Energy dissipating restrainers for highway bridges

Recent destructive earthquakes have demonstrated the vulnerability of highway bridges to collapse due to excessive movement beyond the available seat widths at expansion joints. This paper investigates the efficacy of using energy dissipating restrainers at expansion joints for preventing collapse of highway bridges in the event of a severe earthquake. The restrainer consists of a nonlinear viscous damper and an elastic spring connected in parallel or in series. Two-dimensional finite element analysis using bilinear hysteretic models for bridge substructure joints and nonlinear gap elements for expansion joints is performed on example bridges with one or two expansion joints. The analytical study demonstrates that the energy dissipating restrainers are effective in reducing the relative opening displacements and impact forces due to pounding at the expansion joints, without significantly increasing ductility demands in the bridge substructures.     

Inelastic seismic response of stiffening systems and development of demand spectrum: Application to MSSS bridges

A stiffening system is a system that increases its stiffness as it goes under large displacements. Such behavioural characteristic can result from constitutive behaviour or at the structural level often from closure of gaps between various components (sub‐systems) of the structure. An example of the latter situation is multi‐span simply supported (MSSS) bridges under horizontal earthquake ground motion. Unlike softening systems, stiffening systems have not been studied. In addition to the need for more understanding of the seismic response of stiffening systems, there is a need to develop response spectrum that can be used in design. Several parameters including gap size and ratios of sub‐systems stiffness, strength, and mass control the behaviour of a stiffening system. In this study, a simplified stiffening model is developed and over 367 000 cases are analysed to investigate the nonlinear stiffening behaviour and pounding. Parameters considered also include ground motion characteristic. Results are evaluated and compared in terms of displacement and dissipated hysteretic energy. Parameter study results show that, on average, the displacement response is lower for stiffening systems, however, they dissipates higher hysteretic energy, due to higher yield cycles and yield excursions, and can possibly sustain more damage than a bilinear, elastic–plastic system. Using parameter study database, design response spectrum for stiffening systems is also proposed and its practical application is demonstrated through its application to an MSSS bridge. Results of this study goes beyond MSSS bridges and will have application for many structural systems where response is characterized by a stiffening behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Choice between series and parallel connections of hysteretic system and viscous damper for seismic protection of structures

Supplemental viscous damping devices are generally envisioned to be connected in parallel to the inelastic parent structure or hysteretic damping devices. This gives rise to higher base shear, and often greater ductility demand of the hysteretic system. The series connection of the viscous and hysteretic system (the inelastic structure or a damper) is an alternative approach. In this paper, comparisons between the series and parallel connections of the hysteretic system and viscous dampers are done through response spectra analyses of single degree of freedom structures. Ductility demand of the hysteretic system and the total base shear are chosen as the response quantities. For the series model, a semi‐implicit solution scheme for classical Maxwell model is modified to include the inelasticity of the time‐independent hysteretic spring. It is observed that the series connection of the 2 dampers gives lower base shear than does the parallel connection. For long‐period and low‐damping structures, the ductility demand of the hysteretic system in series connection is higher than that in parallel connection. Increasing the viscous damping in series connection reduces the ductility demand substantially, lower than that obtained in parallel connection. Practical methods for implementing the series and parallel connections, in line with roof isolation, are also suggested.     

Inelastic seismic response of simple eccentric structures

The maximum ductility demand and the edge displacement of a simple single mass eccentric model is evaluated when the system is subjected to ground motions represented by the El Centro 1940 and Taft 1952 earthquake records. The resisting elements are taken to be bilinear hysteretic. It is found that the ductility demand depends to a great extent on the energy content of the ground motions, particularly in the period range beyond the elastic period of the system. Unlike elastic response, the coincidence of uncoupled torsional and lateral frequencies does not lead to exceptionally high inelastic response. An increase by a factor of two in ductility demand is not uncommon for a system with large eccentricity as compared to a symmetrical system. Therefore, system eccentricity has a larger effect on ductility demand than earlier studies indicated. Using Clough's model to allow for stiffness degradation effect, results are found to be within 20 per cent of those calculated based on the bilinear hysteretic model.     

型钢混凝土异形柱恢复力特性的试验研究

为了研究型钢混凝土异形柱的抗震性能,进行了17根型钢混凝土异形柱模型的拟静力试验,得到了型钢混凝土异形柱模型在低周反复荷载作用下的滞回曲线和P-△骨架曲线。通过试验结果的分析,给出了各关键点的试验数据及刚度退化规律,建议型钢混凝土异形柱恢复力模型采用双线型模型和退化三线型模型,并给出了恢复力模型各阶段刚度参数的计算公式,为型钢混凝土异形柱的非线性地震反应分析提供了理论参考。     

An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy (R_E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude.Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio.The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.     

