Appropriate viscous damping for nonlinear time‐history analysis of base‐isolated reinforced concrete buildings

There is no consensus at the present time regarding an appropriate approach to model viscous damping in nonlinear time‐history analysis of base‐isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous damping on the response of base‐isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced‐scale three‐story building previously tested on a shaking table are compared with three‐dimensional finite element simulation results. The study is primarily focused on nonlinear direct‐integration time‐history analysis, where many different approaches of modeling viscous damping, developed within the framework of Rayleigh damping are considered. Nonlinear direct‐integration time‐history analysis results reveal that the damping ratio as well as the approach used to model damping has significant effects on the response, and quite importantly, a damping ratio of 1% is more appropriate in simulating the response than a damping ratio of 5%. It is shown that stiffness‐proportional damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base‐isolated building with the post‐elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time‐history analyses using constant as well as frequency‐dependent modal damping are also performed for comparison purposes. It was found that for nonlinear modal time‐history analysis, frequency‐dependent damping, where zero damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed‐base condition and 5% damping is assigned to all other frequencies, is more appropriate, than 5% constant damping. Copyright © 2013 John Wiley & Sons, Ltd.     

随机地震荷载作用下黄土动本构关系的试验研究

本文利用动三轴试验系统,试验研究了随机地震荷载作用下,非饱和原状黄土的动本构关系。结果表明,其本构关系依然服从双曲线模型,但模型参数随所施加的随机地震荷载时程的不同而不同。在试验中还对不同随机地震荷载和正弦波等效荷载作用下的模型参数、剪切模量和阻尼比进行了对比研究,初步建立了动本构模型参数与所施加的随机地震荷载的卓越周期之间的定量关系。通过试验和计算,证实了曼辛准则对黄土的适用性。     

A method of calculating the non‐linear seismic response of a building braced with viscoelastic dampers

Buildings are continually subject to dynamic loads, such as wind load, seismic ground motion, and even the load from internal utility machines. The recent trend of constructing more flexible high‐rise buildings underscores the importance of including viscoelastic dampers in building designs. Viscoelastic dampers are used to control the dynamic response of a building. If the seismic design is based only on the linear response spectrum, considerable error may occur when calculating the seismic response of a building; rubber viscoelastic dampers show non‐linear hysteretic damping that is quite different from viscous damping. This study generated a non‐linear response spectrum using a non‐linear oscillator model to simulate a building with viscoelastic dampers installed. The parameters used in the non‐linear damper model were obtained experimentally from dynamic loading tests. The results show that viscoelastic dampers effectively reduce the seismic displacement response of a structure, but transmit more seismic force to the structure, which essentially increases its seismic acceleration response. Copyright © 2003 John Wiley & Sons, Ltd.     

Validation of nonlinear time history analysis models for single‐storey concentrically braced frames using full‐scale shake table tests

The concentrically braced frame (CBF) structure is one of the most efficient steel structural systems to resist earthquakes. This system can dissipate energy during earthquakes through braces, which are expected to yield in tension and buckle in compression, while all other elements such as columns, beams and connections are expected to behave elastically. In this paper, the performance of single‐storey CBFs is assessed with nonlinear time‐history analysis, where a robust numerical model that simulates the behaviour of shake table tests is developed. The numerical model of the brace element used in the analysis was calibrated using data measured in physical tests on brace members subjected to cyclic loading. The model is then validated by comparing predictions from nonlinear time‐history analysis to measured performance of brace members in full scale shake table tests. Furthermore, the sensitivity of the performance of the CBF to different earthquake ground motions is investigated by subjecting the CBF to eight ground motions that have been scaled to have similar displacement response spectra. The comparative assessments presented in this work indicate that these developed numerical models can accurately capture the salient features related to the seismic behaviour of CBFs. A good agreement is found between the performance of the numerical and physical models in terms of maximum displacement, base shear force, energy dissipated and the equivalent viscous damping. The energy dissipated and, more particular, the equivalent viscous damping, are important parameters required when developing an accurate displacement‐based design methodology for CBFs subjected to earthquake loading. In this study, a relatively good prediction of the equivalent viscous damping is obtained from the numerical model when compared with data measured during the shake table tests. However, it was found that already established equations to determine the equivalent viscous damping of CBFs may give closer values to those obtained from the physical tests. Copyright © 2012 John Wiley & Sons, Ltd.     

