Evaluation of fundamental period of low‐rise and mid‐rise reinforced concrete buildings

Fundamental period of vibration appears to be one of the most critical parameter for the seismic design of buildings because this period strongly affects the magnitude of seismic forces. In this paper, an empirical formula for estimating the fundamental period of reinforced concrete structures is recommended, on the basis of the vibration analysis of 20 different real building configurations. These structures have already been constructed in Greece, and they are analyzed by using in detail 3‐D finite element models and modal eigenvalue analysis. These models take into account the presence of external and internal infill walls, which are usually ignored as nonstructural elements. This neglect leads to unreliable evaluation of period because the infill walls' contribution to the lateral stiffness and therefore to the fundamental period of vibration is also ignored. Furthermore, taking into account that the flexibility of soil elongates the fundamental period, the soil–structure interaction effect is also considered. To achieve a unique, simple, and effective empirical expression for the fundamental period of vibration, a comprehensive nonlinear regression analysis is applied for the datasets of buildings under consideration. This empirical expression is also compared with the similar expressions from the pertinent literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Empirical formula for fundamental vibration periods of reinforced concrete buildings in Taiwan

More than 30 buildings around Taiwan have been selected to monitor the floor responses under seismic excitation. The structural array monitoring system in each building controls at most 27 channels of accelerometers distributed in several floors. Those buildings were triggered by many events during the past five years of operation. In each building, the records at the basement can be considered as the ground excitation, and the others at the upper floors are the structural responses. The frequency transfer functions of those buildings can be identified by ARX models, and then the fundamental vibration periods are estimated. The identified fundamental vibration periods using different events are compared in order to ensure the reliability of system identification. An empirical formula in predicting the fundamental vibration period is presented through the regression analysis to the identified fundamental vibration periods of 21 reinforced concrete (RC) moment‐resisting frame (MRF) buildings. It is found that the height of a building plays an important role in predicting the fundamental vibration period, compared with the length, width, and time after completion of the building. It is also found that the RC MRF buildings in Taiwan tend to be stiffer than those in the U.S. Copyright © 2000 John Wiley & Sons, Ltd.     

钢筋混凝土建筑非线性阻尼性能及阻尼比表达式研究

阻尼比是反映结构耗能能力的参数，它对结构的振动反应有重要的影响。目前结构设计阶段通常取阻尼比为常数，这不能真实反映建筑物的阻尼机理，与阻尼比的实测结果也有很大的差距。通过对建筑物阻尼机理、建筑材料、建筑物和建筑模型阻尼性能试验数据的分析，本文对混凝土强度、纵向配筋率、结构形式和结构变形大小等建筑阻尼性能的主要影响因素进行了分析。在此基础上，本文提出了钢筋混凝土结构非线性阻尼比的统一表达式。     

Period formulas of shear wall buildings with flexible bases

The evaluation of the fundamental period of shear wall buildings considering the flexibility of the base is investigated in this paper. This research is motivated by the discrepancy reported between the formulas used in different building codes and the measurement of real buildings. Both experimental and analytical approaches are used to assess the effect of the base flexibility on the fundamental period of shear wall structures. In total, twenty buildings built on different types of soil are tested under ambient vibration. The fundamental period is identified using a non‐parametric linear model in the frequency domain. The results show that fundamental period formulas used by UBC‐97 and NBCC‐95 are inadequate since they do not include the effect of the foundation stiffness. To improve the estimation of the fundamental period of shear wall buildings, an analytical approach is presented. The structure and the foundation are represented by a continuous‐discrete system. The stiffnesses of the base are represented by translational and rotational discrete springs. The rigidities of these springs are evaluated from the elastic uniform compression of the soil mass and the size of the foundation. The analytical predictions improve the estimation of the fundamental period and keep the computation simple. The error between the measured period and the analytical results is, on average, less than 10%. Copyright © 2003 John Wiley & Sons, Ltd.     

Quantification of fundamental frequency drop for unreinforced masonry buildings from dynamic tests

The knowledge of fundamental frequency and damping ratio of structures is of uppermost importance in earthquake engineering, especially to estimate the seismic demand. However, elastic and plastic frequency drops and damping variations make their estimation complex. This study quantifies and models the relative frequency drop affecting low‐rise modern masonry buildings and discusses the damping variations based on two experimental data sets: Pseudo‐dynamic tests at ELSA laboratory in the frame of the ESECMaSE project and in situ forced vibration tests by EMPA and EPFL. The relative structural frequency drop is shown to depend mainly on shaking amplitude, whereas the damping ratio variations could not be explained by the shaking amplitude only. Therefore, the absolute frequency value depends mostly on the frequency at low amplitude level, the amplitude of shaking and the construction material. The decrease in shape does not vary significantly with increasing damage. Hence, this study makes a link between structural dynamic properties, either under ambient vibrations or under strong motions, for low‐rise modern masonry buildings. A value of 2/3 of the ambient vibration frequency is found to be relevant for the earthquake engineering assessment for this building type. However, the effect of soil–structure interaction that is shown to also affect these parameters has to be taken into account. Therefore, an analytical methodology is proposed to derive first the fixed‐base frequency before using these results. Copyright © 2010 John Wiley & Sons, Ltd.     