广东地区地震动衰减和场地响应的研究

根据广东数字地震台网14个地震台的249条波形资料，研究了广东地区的衰减模型和各台站的场地响应. 采用三段几何衰减模型拟合，得到了广东地区的几何衰减函数. 同时也采用线性几何衰减模型和两段几何衰减模型对观测数据进行了拟合. 残差比较表明，线性几何衰减模型的残差最大，两段几何衰减模型的残差其次，而三段几何衰减模型的残差最小. 由此可以推论广东地区采用三段几何衰减模型具合理性和适用性. 得到广东地区非弹性衰减Q值随频率f的关系为Q(f)=481.5·f0.31；14个台站的场地响应均没有显示出明显的放大效应，这与它们均处于岩石地基相符.     

热状态对地震发生的影响

考虑地震是由于震源材料软化导致的一种基本机制,假设区域构造应力场在地震孕育过程中基本不变,震源区震前存在着热异常.我们根据热弹塑性增量理论,提出了两种材料模型,用弹塑性有限单元法模拟热状态对地震发生的影响. 模型1用来模拟断层外部区域的物质,其强度只和塑性变形有关而与热状态无关;模型2用来模拟断层物质,其强度只同热状态有关而与塑性变形无关.断层外部地震的发生被认为是岩石应变软化的结果;而断层内部地震的发生被认为是断层热软化的结果. 本文用上述模型分析了只有单一断层的热软化情况,并且得到了相应的断层错距、应力降和地震距.     

Extraction of hysteretic properties of seismically isolated bridges from quick‐release field tests

A simple procedure for identifying hysteretic properties of seismically isolated bridges from full‐scale quick‐release tests is presented in this paper. An analytical solution for the quick‐release response of a SDOF system with a bilinear spring is derived. Based on the solution, some characteristics of such systems are obtained. A time domain optimization method is employed to identify the hysteretic properties of the lead–rubber bearings installed in seismically isolated bridges. The total damping effects of the isolation system are expressed as a combination of the rate‐independent (hysteretic) damping and the linear viscous damping. The Menegotto–Pinto (MP) model and bilinear model are used to represent the force–displacement relation of the lead–rubber bearings. In both the longitudinal and transverse directions the bridges have been idealized as single degree of freedom (SDOF) systems. Time histories recorded from the field quick‐release tests on two bridges are used for the examples presented herein. The hysteretic loops of the isolators obtained from laboratory tests are compared with those obtained using the optimization method, and they agree well. In conclusion, the procedure shown in this paper can be used to identify the essential in situ hysteretic characteristics of isolation bearings from quick‐release field testing. Copyright © 2001 John Wiley & Sons, Ltd.     

The role of ground motion duration and pulse effects in the collapse of ductile systems

The seismic collapse capacity of ductile single-degree-of-freedom systems vulnerable to P-Δ effects is investigated by examining the respective influence of ground motion duration and acceleration pulses. The main objective is to provide simple relationships for predicting the duration-dependent collapse capacity of modern ductile systems. A novel procedure is proposed for modifying spectrally equivalent records, such that they are also equivalent in terms of pulses. The effect of duration is firstly assessed, without accounting for pulses, by assembling 101 pairs of long and short records with equivalent spectral response. The systems considered exhibit a trilinear backbone curve with an elastic, hardening and negative stiffness segment. The parameters investigated include the period, negative stiffness slope, ductility and strain hardening, for both bilinear and pinching hysteretic models. Incremental dynamic analysis is employed to determine collapse capacities and derive design collapse capacity spectra. It is shown that up to 60% reduction in collapse capacity can occur due to duration effects for flexible bilinear systems subjected to low levels of P-Δ. A comparative evaluation of intensity measures that account for spectral shape, duration or pulses, is also presented. The influence of pulses, quantified through incremental velocity, is then explicitly considered to modify the long records, such that their pulse distribution matches that of their short spectrally equivalent counterparts. The results show the need to account for pulse effects in order to achieve unbiased estimation of the role of duration in flexible ductile systems, as it can influence the duration-induced reduction in collapse capacity by more than 20%.     

不同加载频率及循环应力比条件下舟山海相软黏土动力特性试验研究

不同地域的软黏土表现出不同的动力学特性,针对舟山地区海相软黏土,采用Wille动三轴仪开展了一系列不排水三轴试验,研究了不同加载频率及循环应力比对软黏土的动应力-应变-孔压及软化指数等的影响规律。结果表明：低频荷载的应力-应变滞回曲线对应的面积较大且曲线趋势更倾向于应变轴,随着循环次数的增加土体的软化程度明显增加(软化指数减少),且在高循环应力比下产生较大的累积塑性应变和残余动孔压;在低频较大循环振次和高频荷载作用下,不仅需要关注循环应力比CSR的影响,也需要进一步分别关注围压和轴向偏应力各自数值不同所导致的土体累积塑性应变、残余动孔压的变化;降低循环应力比可以显著减少不同频率荷载对软黏土地基动力特性的影响。此外,实验所测的累积塑性应变和残余动孔压分别采用相关修正模型拟合,取得了一致的拟合结果。该研究将为舟山海相软黏土的工程应用提供参考依据。     

Non-linear seismic behavior of structures with limited hysteretic energy dissipation capacity

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%.     

