Seismic nonlinear static new method of spatial asymmetric multi‐storey reinforced concrete buildings

In order to obtain the seismic demands of spatial asymmetric multi‐storey reinforced concrete (r/c) buildings, a new seismic nonlinear static (pushover) procedure that uses inelastic response acceleration spectra is presented in this paper. The latter makes use of the optimum equivalent nonlinear single degree of freedom system, which is used to represent the general spatial asymmetric multi‐storey r/c building. For each asymmetric multi‐storey building, a total of 12 suitable nonlinear static analyses are needed according to the new proposed procedure, whereas at least 96 suitable nonlinear dynamic analyses are required in the case of nonlinear response history analysis (NLRHA), respectively. In addition, the present paper provides answers to a series of further questions with reference to the spatial action of the two horizontal seismic components in the static nonlinear (pushover) analyses, as well as to the documented calculation of the available behaviour factor of the asymmetric multi‐storey r/c building. According to the paper, this new proposed seismic nonlinear static procedure is a natural extension of the documented equivalent seismic static linear (simplified spectral) method that is recommended by the established contemporary seismic codes, with reference to torsional provisions. Finally, through a restricted parametric analysis carried out in this paper, a relevant numerical example of a two‐storey r/c building is presented for illustration purposes, where the seismic demand floor inelastic displacements are compared with the respective displacements obtained by the NLRHA. Consequently, the new proposed seismic nonlinear static procedure, which uses inelastic response acceleration spectra, can reliably evaluate the extreme values of floor inelastic displacements (on the flexible and stiff side of the building), as is shown by the above comparisons. Copyright © 2010 John Wiley & Sons, Ltd.     

Equivalent non‐linear single‐degree‐of‐freedom system of spatial asymmetric multi‐storey buildings in pushover procedure: theory and applications

In the present paper, the issue of the approximate definition of a new equivalent non‐linear single‐degree‐of‐freedom (NLSDF) system on spatial asymmetric reinforced concrete (r/c) tall multi‐storey buildings is presented. In order to achieve this goal, three different types of r/c systems are examined: the first type refers to multi‐storey planar r/c frames; the second type refers to asymmetric single‐storey r/c building; and the third type refers to asymmetric multi‐storey r/c buildings. The definition of the NLSDF system is mathematically derived, considering suitable dynamic loadings on the masses of each r/c system using simplified assumptions. The NLSDF system is very useful in the seismic design of the r/c systems, since it is widely used in all forms of various pushover analyses that have been published in the past. The use of the equivalent NLSDF system in combination with the inelastic design spectra can give an acceptable evaluation of the maximum required seismic floor displacement for a known design earthquake. The present paper concludes the total theory of definition of the optimum equivalent NLSDF system for the above three types of buildings that possess the required normality by the contemporary seismic codes in elevation. In order to illustrate the theory, three numerical examples are presented, respectively. The final numerical required displacement results by the use of the equivalent NLSDF system are verified and checked by non‐linear response history analyses. Copyright © 2008 John Wiley & Sons, Ltd.     

Strength reduction factor for MDOF soil–structure systems

In most of the seismic design provision, the concept of strength reduction factor has been developed to account for inelastic behavior of structures under seismic excitations. Most recent studies considered soil–structure interaction (SSI) in inelastic response analysis are mainly based on idealized structural models of single degree‐of‐freedom (SDOF) systems. However, an SDOF system might not be able to well capture the SSI and structural response characteristics of real multiple degrees‐of‐freedom (MDOF) systems. In this paper, through a comprehensive parametric study of 21600 MDOF and its equivalent SDOF (E‐SDOF) systems subjected to an ensemble of 30 earthquake ground motions recorded on alluvium and soft soils, effects of SSI on strength reduction factor of MDOF systems have been intensively investigated. It is concluded that generally, SSI reduces the strength reduction factor of both MDOF and more intensively SDOF systems. However, depending on the number of stories, soil flexibility, aspect ratio and inelastic range of vibration, the strength reduction factor of MDOF systems could be significantly different from that of E‐SDOF systems. A new simplified equation, which is a function of fixed‐base fundamental period, ductility ratio, the number of stories, structure slenderness ratio and dimensionless frequency, is proposed to estimate strength reduction factors for MDOF soil–structure systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Probe into several important concepts in Chinese current seismic response spectra