两结构高效阻尼控制系统随机动力反应分析

对由高效阻尼装置(HEDMS)连接的两单自由度相邻结构在过滤白噪声激励下的相对位移响应进行了随机分析。在对阻尼装置滞变位移等价线性化的基础上，采用虚拟激励法计算结构响应的谱密度和互谱密度，研究了该阻尼装置各参数对位移响应方差的影响以及该装置的适用范围。     

Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation

The Rayleigh damping model, which is pervasive in nonlinear response history analysis (RHA) of buildings, is shown to develop ‘spurious’ damping forces and lead to inaccurate response results. We prove that a viscous damping matrix constructed by superposition of modal damping matrices—irrespective of the number of modes included or values assigned to modal damping ratios—completely eliminates the ‘spurious’ damping forces. This is the damping model recommended for nonlinear RHA. Replacing the stiffness‐proportional part of Rayleigh damping by the tangent stiffness matrix is shown to improve response results. However, this model is not recommended because it lacks a physical basis and has conceptual implications that are troubling: hysteresis in damping force–velocity relationship and negative damping at large displacements. Furthermore, the model conflicts with the constant‐damping model that has been the basis for fundamental concepts and accumulated experience about the inelastic response of structures. With a distributed plasticity model, the structural response is not sensitive to the damping model; even the Rayleigh damping model leads to acceptable results. This perspective on damping provides yet another reason to employ the superior distributed plasticity models in nonlinear RHA. OpenSees software has been extended to include a damping matrix defined as the superposition of modal damping matrices. Although this model leads to a full populated damping matrix, the additional computational demands are demonstrated to be minimal. Copyright © 2015 John Wiley & Sons, Ltd.     

基于环境振动的斜拉桥拉索基频识别

斜拉索是现代斜拉桥最重要的结构构件，索力在斜拉桥的施工控制和长期监测中起着重要作用。振动测试法是斜拉桥索力测定、监测和状态评估中应用最广泛的一种方法。振动法测索力的关键在于准确地识别出索的基频。本文使用自功率谱和倒频谱方法，基于MATLAB平台，开发出了斜拉桥拉索环境振动模态分析图形用户交互(GUI)工具箱，实现了斜拉索基频的快速自动识别。应用本文的方法，对福州青洲闽江主跨605m斜拉桥拉索的环境振动实测加速度数据进行了分析处理，斜拉索基频识别方便直观，结果可靠。     

Seismic behaviour of asymmetric buildings with supplemental damping

This paper investigates the response of asymmetric‐plan buildings with supplemental viscous damping to harmonic ground motion using modal analysis techniques. It is shown that most modal parameters, except dynamic amplification factors (DAFs), are affected very little by the plan‐wise distribution of supplemental damping in the practical range of system parameters. Plan‐wise distribution of supplemental damping significantly influences the DAFs, which, in turn, influence the modal deformations. These trends are directly related to the apparent modal damping ratios; the first modal damping ratio increases while the second decreases as CSD moves from right to left of the system plan, and their values increase with larger plan‐wise spread of the supplemental damping. The largest reduction in the flexible edge deformation occurs when damping in the first mode is maximized by distributing the supplemental damping such that the damping eccentricity takes on the largest value with algebraic sign opposite to the structural eccentricity. Copyright © 2000 John Wiley & Sons, Ltd.     

Assessment indices for the seismic vulnerability of existing R.C. buildings

The seismic vulnerability of old multi‐storey reinforced concrete (R.C.) buildings reinforced with substandard details is assessed as a function of interstorey drift demand imposed by the design earthquake while considering brittle termination of elastic response of the critical members of the structure due to a premature shear failure. Interstorey drift demand is related to column and wall translational stiffnesses which are expressed through analytical derivations in terms of the floor area ratios of gravity and lateral load bearing members in the critical floor. Interstorey drift capacity is related to the available transverse reinforcement and the axial load ratio of the vertical members. The significance of the area ratio of vertical members in the typical floor as an index of vulnerability is explored with reference to the limitations in the value of axial load ratio used in R.C. design in order to secure ductile flexural behavior, and also with reference to the stability index of gravity load bearing members. Interstorey Drift Spectra are derived for the existing R.C. buildings suitable for rapid seismic vulnerability screening but also as a guide for rehabilitation of the existing structures. Lightly reinforced or substandard reinforced concrete buildings that reportedly collapsed during previous earthquakes are used as example case studies in order to calibrate the proposed methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

