produce the largest response peak for a design variable of interest. Site conditions, namely rock, stiff soil and deep cohesionless soil, are taken into account through the definition of the class of allowable excitations. The response spectra thus produced are compared with others that have been proposed or used in the past. Results indicate that they lead to realistic if somewhat conservative assessment of structural earthquake resistance. On the other hand, they are derived under assumptions that are rather well supported by seismological observation and avoid other questionable assumptions, especially those regarding the statistics of ground motions. The critical response spectra may thus inspire greater confidence on the part of their users than those currently proposed or relied on.     

An identification methodology for a class of hysteretic structures

This paper presents a method of identification for determining non-linear dynamic models for certain hysteretic structures. Particular attention is given to modelling and identifying the hysteretic behaviour of structures from strong-motion earthquake data. In this method, the response is separated into mode-like components which are analogous to those of a linear system. Based on modelling of the generalized restoring force of each mode-like component, both non-hysteretic and hysteretic non-linear models are incorporated into the general methodology. A non-hysteretic model provides an initial estimate for a final hysteretic model. The approach is applicable even when data are available from only a small number of locations in the structure. The structural model identified from this method provides a means to predict the response to future events and, ultimately, to examine the damage to a structure as a result of an earthquake.     

EQUIVALENT LINEARIZATION OF GENERALLY PINCHING HYSTERETIC,DEGRADING SYSTEMS

Many types of structural systems that undergo cycles of inelastic deformation under severe natural hazard loadings exhibit ‘pinching’ of hysteresis loops. In this paper, a generally pinching hysteretic restoring force model—an extension of the Bouc–Wen differential hysteresis model—is used in stochastic equivalent linearization of single-degree-of-freedom structural systems. The severity and rate of pinching are controlled by the hysteretic energy dissipation and the pinching level can be specified to match experimental data. Under white noise excitations, estimates of reponse statistics from linearization are shown to compare favourably with those from Monte Carlo simulation. Numerical studies on the sensitivity of the accuracy of response statistics obtained by linearization to changes in the hysteresis parameters showed that, for a range of practical cases, the linearization method can be used in lieu of simulation and that, in low-frequency systems, some hysteresis parameters may be set to a constant value a priori to reduce the number of model parameters that needs to be estimated or identified, and to simplify further random vibration analysis and/or performance evaluation studies.     

随机地震动场多点激励下大跨度桥梁地震反应分析方法

地震输入问题一直是工程结构抗震研究关注的焦点。对大跨度桥梁结构，考虑随机地震动场的多点激励而进行地震反应分析较为合理。本文结合大跨度桥梁抗震设计，系统地介绍了随机地震动场的模型以及随机地震动场多点激励下大跨度桥梁地震反应分析的方法。     

Generation of critical stochastic earthquakes

A stochastic critical excitation is defined as that excitation with a given variance that maximizes the variance in the dynamic response of a system. A non-stationary filtered shot noise is used to develop a stochastic critical excitation model of an earthquake ground motion process, and the response statistics for a linear system are determined in both time and frequency domains. The sensitivity of response to several assumed earthquake pulse arrival rate functions is examined. Responses to recorded strong ground motion and to stochastic critical excitations with the same total energy are compared to assess the degree of conservatism in the procedure. An application of the procedure to seismic qualification of equipment is presented.     

An experimental study on using MR damper to mitigate longitudinal seismic response of a suspension bridge

In this paper, the seismic response reduction performance of magnetorheological (MR) damper is experimentally investigated for a suspension bridge. First, the force–displacement and force–velocity curves under a range of excitation frequencies, amplitudes and currents are obtained by mechanical behavior test of the RD1097 type MR damper. Then a new non-linear hysteretic model is proposed to model the mechanical behavior of the MR damper and the model parameters are identified from test data. An experimental method, as well as a set of testing setups with the MR damper for longitudinal seismic response reduction of a SDOF generalized system representing the fundamental longitudinal mode of suspension bridge, is developed. Finally, the seismic response reduction experiment subject to three kinds of earthquake excitations, including the Pingsheng Bridge earthquake wave, the El-Centro wave and the Taft wave, is carried out, and nine control cases, including uncontrolled, six passive control schemes with different input currents and two semi-active Bang–Bang control schemes, are tested. The results verify that the seismic response reduction experimental method is feasible and the good performance of seismic longitudinal response reduction of the suspension bridge can be achieved by MR damper. It is also shown that the passive control with optimum input current outperforms the semi-active Bang–Bang controls.     

