Seismic response analysis of an irregular base isolated building

This paper assesses the reliability of code-compliant linear and nonlinear dynamic analyses for irregular buildings with base isolation system (BIS). Comprehensive analyses are carried out for a case study comprising a large reinforced concrete multi-storey framed hospital with 327 high-damping rubber bearings. Spectral and time history (linear and nonlinear) analyses were performed on the three-dimensional (3D) finite element model (FEM) of the structure; simplified analyses were also conducted on single-degree-of-freedom (SDOF) systems. It is found that, at damageability limit state, the values of maximum interstorey drifts (d/h) computed with spectral analyses on the three-dimensional FEM range between 1/6 and 1/10 of the code limit (d/h = 0.33%); thus more stringent code limits should be required for buildings with BISs. The maximum floor acceleration is reduced by about 70% with respect to the ground acceleration (free field site); the acceleration profile is uniform along the height of the multi-storey frame. Threshold values of floor accelerations to assess the seismic performance of equipments in buildings with BIS are lacking. At ultimate limit state (ULS), spectral analyses provide values of actions and deformations that are less conservative than those derived through time history analyses. To perform reliable dynamic analyses of base isolated buildings it is crucial to select natural earthquake ground motions compliant with the fundamental period of vibration of the structural system. Nevertheless, it is not straightforward to select adequate natural strong motions in the catalogues available world-wide; buildings incorporating BISs possess periods of vibration which are generally higher than 2.0 s. As a result, distant and high-magnitude earthquakes are effective for base isolated buildings; nevertheless, such earthquakes are scarce in the seismic databases. The outcomes of the present study also demonstrate that simplified linear analyses tend to provide estimates of the response quantities, displacements of base isolators and base shear of the superstructure, which can be reliably employed at preliminary design stage. Spectral analysis results of the 3D model tend to match those of the SDOF systems, even for irregular superstructure, provided that modal mass participating ratios are greater than 85–90%. The results of spectral analyses on both SDOF and three-dimensional FEM envelope the outcomes of linear time histories.     

Parametric earthquake response of torsionally coupled buildings with foundation interaction

A study is made of the effect of soil-structure interaction on the coupled lateral and torsional responses of asymmetric buildings subjected to a series of historical free-field earthquake base motions. It sh shown that for particular classes of actual buildings the equivalent rigid-base responses are significantly increased for structures founded on medium-stiff soils, and hence the assumption of the major building codes that a conservative estimate of response is obtained by considering the structure to be fixed rigidly at its base is shown to be inconsistent with the presented dynamic results. It is shown that foundation interaction produces greatest amplification of torsional coupling effects for structures subjected to a particular class of European strong-motion earthquake records, identified by similarities in their spectral shape, for which the vibrational energy of the ground motion is distributed approximately uniformly over the range of frequencies which are of interest for real structures. It is recommended that provision be made in the torsional design procedures of building codes for the increase in the coupled torsional response due to soil-structure interaction as indicated in this study. Such provision should be based on the results of comprehensive parametric studies employing a wide selection of earthquake records and accounting for expected variations in localized soil conditions.     

Soil-structure interaction effects on the steady-state response of torsionally coupled buildings

The work presented in this paper investigates the effect of the foundation flexibility on the coupled lateral-torsional response of single-storey buildings excited by translational ground motion. The eccentricity between the centre of mass and the centre of resistance is considered to be the only cause of coupling of the lateral and torsional response of the building. The study is confined to the steady-state response of rigidly supported and flexibly supported torsionally coupled buildings subjected to harmonic free-field ground displacement perpendicular to the direction of the eccentricity. In the case of the flexibly supported building the foundation medium is assumed to be an elastic homogeneous isotropic half-space. The effect of the controlling parameters on lateral-torsional coupling is investigated. It is concluded that for a particular range of values of these parameters (representing most cases of actual buildings) their effect on the coupling of lateral and torsional response is not qualitatively affected by increases in the flexibility of the foundation medium.     