附加或不附加粘滞阻尼墙的RC框架试验与分析

本文阐述了附加或不附加粘滞阻尼墙的2个相同的RC框架模型振动台试验和理论分析的情况.这2个钢筋混凝土框架模型为3层1跨两开间,几何相似关系大致为1：2.将阻尼墙附加到一个RC框架模型当中,先后对附加或不附加阻尼墙的2个相同的RC框架模型进行振动台试验.试验结果表明,阻尼墙有效减小了框架模型的地震反应.对耗能框架模型和普通框架模型进行了弹性和弹塑性时程分析,计算结果和试验结果吻合良好.改变阻尼墙的参数进行分析,结果表明选取合适的阻尼墙参数,才能达到最好的耗能减振效果;适当减小层间位移较小处的阻尼墙参数,对减振效果影响很小而又能节省投资.     

Discussion of ‘Modelling viscous damping in nonlinear response history analysis of buildings for earthquake excitation’ by Anil K. Chopra and Frank McKenna

This discussion deals with recommendations in the paper on appropriate damping formulations for use in nonlinear response history analysis of buildings. Concern over potentially excessive damping forces and moments should extend beyond the damping moments produced by the stiffness proportional part of Rayleigh damping that corresponds to rotational springs used to explicitly model plastic hinges. The key to an appropriate damping formulation for nonlinear analysis is a realistic mechanism that allows all damping forces and moments to be meaningfully assessed. Then features can be added to keep these forces and moments within reasonable bounds. Copyright © 2016 John Wiley & Sons, Ltd.     

Developing collapse fragility curves for base-isolated buildings

Seismic isolation technique is increasingly used both for the design of new buildings and for the seismic retrofit of existing buildings. Nevertheless, so far, little attention has been paid on the collapse capacity of these structures, mainly because it requires refined nonlinear models and careful consideration of different sources of uncertainties. To fill this gap, a set of collapse fragility functions for existing reinforced concrete-frame buildings, designed for gravity loads only and then retrofitted with different isolation systems (including rubber-based and friction-based isolation systems), are derived in this study. For completeness, buildings with low and high seismic resistance are also considered. Collapse fragility functions are derived through incremental dynamic analysis, considering different collapse conditions both for isolation system and superstructure. For each case study building, mean and dispersion values are obtained considering both aleatory and epistemic uncertainties, due to record-to record and model variability, respectively. Finally, some comments on the possible use of the results of this study for practical applications are made.     

考虑接连两次地震影响的群体建筑物震害预测方法

利用文献[2]推荐的方法得到了不同地震组合情况下的等效地震影响系数,将其与传统的钢筋混凝土框架结构震害预测方法相结合,得到两次地震作用对建筑物所造成的损伤,进而得到了该类建筑物的群体震害预测结果。结果分析表明,接连两次地震对建筑物的累积破坏作用显著。最后以福建省泉州市规划区范围内的钢筋混凝土框架结构群体震害预测为例,证明了该方法具有简便实用的特点。     

Influence of the soil–structure interaction on the fundamental period of buildings

This paper includes an investigation of the influence of the soil–structure interaction (SSI) on the fundamental period of buildings. The behaviour of both the soil and the structure is assumed to be elastic. The soil‐foundation system is modelled using translational and rotational discrete springs. Analysis is first conducted for one‐storey buildings. It shows that the influence of the SSI on the fundamental frequency of building depends on the soil–structure relative rigidity K_ss. Analysis is then extended for multi‐storey buildings. It allows the generalization of the soil–structure relative rigidity K_s to such complex structures. Charts are proposed for taking into account the influence of the SSI in the calculation of the fundamental frequency of a wide range of buildings. Copyright © 2007 John Wiley & Sons, Ltd.     

Development of a seismic damage and loss scenario for contemporary and historical buildings in Thessaloniki, Greece

The methodologies used in Greece for estimating direct losses in both reinforced concrete (R/C) and masonry buildings (also including monuments) are summarised, the critical issue of data collection is addressed, and practical solutions that have been tried are discussed. The development of a seismic risk scenario for contemporary and historical buildings in Thessaloniki is then presented and some key results are given, including the expected geographical distribution of building damage (due to the scenario earthquake) in the municipality of Thessaloniki; damage is described both in structural and in economic terms.     