Response of tanks to vertical seismic excitations

A method for analyzing the earthquake response of elastic, cylindrical liquid storage tanks under vertical excitations is presented. The method is based on superposition of the free axisymmetrical vibrational modes obtained numerically by the finite element method. The validity of these modes has been checked analytically and the formulation of the load vector has been confirmed by a static analysis. Two forms of ground excitations have been used: step functions and recorded seismic components. The radial and axial displacements are computed and the corresponding stresses are presented. Both fixed and partly fixed tanks are considered to evaluate the effect of base fixation on tank behaviour. Finally, tank response under the simultaneous action of both vertical and lateral excitations is calculated to evaluate the relative importance of the vertical component of ground acceleration on the overall seismic behaviour of liquid storage tanks.     

大跨度空间网格结构多维多点随机地震反应分析

本文建立了三维正交地震动多点激励下大跨度空间网格结构的随机地震反应分析方法,依据现行抗震设计规范的有关规定,确定了平稳随机地震动功率谱密度的模型参数。数值仿真分析了一柱距80m的正方形平板网架分别在一维地震动或三维地震动的一致激励、行波激励和考虑部分相干效应的随机激励下的地震反应。结果表明:考虑地震动的空间效应会很大程度地改变结构杆件的内力,其中控制杆件的内力增幅达到30%;地震动的行波效应对结构杆件内力的影响比随机地震动的部分相干效应的影响更大;三维地震作用比一维地震作用下结构杆件的内力大。由此得出结论,对于大跨度空间网格结构,必须进行多维多点地震激励下的随机地震反应分析。     

Tuned inerter dampers with linear hysteretic damping

This paper explores the influence of linear hysteretic damping on the performance of passive tuned-inerter devices. An inerter is a device that produces a force proportional to the relative acceleration across its two terminals; devices incorporating inerters have received widespread attention in the earthquake engineering community, because they offer the ability to improve the seismic response of structures. However, the majority of this research has assumed that the damping components within the tuned-inerter device exhibit viscous, rather than hysteretic, damping. This restriction imposes an essential question on how the hysteretic damping model will change the performance of the device compared with the viscous damping model. It is shown that the response of viscous and hysteretic inerter systems have significant differences in displacement amplitude due to the frequency dependency of the damping. Therefore, a new formulation for obtaining the optimum loss factor of the hysteretic damping in the inerter system is proposed. Next, the challenges associated with accurately predicting the time-response of a hysteretically damped system are discussed. A numerical time-integration method is extended to address these challenges, using a new formulation that has the benefit of being broadly applicable to multidegree-of-freedom hysteretic linear systems and nonstationary random signals. The results show that the earthquake responses from the hysteretic damping model can differ significantly from the ones obtained via the viscous model.     

苏通大桥南引桥场地土层地震反应的数值分析

针对苏通引桥建设的实际背景和软弱地基的特点,利用二维有限元整体分析法,对其场地进行了地震反应数值分析。采用等效线性化模型描述土的非线性性质,研究了基岩在一致输入及采用不同行波输入下的场地地震反应特点。计算结果表明,不同的行波速度和行波输入方向,对地表加速度以及相对位移的峰值和相位均有不同程度的影响,对于重要结构来说进行多点地震波输入下的地震反应分析,有助于科学合理地确定结构的地震动输入模式。     

密肋壁板结构宏观模型及非线性时程反应分析

采用SAP程序中的Link单元进行了密肋壁板结构非线性时程反应分析。推导了Link单元的刚度矩阵,确定了相对转动中心高度。并结合钢筋混凝土柱轴向恢复力模型和密肋复合墙体水平抗侧恢复力模型,给出了Link单元竖向和水平连接弹簧非线性力-位移关系的计算公式。采用Link单元建立了密肋壁板结构宏观有限元分析模型,并对1/10比例振动台模型试验进行了非线性时程反应分析。结果表明:计算结果与试验结果吻合良好,这说明采用Link单元可以较好的模拟密肋壁板结构的动力非线性行为。