在使用规范反应谱时常将绝对加速度谱、拟加速度谱、伪加速度谱概念等同或者混乱使用,尤其对于大阻尼比且长周期的结构,采用“拟谱关系”能够获得相应谱的谱值却换算不了相应谱的频谱特性。也有认为利用“拟谱关系” 所导出的相对位移谱不符合结构动力学原理及强震反应谱统计特征。基于此,对我国现行抗震规范地震反应谱所涉及到的绝对加速度反应谱、伪加速度反应谱和拟反应谱等作了较为详细的对比,重点阐明了伪谱与拟谱,绝对加速度谱与伪加速度谱在概念上的区别与联系。鉴于我国现行《建筑抗震设计规范》反应谱是由绝对加速度反应谱标定,利用“拟谱关系”仅是一种数值近似手段,并不具有频谱特性的转换功能,分析了绝对加速度反应谱和伪加速度反应谱在抗震设计过程中的差异。基于绝对加速度反应谱进行标定的规范反应谱,总结了其在目前建筑结构抗震设计中所存在的问题,尤其是在针对超高层结构消能减震结构分析中存在不足：长周期且大阻尼比结构所受设计地震作用与其弹性内力相比明显偏大,设计偏保守;用“拟谱关系”所得换算谱的频谱特性混乱且用于设计缺乏可靠性验证。为此,提出了应分类构建反应谱的建议。     

Optimal design and seismic performance of Multi‐Tuned Mass Damper Inerter (MTMDI) applied to adjacent high‐rise buildings

The tuned mass damper inerter (TMDI) is an enhanced variant of the tuned mass damper (TMD) that benefits from the mass‐amplification effect of the inerter. Here, a multi‐TMDI (MTMDI) system (comprising more than one TMDI) linking two adjacent high‐rise buildings is presented as an unconventional seismic protection strategy. The relative acceleration response of the adjacent structures triggers large reaction forces of the inerter devices in the MTMDI, which in turn efficiently improve the seismic performance of the two buildings. By addressing a real project of two adjacent high‐rise buildings connected by two corridors equipped with the proposed MTMDI system, the displacement‐, interstory drift‐, and acceleration‐based parametric optimizations are separately performed by employing Nondominated Sorting Genetic Algorithm II (NSGA‐II) under 44 ground motions from the FEMA P695 far‐field record set. It is found that the frequency content of the seismic input has strong impact on the MTMDI mitigation performance. Adopting realistic mass ratio constraints, the optimally designed MTMDI outperforms both conventional MTMD and single TMDI in acceleration control, while it is not much effective in mitigating the displacement response due to the highly flexible nature of the high‐rise buildings, in contrast to other literature studies generally focused on low‐to‐medium rise buildings.     

Seismic fragility relationships of reinforced concrete high‐rise buildings

A complete methodology is presented for the seismic fragility assessment of reinforced concrete high‐rise buildings. The key steps of the methodology are illustrated through an example of the fragility assessment of an existing 54‐story building with a dual core wall system. The set of rigorously derived probabilistic fragilities are the first published for high‐rise reinforced concrete buildings. The inelastic nonlinear dynamic analyses for the fragility assessments are made using a simplified lumped‐parameter model that was derived from highly detailed FE models using genetic algorithms. New definitions for performance limit states were based on the results of detailed pushover analyses of a distributed inelastic nonlinear finite element model that includes shear–flexure–axial interaction effects. To develop the fragility relationships, 1800 dynamic response history analyses were conducted. This study considered uncertainty in structural material values as well as in seismic demand. Thirty strong motion records were selected for use in the analyses that would produce an appropriate range in structural response characteristics due to variation in magnitude, distance and site condition. The overall approach is generic and can be applied to developing computationally efficient and probabilistically‐based seismic fragility relationships for reinforced concrete high‐rise buildings of different configurations. Copyright © 2007 John Wiley & Sons, Ltd.     