A study on damage scenarios for residential buildings in Catania city

The main purpose of this study is to obtain the damage scenario for residential buildings in the occurrence of a destructive earthquake (M = 7+) in the city area of Catania, Eastern Sicily, and to illustrate the comparative performance of two alternative methods used for this purpose. The methods are representative of two different approaches to estimating the seismic vulnerability of structures, i.e., an empirical approach based on statistical score assignments (widely used in Italy and other countries) and a more recent, mechanical approach that uses displacement limit states associated with well-defined thresholds of structural damage. A special concern for seismic vulnerability in Catania is caused by the fact that earthquake design norms were enforced in its municipal area only since 1981. We emphasise some typical problems encountered in earthquake scenario work, such as the difficulty of assembling a reliable building inventory, and the uncertainties inherent in the vulnerability assessments through different probabilistic assumptions. Different criteria for the representation of damage are applied and discussed. It is shown that the main scenarios obtained by the two methods are in reasonable agreement, provided a suitable percentile level for damage is chosen in the statistical score assignment approach.     

Empirical relationships between natural vibration period and height of buildings in Singapore

Singapore is a classic case of a modern metropolis with low hazard but high exposure to the seismicity in Sumatra. Because of land shortage, more than 80% of the population lives in high‐rise residential buildings. As part of the efforts to assess the seismic performance of buildings in Singapore subjected to long‐distance Sumatran earthquakes, relationships between the natural vibration period and height of high‐rise public residential buildings in Singapore are derived empirically by conducting ambient vibration tests on 116 buildings. The measured buildings have a height ranging from 4 to 30 stories. The aspect ratio of buildings in plan is found to be insignificant in affecting the natural vibration period of the first mode of the buildings. The period‐height relationships are derived using regression analysis considering the site properties of a building. It is concluded that the vibration periods estimated from the proposed period‐height relationship for buildings located at soft‐soil site are about 40% longer than the vibration periods estimated for buildings located at firm‐soil site. Measurements are also conducted to study the influence of buildings on the measured frequency of the surrounding soil. For this purpose, two buildings with 25 and 30 stories located at firm‐soil site and soft‐soil site, respectively, are selected. It is found that the distance of building influence on the measured frequency of the surrounding soil may reach up to one building height for a firm‐soil site and two building heights for a soft‐soil site. Additional data of natural vibration periods of 19 instrumented residential buildings, which have height ranging from 9 to 30 stories, were obtained from the building response recorded during the September 30, 2009 Sumatran earthquake event. The natural vibration periods of these buildings are compared with those estimated using the proposed period‐height relationships, and the absolute differences are found to be less than 12%. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of earthquake direction on the seismic response of irregular plan RC frame buildings

The nonlinear response of structures is usually evaluated by considering two accelerograms acting simultaneously along the orthogonal directions. In this study, the infl uence of the earthquake direction on the seismic response of building structures is examined. Three multi-story RC buildings, representing a very common structural typology in Italy, are used as case studies for the evaluation. They are, respectively, a rectangular plan shape, an L plan shape and a rectangular plan shape with courtyard buildings. Nonlinear static and dynamic analyses are performed by considering different seismic levels, characterized by peak ground acceleration on stiff soil equal to 0.35 g, 0.25 g and 0.15 g. Nonlinear dynamic analyses are carried out by considering twelve different earthquake directions, and rotating the direction of both the orthogonal components by 30° for each analysis(from 0° to 330°). The survey is carried out on the L plan shape structure. The results show that the angle of the seismic input motion signifi cantly infl uences the response of RC structures; the critical seismic angle, i.e., the incidence angle that produces the maximum demand, provides an increase of up to 37% in terms of both roof displacements and plastic hinge rotations.     

钢筋混凝土高层建筑抗震时程分析选波方法比较研究

针对钢筋混凝土高层建筑抗震时程分析输入地震波选择问题,以《建筑抗震设计规范》（GB 50011-2016）设计谱为目标谱,将满足谱匹配原则的加权调幅选波方法与国内学者建议的其它输入地震波选择方法进行了对比研究。以3栋钢筋混凝土高层建筑（15层、30层和44层）为实例,针对8度罕遇地震作用和Ⅱ类场地条件,将上述方法建议的各7条地震波输入结构进行弹塑性时程分析。以结构最大层间位移角均值沿楼层分布为比较参数。结果表明:加权调幅法可用于钢筋混凝土高层建筑抗震时程分析,可以较好地降低结构地震反应均值的离散性。在8度罕遇地震作用条件下,以不同学者建议选择的地震波为输入,高层建筑时程分析结果仍呈现出较大的不同。