Parameter identification of torsionally coupled shear buildings from earthquake response records

This paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state‐space model of the structure using the cross‐correlations among the measured responses. The dynamic characteristics of the structure are determined from the state‐space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight‐storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic response of structures with coupled vertical stiffness–strength irregularities

Several seismic design codes around the world restrict the use of theit Equivalent Lateral Force analysis method to structures satisfying structural regularity limits. These regularity limits are based on engineering judgement and lack quantitative justification. One common irregularity is that of a change in vertical stiffness over the building height. This stiffness irregularity is almost always associated with a change in vertical strength over the building height. For this reason, the effect of various realistic combinations of stiffness–strength irregularity in shear‐type buildings is evaluated to quantify regularity limits. Structures analysed had 3, 5, 9 and 15 storeys, and the floor mass at all the levels were kept the same. Both regular and irregular structures were designed in accordance with the Equivalent Lateral Force procedure to produce the same engineering demand parameter. Structural ductility factors of 1, 2, 3, 4 and 6, and target (design) interstorey drift ratios ranging between 0.5 and 3%, were used in this study. The irregular structures were created by modifying specific storey lateral stiffnesses from that of the regular structure. Strengths at these storeys were also modified to ensure realistic relationships between stiffness and strength. The modified structures were then redesigned until the target interstorey drift ratio was achieved at the critical storey. Inelastic dynamic time‐history analysis was conducted to compare the maximum interstorey drift ratio demands of the regular and irregular structures. Simple equations were developed to estimate possible variations in demand due to vertical stiffness–strength irregularity applied at critical locations in structures. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic displacements of torsionally unbalanced buildings

A parametric study is carried out to evaluate the seismic displacements at the flexible edge of torsionally unbalanced (TU) structural systems. Guidelines are provided to estimate these displacements so that they can be incorporated in the formulation of the displacement-based seismic design approach for the design of TU buildings. The ability of three code procedures to estimate the flexible-edge displacement is examined to show that not all procedures lead to conservative estimates. Finally, it is shown that elastic spectrum analysis incorporating accidental torsion effect is a viable means to estimate the flexible-edge displacements.     

主体结构隔震的二次结构减振分析

二次结构常常在大震甚至中小地震中发生损坏或中断工作，急需寻找安全有效的设计方法。对一幢典型结构，考虑不同场地条件、主体结构隔震以及二次结构不同阻尼比的影响，计算各层的楼面绝对加速度与相对位移反应谱。分析表明，主体结构隔震或同时增大二次结构阻尼是取得二次结构较好减振效果的有效途径，主体结构的隔震阻尼不宜太大，主体结构隔震后二次结构对所在楼层位置的敏感性大大降低。     

Seismic response of base isolated buildings including p-Δ effects of isolation bearings

In order to achieve a low isolation frequency, elastomeric bearings used for base isolation of buildings usually have low shear rigidity which leads to a significant reduction in the buckling load. The effects of compression load on the bearing behaviour are therefore an important consideration. A study of seismic response of base isolated buildings is presented in this paper, fully accounting for the P-Δ effects of isolation bearings. An analytical procedure is formulated that treats separately the superstructure and the supporting bearings and assembles the governing equations via the interaction forces at the base deck. The resulting equations are then solved step-by-step numerically. Numerical results obtained for a base isolated five-storey shear building show that neglecting the P-Δ effects can lead to considerable errors in the computed seismic response when the buckling safety factor of bearings is low.     

Elastic earthquake analysis of torsionally coupled multistorey buildings

With the aid of perturbation analysis of vibration frequencies and mode shapes it is shown that any lower vibration mode of a torsionally coupled building may be approximated as a linear combination of three vibration modes of the corresponding torsionally uncoupled system (a system with coincident centres of mass and resistance but all other properties are identical to the actual system): one translational mode along each of the two principal axes of resistance and one mode in torsional vibration. This result provides the motivation for a simpler—relative to the standard—procedure for analysing the response of torsionally coupled multistorey buildings to earthquake ground motion. To illustrate the application and accuracy of this procedure two numerical examples are presented.     