弹塑性位移谱法与振动台试验比值的数值分布特征

本文将弹塑性位移谱法的计算结果与12层钢筋混凝土模型框架结构振动台试验作了比较。振动台输入峰值加速度依次为:0.090、0.2580、.388、0.517、0.646、0.775和0.904g。利用弹塑性位移谱法计算出各工况下模型框架的楼层位移和层间位移角需求及其与试验结果的比值,讨论了楼层位移比、层间位移角比随输入峰值的变化情况,以及楼层位移比、层间位移角比的数值分布特征。比较分析可知:弹塑性位移谱法的计算结果较为接近结构的真实地震反应,可在基于性能的抗震设计中应用。     

An improved consecutive modal pushover procedure for estimating seismic demands of multi‐storey framed buildings

An improved consecutive modal pushover (ICMP) procedure is proposed to enhance the accuracy of conventional CMP procedure for estimating seismic demands of tall buildings. It accounts for inelastic structural properties and interaction between vibration modes. The displacement increment at the roof of buildings used in each stage of pushover analyses is modified based on the displacement contribution of each mode. The performance of the proposed ICMP procedure is verified against three high‐rise frames subjected to various ground motions. The results obtained from the ICMP procedure are compared with those from the nonlinear time history analysis, conventional pushover analysis, and CMP analysis. The comparison shows the advantages of the ICMP over the other pushover procedures. It is concluded that the ICMP procedure is more accurate than the CMP procedure.     

On the applicability of pushover analysis for seismic evaluation of medium‐ and high‐rise buildings

The assumption that the dynamic performance of structures is mainly determined from the corresponding single‐degree‐of‐freedom system in pushover analysis is generally valid for low‐rise structures, where the structural behaviour is dominated by the first vibration mode. However, higher modes of medium‐ and high‐rise structures will have significant effect on the dynamic characteristics. In this paper, the applicability of pushover analysis for seismic evaluation of medium‐to‐high‐rise shear‐wall structures is investigated. The displacements and internal forces of shear wall structures with different heights are determined by nonlinear response history analysis, where the shear walls are considered as multi‐degree‐of‐freedom systems and modelled by fibre elements. The results of the analysis are compared with those from the pushover procedure. It is shown that pushover analysis generally underestimates inter‐storey drifts and rotations, in particular those at upper storeys of buildings, and overestimates the peak roof displacement at inelastic deformation stage. It is shown that neglecting higher mode effects in the analysis will significantly underestimate the shear force and overturning moment. It is suggested that pushover analysis may not be suitable for analysing high‐rise shear‐wall or wall‐frame structures. New procedures of seismic evaluation for shear‐wall and wall‐frame structures based on nonlinear response history analysis should be developed. Copyright © 2009 John Wiley & Sons, Ltd.     

A modified response spectrum analysis procedure to determine nonlinear seismic demands of high‐rise buildings with shear walls

The standard response spectrum analysis (RSA) procedure prescribed in various design codes is commonly used by practicing engineers to determine the seismic demands for structural design purpose. In this procedure, the elastic force demands of all significant vibration modes are first combined and then reduced by a response modification factor (R) to get the inelastic design demands. Recent studies, however, have shown that the response of higher vibration modes may experience much lower level of nonlinearity, and therefore, it may not be appropriate to reduce their demand contributions by the same factor. In this study, a modified RSA procedure based on equivalent linearization concept is presented. The underlying assumptions are that the nonlinear seismic demands can be approximately obtained by summing up the individual modal responses and that the responses of each vibration mode can be approximately represented by those of an equivalent linear SDF system. Using 3 high‐rise buildings with reinforced concrete shear walls (20‐, 33‐, and 44‐story high), the accuracy of this procedure is examined. The inelastic demands computed by the nonlinear response history analysis procedure are used as benchmark. The modified RSA procedure is found to provide reasonably accurate demand estimations for all case study buildings.     