ENERGY INPUT AND DISSIPATION BEHAVIOUR OF STRUCTURES WITH HYSTERETIC DAMPERS

This paper presents qualitative investigations on the energy behaviour of structures into which hysteretic dampers are incorporated. Emphasis was given to the ratio of the structural stiffness after the yielding of hysteretic dampers to the initial elastic stiffness, with a premise that this ratio, termed α in this study, tends to be large for structures with hysteretic dampers. Structures concerned were represented by discrete spring–mass systems having bilinear restoring force behaviour, in which the second stiffness relative to the initial stiffness is α. It was found that with the increase of α the total input energy tends to increase, but the increase is confined to a narrow range of natural periods. Both the total input energy and hysteretic energy were found to become less sensitive to the yield strength with the increase of α. A simple formula was also proposed to estimate the maximum deformation given the knowledge of the hysteretic energy. Analysis of MDOF systems revealed that, even when α is large, the total input energy and hysteretic energy for MDOF systems are approximately the same as those of the equivalent SDOF system, and the hysteretic energy can be distributed uniformly over the stories if α is large.     

Optimum hysteretic damper design for multi-story timber structures represented by an improved pinching model

Timber structures are characterized by a pinching phenomenon that leads to reduced dissipative capability. A few hysteretic models have been proposed to simulate the mechanical behavior of timber structures, among which the one composed of a bilinear element and a slip element in parallel has been popular in practice. Based on this model, this paper expands on the existing seismic control design methodology to determine the capacity of hysteretic dampers for multi-story timber structures. The equivalent linearization method for a single-degree-of-freedom timber structure with added hysteretic damper is established and is verified through nonlinear timber history analysis over a wide range of structural parameters. The design formulas for determining the damper capacity for a multi-degree-of-freedom system are derived, based on the concept of adjusting the distribution of equivalent stiffness of structure. The seismic control design is applied to many buildings with randomly generated parameters and the effectiveness is confirmed through a nonlinear time history analysis with four sets of seismic excitations. An extended study has shown that the shear force pattern plays an important role in the seismic control design results and thus the performance of structures. The effectiveness of the control of residual deformations by adding dampers is also studied.     

地质体材料剪切带内部的常剪切应变点及速度分布分析

对于峰后线性应变软化的地质体材料,剪切带内部的总剪切应变等于弹性剪切应变（由经典弹性理论描述）及由微结构效应而引起的局部塑性剪切应变（由非局部理论或梯度塑性理论描述）之和。若剪切应力-塑性剪切应变曲线的斜率的绝对值（称之为软化模董）小于剪切弹性模量的两倍,则在剪切带的任一剖面内存在两个总剪切应变不依赖于剪切应力的点,称之为常剪切应变点。在这两个点上,弹性剪切应变的降低和局部塑性剪切应变的增加处于平衡状态,总剪切速度达到它的最大值或最小值。在两个常剪切应变点之间,局部总速度随剪切应力率的降低而增加。剪切带内部的局部总速度分布是非线性的,这与通常采用的剪切带内部速度的线性分布假定（忽略微结构效应）不同。     

Elastk-plastic dynamic analysis of structures using known elastic solutions

A numerical method is shown to analyse the dynamic elastic-plastic responses of those structures with known elastic solutions. The displacement at one point at time t caused by a unit load applied at another point at zero time, called dynamic influence coefficient, is calculated from the known elastic solutions. Incremental plastic strain is accounted for by a set of additional incremental loads, so the stiffness matrix and the eigenvectors do not vary with time. From the incremental load including that caused by the incremental plastic strain, the displacement vs. time of the structure is obtained. This method is applied to simply supported beams with bilinear stress-strain relations with different strain-hardening rates and to a simply supported elastic-ideally plastic rectangular plate. This procedure can be extended to structures with no available known analytical elastic solutions. For these structures, the elastic solutions can be obtained by the finite element method.     

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.     

Hysteretic response of a nine-storey reinforced concrete building

The Millikan Library on the campus of the California Institute of Technology was strongly shaken during the San Fernando earthquake of 9 February 1971. The building was not damaged structurally, but the observed E-W response of the building showed a fundamental period of about 1.0 sec, significantly longer than the 0.66 sec observed in pre-earthquake vibration tests. In this study, the response of the fundamental mode was treated as that of a single-degree-of-freedom hysteretic structure, and four simple models, two stationary and two with changing properties, were examined to see if they could describe the observed response. It was found that an equivalent linear model and a bilinear hysteretic model both could match the response, provided their properties were changed during the earthquake. (Four changes were used.) A linear model with constant properties and a stationary, bilinear hysteretic model did not give nearly as good agreement as the non-stationary models. The results indicated, in general, a degrading of the stiffness and energy dissipation capacity of the building, with the suggestion that the changes were sudden rather than gradual.