Seismic design and response evaluation of unbonded post‐tensioned hybrid coupled wall structures

This paper presents an analytical investigation on the seismic design and response of coupled wall structures that use unbonded post‐tensioned steel coupling beams. Both monolithic cast‐in‐place reinforced concrete wall piers and precast concrete wall piers are considered. Steel top and seat angles are used at the coupling beam ends for energy dissipation. The seismic design of prototype structures to achieve target displacement‐based performance objectives is evaluated based on nonlinear static and dynamic time history analyses. Additional recommendations are provided on shear design. Comparisons with ‘conventional’ structures that use embedded steel coupling beams as well as isolated walls with no coupling are provided. The results indicate that while the peak lateral displacements of unbonded post‐tensioned coupled wall structures are larger than the peak displacements of structures with embedded beams, the residual displacements are significantly reduced as a result of the restoring effect of the post‐tensioning steel. Copyright © 2008 John Wiley & Sons, Ltd.     

Floor spectra of mixed base isolated structures

This work investigates the efficiency of mixed base isolation, combining passive isolation bearings with semi-active (SAC) devices, to reduce the floor spectral acceleration in the vicinity of the non-isolated modes’ frequencies. Both analytical and experimental studies have been carried out. Analytical results of the behaviour of a multiple degree of freedom base isolated structure demonstrate the efficacy of the method. Though the considered controller is based on a reduced order model with only two degrees of freedom (2 DOF) without spillover compensation, the results show that, for the type of structures studied here, spillover effects are not considerable. An experimental study of a 2 DOF model of a base isolated structure equipped with a semi-active magneto-rheological (MR) damper has been carried out. Due to limitations of the experimental set-up, it has not been possible to obtain direct experimental evidence of the efficacy of SAC control to improve floor spectra. Nevertheless, based on the good agreement between analytical and experimental results which validate the considered MR model and control algorithm, numerical analyses of more relevant configurations illustrated the benefit of the utilization of such devices.     

Multiobjective optimal FLC driven hybrid mass damper system for torsionally coupled,seismically excited structures

In most of the research work on structural vibration control only two‐dimensional plane structural modelling has been considered, although only a few practical building structures can be modelled as planar structures. Therefore, these methods are not directly applicable to the majority of the practical building structures. This paper discusses the design of a multiobjective optimal fuzzy logic controller (FLC) driven hybrid mass damper (HMD) system for seismically excited torsionally coupled building structures. Floor acceleration and velocity information have been used as feedback to the fuzzy logic controller. A three branch tournament Genetic Algorithm has been used for the multiobjective optimal design of the FLC driven HMD system, where the minimization of the non‐dimensionalized peak displacement, acceleration and rotation of the structure about its vertical axis, have been as the three objective functions. The proposed multiobjective optimal fuzzy logic controller has been verified for an example problem reported in the literature. This HMD system consists of four HMDs arranged in such a way that the system can control the torsional mode of vibration effectively in addition to the flexure modes of vibration. Copyright © 2002 John Wiley & Sons, Ltd.     

基础隔震结构的耗能分析

采用Bouc-wen模型,利用状态空间迭代法,对基础隔震结构进行了多质点的弹塑性时程分析,并根据此结果,利用能量方程,求得隔震结构的各项能量,绘制了各能量项时程曲线。以一实际工程为例,求得隔震结构的各项耗能情况,说明了基础隔震结构以减少地震输入和隔震层滞回耗能来减小对上部结构的损坏。     

电梯轿厢和导轨耦合系统的地震响应分析

为了研究电梯的抗震性能,本文以电梯轿厢体-轿厢架-导轨耦合系统为研究对象,利用Lagrange方程和柔性动力学分别建立了轿厢体-轿厢架振动模型和导轨振动模型,并通过导靴与导轨之间的接触力,得到了轿厢体-轿厢架-导轨耦合振动方程.研究在地震激励作用下电梯轿厢和导轨耦合系统的地震响应.结果表明,轿厢体-轿厢架-导轨耦合模型可以反映出电梯轿厢、轿厢架和导轨之间的耦合振动以及模拟导靴与导轨的接触或脱离的关系.研究成果为电梯的抗震设计提供了一种有效的分析方法.     