Estimation of inelastic displacement factor of soil‐shallow‐foundation MDOF systems incorporating higher modes effect

This study attempts to investigate the higher‐mode effects on the constant‐ductility inelastic displacement factors of multi‐degree‐of‐freedom (MDOF) systems considering soil‐structure interaction. These factors were computed for 12,600 two‐dimensional superstructure models of shear buildings and their corresponding equivalent single‐degree‐of‐freedom (ESDOF) systems under 26 ground motions recorded on alluvium and soft soil. An intensive parametric study was carried out for a wide range of non‐dimensional parameters, which completely define the problem. The underlying soil is considered as a homogeneous half‐space based on the concept of cone model. The higher‐mode effects were then investigated through defining the ratio of inelastic displacement factor of MDOF system to that of the corresponding ESDOF one. The influence of soil‐structure interaction key parameters, fundamental period, ductility ratio, the number of stories, and dispersion of the results are evaluated and discussed. Results indicate that as the base becomes very flexible, unlike to the fixed‐base systems, in which the defined ratios are greater than unity, using the inelastic displacement factors of ESDOF models for MDOF ones would result in a remarkable overestimation of maximum inter‐story displacement demand. A new expression is proposed to estimate the ratio of inelastic displacement factor of MDOF soil‐structure systems to that of SDOF counterpart.     

Response of nonlinear single-degree-of-freedom structures to random acceleration sequences

Current seismic codes specify design earthquake loads as single events. The structure, however, may experience multiple ground accelerations in a short period of time. The evidence from recent earthquakes confirms this scenario. For instance, the 2004 Niigata earthquake consisted of two acceleration sequences. An earthquake of repeated sequences can cause more damage to the structure than a single ordinary event, due to the accumulation of inelastic deformations. However, information on repeated acceleration sequences is currently limited. This paper proposes a simple stochastic model for representing repeated acceleration sequences. Subsequently, the model is used in investigating the response of nonlinear single-degree-of-freedom (SDOF) structures to random earthquakes of repeated sequences. The ground acceleration is represented as a stationary Gaussian random process modulated by an envelope function of repeated character. The structural response is quantified in terms of the input and hysteretic energies, ductility demand, damage indices and failure probability. Numerical demonstrations of the response of nonlinear SDOF systems to acceleration sequences are provided.     

Fuzzy‐Valued Intensity Measures for Near‐Fault Pulse‐Like Ground Motions

Two fuzzy‐valued (FV) structure‐specific intensity measures (IMs), one based on squared spectral velocity and the other on inelastic spectral displacement, are presented to characterize near‐fault pulse‐like ground motions for performance‐based seismic design and assessment of concrete frame structures. The first IM is designed through fuzzying structural fundamental period to account for the period shift effect due to stiffness degradation, whereas the second IM is developed to take into account higher mode contribution in high‐rise buildings by employing a fuzzy combination of the first two or three modes for the lateral loading pattern in pushover analysis. A benchmark study of three example reinforced concrete frame structures shows that for moderate‐ to medium‐period structures, both of the proposed IMs improve prediction accuracy in comparison with the existing IMs. For short‐period structures, the FV inelastic spectral displacement is the best.     