System identification estimation of soil properties at the Lotung site

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input–output data sets) using both time-invariant and time-variant parametric modeling methods (system identification). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratios were calculated for 8 events with M_L ranging from 4.5 to 7.0. Shear stiffness ranged between 0.5 and 6 MN/m, inversely proportional to PGA. The equivalent viscous damping ratio varied from 2 to 30% of critical damping, proportional to PGA. Degradation of soil behavior, while less pronounced with increasing depth, consistently occurs above a peak input acceleration of 0.07 g. Although “non-linear” behavior is evident above 0.17 g, Event 7 (0.21 g) is accurately predicted using a linear constant parameter model estimated from the smaller Event 8 aftershock ground motions.     

新型扇形盘式消能器减震性能参数分析

提出了一种新型扇形盘式效能器(fanshaped disc-type energy dissipator,FDED),阐明了其原理、特点,导出其设计要点和设计理论,采用数值方法分析了FDED的减震性能,研究不同设计参数对FDED减震性能的影响。结果表明:FDED设计原理可行,减震机理明确,其转盘式的构造可起到有效的位移放大效果,使得消能器在小激励位移下发挥耗能作用;FDED具有明显的双线性恢复力特性和稳定的耗能性能,等效黏滞阻尼系数可达50%以上;阻尼件中橡胶硬度的改变对FDED初始刚度的影响不敏感,但对FDED屈服后刚度和等效黏滞阻尼系数的影响较为明显。随着橡胶硬度的增大,FDEDE的屈服后刚度上升,等效黏滞阻尼系数降低;保持阻尼层中橡胶层的总厚度不变,通过增减叠层钢板改变单层橡胶层的厚度对于调整FDED的减震性能影响不大;调整铅芯直径的大小主要影响FDED的屈服力和耗能性能。随着铅芯直径的增大,FDED的屈服力也增大,耗能能力逐渐提高。     

无填充墙基础隔震RC框架在环境激励下的动力特性

对一基础隔震钢筋混凝土框架结构在无填充墙情况下进行了环境激励下的动力测试,重点利用Hilbert-Huang变换与随机减量技术相结合的方法识别了其模态参数,并与随机子空间识别法、有理分式多项式法识别的结果进行了对比。识别结果表明在环境激励下,基础隔震结构的基本周期远小于多遇和罕遇地震工况下设计计算的基本周期;等效黏滞阻尼比很小,近乎于基础固定模型。对隔震层阻尼特性的分析表明,环境激励下可以将基础隔震结构视为经典的比例阻尼系统。进一步以识别的模态参数为基准,采用优化的方法数值反演了环境激励下该结构隔震层的实际水平等效刚度,结果表明其值为多遇地震下计算刚度取值的10.75倍。     

Optimum lateral load pattern for seismic design of elastic shear‐buildings incorporating soil–structure interaction effects

Recently, several new optimum loading patterns have been proposed by researchers for fixed‐base systems while their adequacy for soil–structure systems has not been evaluated yet. Through intensive dynamic analyses of multistory shear‐building models with soil–structure interaction subjected to a group of 21 artificial earthquakes adjusted to soft soil design spectrum, the adequacy of these optimum patterns is investigated. It is concluded that using these patterns the structures generally achieve near optimum performance in some range of periods. However, their efficiency reduces as soil flexibility increases especially when soil–structure interaction effects are significant. In the present paper, using the uniform distribution of damage over the height of structures, as the criterion, an optimization algorithm for seismic design of elastic soil–structure systems is developed. The effects of fundamental period, number of stories, earthquake excitation, soil flexibility, building aspect ratio, damping ratio and damping model on optimum distribution pattern are investigated. On the basis of 30,240 optimum load patterns derived from numerical simulations and nonlinear statistical regression analyses, a new lateral load pattern for elastic soil–structure systems is proposed. It is a function of the fundamental period of the structure, soil flexibility and structural slenderness ratio. It is shown that the seismic performance of such a structure is superior to those designed by code‐compliant or recently proposed patterns by researchers for fixed‐base structures. Using the proposed load pattern in this study, the designed structures experience up to 40% less structural weight as compared with the code‐compliant or optimum patterns developed based on fixed‐base structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic performance of recycled concrete-filled square steel tube columns

An experimental study on the seismic performance of recycled concrete-filled square steel tube (RCFST) columns is carried out. Six specimens were designed and tested under constant axial compression and cyclic lateral loading. Two parameters, replacement percentage of recycled coarse aggregate (RCA) and axial compression level, were considered in the test. Based on the experimental data, the hysteretic loops, skeleton curves, ductility, energy dissipation capacity and stiffness degradation of RCFST columns were analyzed. The test results indicate that the failure modes of RCFST columns are the local buckling of the steel tube at the bottom of the columns, and the hysteretic loops are full and their shapes are similar to normal CFST columns. Furthermore, the ductility coefficient of all specimens are close to 3.0, and the equivalent viscous damping coefficient corresponding to the ultimate lateral load ranges from 0.323 to 0.360, which demonstrates that RCFST columns exhibit remarkable seismic performance.     