Seismic response analysis of two-dimensional absorbing structures

Summary A computational method (based on finite differences) is proposed for the seismic response analysis of the Earth's structures. The method is applied to the earth fill and the sedimentary basin. It was found that the lateral inhomogeneity of non-absorbing structures caused remarkable effects on synthetic seismograms, viz. strong horizontal reflections at later arrivals. In absorbing structures these effects are much less pronounced and the response is determined primarily by the variable thickness of the structures. The responses of structures with non-causal or causal absorption differ only slightly, but they are strongly influenced by the magnitude of the absorption itself.     

Seismic response of heavily damped base isolation systems

The development of an efficient energy-dissipating mechanism that works in conjunction with laminated elastomeric bearings in order to reduce the lateral deformation of the isolation system has always been a goal of base isolation research. Theoretically, this deformation will be reduced to the minimum if damping augmentation of the isolation system can reach a critical value. However, augmenting the isolation damping may cause some unwanted side effects. The purpose of this paper is to study the influence of isolation damping on the seismic response of heavily damped base-isolated buildings. The base isolation system is assumed to be linearly viscoelastic and is analysed using the complex mode method. Solutions derived by using perturbation techniques for a two-degree-of-freedom system and the computer simulation for a multiple-degree-of-freedom system reveal that augmenting the isolation damping can reduce efficiently the deformation of the isolation system, but at the price of increasing the high-frequency vibration in the superstructure. When the damping ratio of the isolation system is beyond some level, increasing the isolation damping will enlarge the extreme values of the base and superstructural accelerations. It is also found that approximate solutions derived from the use of classical damping and classical modes of vibration in the seismic analysis of heavily damped base isolation systems can be substantially in error.     

不规则框架-剪力墙结构的地震反应

本文用墙单元将剪力墙中断的框架-剪力墙结构离散,利用传递矩阵技术探讨此不规则框架-剪力墙结构的地震反应,四阶Runge-Kutta法用来求解用正则坐标写出的对应于第j个振型的运动方程.将得到的3个不同剪力墙高度的钢筋混凝土框架-剪力墙模型结构的固有频率、最大位移反应和基底剪力与振动台的试验结果进行对比,说明本数值方法是正确的、有效的.最后得出了并不是对所有的框架-剪力墙结构都需把其剪力墙延伸到整个结构高度的结论以及用墙单元和传递矩阵技术求解能有效地减少计算单元、取得同样精度的计算结果.     

Comparative response and performance of base‐isolated and fixed‐base structures

A building with a seismic isolation system, in an earthquake, is recognized as producing substantially smaller accelerations and deformations compared with a building that use other systems. This type of system is therefore expected to better protect the building's nonstructural components, equipment, and other contents that are essential for the activities conducted in the building. Unlike many available studies on building responses, only a small number of studies on a buildings' nonstructural component responses are available, and no study has directly addressed building performance with regard to nonstructural component protection. This paper therefore measures the performance of various seismically isolated buildings. Specifically, the effects of important structural parameters, namely, isolation stiffness, isolation damping ratio, and number of stories on the response of base‐isolated structures are investigated parametrically. Ground motions with 2% exceedence in 50years Maximum Considered Earthquake (MCE) are used. Performance is compared with that of fixed‐base structures in order to present data that will be useful in justifying the more costly technology. The buildings are 3, 9, and 20 stories, represented by MDOF shear‐beam models. As examples of displacement‐sensitive and acceleration‐sensitive components, partition walls and ceilings are considered, respectively. The Pacific Earthquake Engineering Research Center performance‐based earthquake engineering methodology is adopted to evaluate the failure return periods of the examples based on their available fragility curves. In addition, the curves are varied hypothetically to understand the sensitivity of the return period to the curve features. Then, the median and dispersion of fragility curves required to satisfy the components' desired failure return period are obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

Modal damping for torsionally coupled buildings on elastic foundation

A method to determine the approximate normal modes and the modal damping for torsionally coupled buildings on an elastic foundation is presented. The modal damping is determined by an iterative procedure which matches the approximate normal mode solution with the rigorous solution. The response quantity to be matched is selected in a consistent and logical manner. The normal modes and the damping ratios thus found are then used to determine the seismic response of the interaction system by the response spectrum technique.