在用RC框架结构基于位移的抗震性能评估

根据能力谱方法的基本原理 ,建立了在用RC框架结构基于位移抗震性能的评估方法。该方法采用了振型分解法建立的多自由度体系和等效单自由度体系之间的转换关系 ,以及由现行《建筑抗震设计规范》的反应谱曲线建立的结构抗震要求曲线。用本文方法对清华大学主楼 1 0层钢筋混凝土框架结构进行了抗震性能评估 ,同时进行了小震和大震作用下的弹塑性时程分析。本文方法得到的顶点位移角、层间位移角和塑性铰分布与时程分析的结果比较符合     

Optimal reduction of inelastic seismic demands in high‐rise reinforced concrete core wall buildings using energy‐dissipating devices

Recently, the issue of large inelastic seismic force demands at severe ground shakings such as maximum considered earthquake level has been highlighted in the conventionally designed high‐rise reinforced concrete core wall buildings. Uncoupled modal response history analysis was used in this study to identify the modes responsible for the large inelastic seismic force demands. The identification of dominant modes and mean elastic design spectra of seven representative ground motions for different damping ratios has led to the identification of three control measures: plastic hinges (PHs), buckling‐restrained braces (BRBs) and fluid viscous dampers (FVDs). The identified control measures were designed to suppress the dominant modes responsible for the large inelastic seismic force demands. A case‐study building was examined in detail. Comparison of the modal as well as the total responses of the case‐study building with and without the control measures shows that all the control measures were effective and able to reduce the inelastic seismic demands. A reduction of 33%, 22% and 27% in the inelastic shear demand at the base and a reduction of 60%, 22% and 26% in the inelastic moment demand at mid‐height were achieved using the PHs, BRBs and FVDs, respectively. Furthermore, a reduction of about 30–40% in the inelastic seismic deformation demands was achieved for the case of the BRBs and FVDs. The study enables us to gain insight to the complex inelastic behavior of high‐rise wall buildings with and without the control measures. Copyright © 2011 John Wiley & Sons, Ltd.     

关于设计反应谱、时程法和能量方法的探讨

强震地面运动长周期分量对超高层建筑和大跨巨型结构具有重要影响,而现行的振型分解反 应谱法所采用的设计反应谱具有明显的局限性,基于地震加速度的结构动力方程式亦无法正确地估 计这种影响。本文探讨了采用速度反应谱和位移反应谱分析的可行性;对结构时程分析法的工程应 用价值和可操作性提出看法。讨论了能量方法的理论意义和实用价值,建立瞬时能量与结构最大地 震位移反应的关系,从而为结构地震反应分析和破坏准则,提供具有工程实用意义的新途径。     

The effect of foundation flexibility and structural strength on response reduction factor of RC frame structures

Current force‐based design procedure adopted by most seismic design codes allows the seismic design of building structures to be based on static or dynamic analyses of elastic models of the structure using elastic design spectra. The codes anticipate that structures will undergo inelastic deformations under strong seismic events; therefore, such inelastic behaviour is usually incorporated into the design by dividing the elastic spectra by a factor, R, which reduces the spectrum from its original elastic demand level to a design level. The most important factors determining response reduction factors are the structural ductility and overstrength capacity. For a structure supporting on flexible foundation, as Soil Structure Interaction (SSI) extends the elastic period and increases damping of the structure‐foundation elastic system, the structural ductility could also be affected by frequency‐dependent foundation‐soil compliances. For inelastic systems supporting on flexible foundations, the inelastic spectra ordinates are greater than for elastic systems when presented in terms of flexible‐base structure's period. This implies that the reduction factors, which are currently not affected by the SSI effect, could be altered; therefore, the objective of this research is to evaluate the significance of foundation flexibility on force reduction factors of RC frame structures. In this research, by developing some generic RC frame models supporting on flexible foundations, effects of stiffness and strength of the structure on force reduction factors are evaluated for different relative stiffnesses between the structure and the supporting soil. Using a set of artificial earthquake records, repeated linear and nonlinear analyses were performed by gradually increasing the intensity of acceleration time histories to a level, where first yielding of steel in linear analysis and a level in which collapse of the structure in nonlinear analysis are observed. The difference between inelastic and elastic resistance in terms of displacement ductility factors has been quantified. The results indicated that the foundation flexibility could significantly change the response reduction factors of the system and neglecting this phenomenon may lead to erroneous conclusions in the prediction of seismic performance of flexibly supported RC frame structures. Copyright © 2010 John Wiley & Sons, Ltd.     