Stiffness‐damping simultaneous identification using limited earthquake records

A new method of stiffness‐damping simultaneous identification of building structures is proposed using limited earthquake records. It is shown that when horizontal accelerations are recorded at the floors just above and below a specific storey in a shear building model, the storey stiffness and the damping ratio can be identified uniquely. The viscous damping coefficient and the linear hysteretic damping ratio can also be identified simultaneously in a numerical model structure. The accuracy of the present identification method is investigated through the actual limited earthquake records in a base‐isolated building. It is further shown that an advanced identification technique for mechanical properties of a Maxwell‐type model can be developed by combining the present method with a perturbation technique. Copyright © 2000 John Wiley & Sons, Ltd.     

Simplified analysis of mid‐story seismically isolated buildings

The mid‐story isolation design method is recently gaining popularity for the seismic protective design of buildings located in the areas of high population. In a mid‐story isolated building, the isolation system is incorporated into the mid‐story rather than the base of the building. In this paper, the dynamic characteristics and seismic responses of mid‐story isolated buildings are investigated using a simplified three‐lumped‐mass structural model for which equivalent linear properties are formulated. From the parametric study, it is found that the nominal frequencies of the superstructure and the substructure, respectively, above and below the isolation system have significant influences on the isolation frequency and equivalent damping ratio of a mid‐story isolated building. Moreover, the mass and stiffness of the substructure are of greater significance than the superstructure in affecting the dynamic characteristics of the isolated building. Besides, based on the response spectrum analysis, it is noted that the higher mode responses may contribute significantly to the story shear force of the substructure. Consequently, the equivalent lateral force procedure of design codes should carefully include the effects of higher modes. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic performance of buildings retrofitted with nonlinear viscous dampers and adjacent reaction towers

An effective strategy of seismic retrofitting consists of installing nonlinear viscous dampers between the existing building, with insufficient lateral resistance, and some auxiliary towers, specially designed and erected as reaction structures. This allows improving the seismic performance of the existing building without any major alteration to its structural and nonstructural elements, which makes this approach particularly appealing for buildings with heritage value. In this paper, the nonlinear governing equations of the coupled lateral‐torsional seismic motion are derived from first principles for the general case of a multistory building connected at various locations in plan and in elevation to an arbitrary number of multistory towers. This formulation is then used to assess the performance of the proposed retrofitting strategy for a real case study, namely, a 5‐story student hall of residence in the city of Messina, Italy. The results of extensive time‐history analyses highlight the key design considerations associated with the stiffness of the reaction towers and the mechanical parameters of the nonlinear viscous dampers, confirming the validity of this approach.     

Damping‐adjusted combination rule for the response spectrum analysis of base‐isolated buildings

The classical response spectrum method continues to be the most popular approach for designing base‐isolated buildings, therefore avoiding computationally expensive nonlinear time‐history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex‐valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real‐valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS‐superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping‐adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS‐superstructure assembly. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic performance evaluation of single damped‐outrigger system incorporating buckling‐restrained braces

The outrigger system is an effective means of controlling the seismic response of core‐tube type tall buildings by mobilizing the axial stiffness of the perimeter columns. This study investigates the damped‐outrigger, incorporating the buckling‐restrained brace (BRB) as energy dissipation device (BRB‐outrigger system). The building's seismic responses are expected to be effectively reduced because of the high BRB elastic stiffness during minor earthquakes and through the stable energy dissipation mechanism of the BRB during large earthquakes. The seismic behavior of the BRB‐outrigger system was investigated by performing a spectral analysis considering the equivalent damping to incorporate the effects of BRB inelastic deformation. Nonlinear response history analyses were performed to verify the spectral analysis results. The analytical models with building heights of 64, 128, and 256 m were utilized to investigate the optimal outrigger elevation and the relationships between the outrigger truss flexural stiffness, BRB axial stiffness, and perimeter column axial stiffness to achieve the minimum roof drift and acceleration responses. The method of determining the BRB yield deformation and its effect on overall seismic performance were also investigated. The study concludes with a design recommendation for the single BRB‐outrigger system.     

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.     

Direct displacement-based design for seismic retrofit of existing buildings using nonlinear viscous dampers

This paper presents a direct displacement-based design procedure for seismic retrofit of existing buildings using nonlinear viscous dampers according to equivalent linear systems. Unlike conventional methods, the equivalent linear viscous damping provided by the nonlinear viscous dampers is derived based on the assumption that the average energy dissipated between the linear and the nonlinear viscous dampers is equal. Also, the equivalent period and viscous damping for the equivalent linear systems which are used for representing the behavior of bare frames (the buildings without dampers) are derived from the concept of average storage energy and average dissipated energy, respectively. It is shown from nonlinear time-history analyses that the nonlinear action of the retrofitted structures can be reasonably captured by the presented direct displacement-based procedure.     

Seismic response of steel frame structures with hybrid passive control systems

The concept of the hybrid passive control system is studied analytically by investigating the seismic response of steel frame structures. Hybrid control systems consist of two different passive elements combined into a single device or system. The hybrid systems investigated in this research consist of a rate‐dependent damping device paired with a rate‐independent energy dissipation element. The innovative configurations exploit individual element strengths and offset their weaknesses through multiphased behavior. A nine‐story, five‐bay steel moment‐frame was used for the analysis. Six different seismic resisting systems were analyzed and compared. The conventional systems included a special moment‐resisting frame (SMRF) and a dual SMRF–buckling‐restrained brace (BRB) system. The final four configurations are hybrid passive systems. The different hybrid configurations utilize a BRB and either a high‐damping rubber damper or viscous fluid damper. The analyses were run in the form of an incremental dynamic analysis. Several damage measures were calculated, including maximum roof drift, base shear, and total roof acceleration. The results demonstrate the capability of hybrid passive control systems to improve structural response compared with conventional lateral systems and to be effective for performance‐based seismic design. Each hybrid configuration improved some aspect of structural response with some providing benefits for multiple damage measures. The multiphased nature provides improved response for frequent and severe seismic events. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of the construction process and nonstructural components on the modal properties of a five‐story building

A full‐scale five‐story reinforced concrete building was built and tested on the NEES‐UCSD shake table during the period from May 2011 to May 2012. The purpose of this test program was to study the response of the structure and nonstructural components and systems (NCSs) and their dynamic interaction during seismic base excitation of different intensities. The building specimen was tested first under a base‐isolated condition and then under a fixed‐based condition. As the building was being erected, an accelerometer array was deployed on the specimen to study the evolution of its modal parameters during the construction process and placement of major NCSs. A sequence of dynamic tests, including daily ambient vibration, shock (free vibration) and forced vibration tests (low‐amplitude white noise and seismic base excitations), were performed on the building at different stages of construction. Different state‐of‐the‐art system identification methods, including three output‐only and two input‐output methods, were used to estimate the modal properties of the building. The obtained results allow to investigate in detail the effects of the construction process and NCSs on the dynamic parameters of this building system and to compare the modal properties obtained from different methods, as well as the performance of these methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection

A new passive seismic response control device has been developed, fabricated, and tested by the authors and shown to be capable of producing negative stiffness via a purely mechanical mechanism, thus representing a new generation of seismic protection devices. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (the desired relationship being that the product of restoring force and displacement is nonnegative), when implemented in parallel with a structure having positive stiffness, the combined system appears to have substantially reduced stiffness while remaining stable. Thus, there is an ‘apparent weakening and softening’ of the structure that results in reduced forces and increased displacements (where the weakening and softening is of a non‐damaging nature in that it occurs in a seismic protection device rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the negative stiffness device. The combination of negative stiffness and passive damping provides a large degree of control over the expected performance of the structure. In this paper, a numerical study is presented on the performance of a seismically isolated highway bridge model that is subjected to various strong earthquake ground motions. The Negative Stiffness Devices (NSDs) are described along with their hysteretic behavior as obtained from a series of cyclic tests wherein the tests were conducted using a modified design of the NSDs (modified for testing within the bridge model). Using the results from the cyclic tests, numerical simulations of the seismic response of the isolated bridge model were conducted for various configurations (with/without negative stiffness devices and/or viscous dampers). The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. This assessment was conducted as part of a NEES (Network for Earthquake Engineering Simulation) project which included shaking table tests of a quarter‐scale highway bridge model. Copyright © 2014 John Wiley & Sons, Ltd.     

巨子型有控结构体系中黏滞阻尼器参数研究

巨子型有控结构体系(Mega-sub Controlled Structure System,即MSCSS)是一种新型的超高层建筑结构体系.本文针对MSCSS的构造特点,提出一种安装黏滞阻尼器的新的布置方案,通过研究该布置方案中取不同黏滞阻尼器参数时巨子型有控结构体系在罕遇地震作用下的动力响应,提出了与该结构体系动力特...