Using orthogonal pairs of rollers on concave beds (OPRCB) as a base isolation system—part I: analytical,experimental and numerical studies of OPRCB isolators

A somehow new isolating system is introduced for short‐ to mid‐rise buildings. It does not need high technology for manufacturing and is not costly, contrary to other existing systems like lead‐rubber bearing or friction pendulum bearing systems. Each isolator of the proposed system consists of two Orthogonal Pairs of Rollers on Concave Beds (OPRCB). Rolling rods installed in two orthogonal directions make possible the movement of the superstructure in all horizontal directions. The concave beds, in addition to giving the system both restoring and re‐centring capabilities, make the force–displacement behaviour of the isolators to be of hardening type. The results of the studies on the specifications of the proposed isolating system and its application to buildings can be presented in two parts. Part I relates to the analytical formulations and the results of experimental and numerical studies of the system's mechanical feature, including its dynamical properties, and part II focuses on the effectiveness of the proposed isolation system in seismic response reduction of low‐ to mid‐rise buildings. In part I of the work, presented in this paper, at first general features of the OPRCB isolator are explained and the analytical formulation, governing its dynamic motion, is derived and discussed in detail. Then, the results of experimental and numerical investigations, including the lateral load displacement relationship of the OPRCB isolators under various vertical loads, obtained by both Finite Element Analyses (FEA) and laboratory tests are presented (FEA results have been verified by the laboratory tests). Finally, responses of some Single Degree of Freedom (SDOF) systems, isolated by OPRCB devices, subjected to simultaneous effect of horizontal and vertical ground motions, are presented and compared with responses of their fixed‐base counterparts. Based on the numerical calculations, it is observed that the oscillation period of the isolated SDOF system is independent of its mass, the initial amplitude of its free vibration response and the value of rolling resistance coefficient. With regard to seismic response reduction it is seen that the amount of absolute accelerations in the SDOF systems, isolated by OPRCB devices, can be reduced drastically in comparison with the fixed‐base systems. Results also show that if the rollers and cylindrical beds are made of high‐strength steel materials, the system can be used effectively under the vertical loads of about the axial forces of ground floor columns in ordinary buildings up to 14 storeys. Copyright © 2010 John Wiley & Sons, Ltd.     

框架结构静力弹塑性分析方法与非线性动力分析方法的对比

介绍了静力弹塑性(Pushover)和非线性动力基本分析方法和原理,为了探讨两种方法下结构分析的差异,对一按现行抗震规范设计的8层钢筋混凝土结构进行了3条地震波作用下的时程分析和5种侧向加载方式的静力弹塑性分析。通过结果的比较,提出对现行规范反应谱中长周期结构罕遇地震作用取值修改的建议。修改后,由两种方法分析所得到的结构在大震下的顶点位移、基底剪力、楼层位移和层间位移等结构反应非常接近。     

A study on vortex‐induced vibration of supertall buildings in acrosswind

Modern tall buildings using innovative structural systems and high‐strength materials tend to be slender and lightly damped. Hence, they are vulnerable to the dynamic action of wind. Crosswind excitation on tall buildings can result in aeroelastic problems. Vortex‐induced vibration (VIV) is the prime problem in self‐excited vibration of the flexible structures, and it should be especially observed in order to avoid the ultimate limit state in the design stage. In order to predict the vortex‐induced response of a supertall building in China with the single‐degree‐of‐freedom (SDOF) mathematical model, wind tunnel tests were carried out with an improved aeroelastic model according to the similitude. The measured top acceleration of the structure showed that VIV was quite significant at some wind speeds and should be considered in the design. Based on the experimental data, the aerodynamic parameters were determined and the characteristics of VIV were investigated in some details. The time history of acceleration at the lock‐in wind speed was then obtained using the Runge–Kutta method with the SDOF model. The numerical results are in accordance with the measurements. Copyright © 2009 John Wiley & Sons, Ltd.