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.     

新型伸臂消能体系的抗震性能研究

以天津某实际工程项目为例,对新型伸臂消能结构体系中消能伸臂的数量、位置和黏滞阻尼器参数进行了优化,比较了这一新型消能体系与常规消能减震方案的减震效果.研究表明,相对于常规消能减震方案,新型伸臂消能结构体系可在布置较少数量阻尼器时,仍获得较好的减震效果,其经济性十分明显,可望在实际工程中进一步推广应用.     

Seismic analysis of structures with a fractional derivative model of viscoelastic dampers

Viscoelastic dampers are now among some of the preferred energy dissipation devices used for passive seismic response control. To evaluate the performance of structures installed with viscoelastic dampers, different analytical models have been used to characterize their dynamic force deformation characteristics. The fractional derivative models have received favorable attention as they can capture the frequency dependence of the material stiffness and damping properties observed in the tests very well. However, accurate analytical procedures are needed to calculate the response of structures with such damper models. This paper presents a modal analysis approach, similar to that used for the analysis of linear systems, for solving the equations of motion with fractional derivative terms for arbitrary forcing functions such as those caused by earthquake induced ground motions. The uncoupled modal equations still have fractional derivatives, but can be solved by numerical or analytical procedures. Both numerical and analytical procedures are formulated. These procedures are then used to calculate the dynamic response of a multi-degree of freedom shear beam structure excited by ground motions. Numerical results demonstrating the response reducing effect of viscoelastic dampers are also presented.     

Higher-mode effect on the seismic responses of buildings with viscoelastic dampers

In conventional modal analysis procedures, usually only a few dominant modes are required to describe the dynamic behavior of multi-degrees-of-freedom buildings. The number of modes needed in the dynamic analysis depends on the higher-mode contribution to the structural response, which is called the higher-mode effect. The modal analysis approach, however, may not be directly applied to the dynamic analysis of viscoelastically damped buildings. This is because the dynamic properties of the viscoelastic dampers depend on their vibration frequency. Therefore, the structural stiffness and damping contributed from those dampers would be different for each mode. In this study, the higher-mode effect is referred to as the response difference induced by the frequency-dependent property of viscoelastic dampers at higher modes. Modal analysis procedures for buildings with viscoelastic dampers distributed proportionally and non-proportionally to the stiffness of the buildings are developed to consider the higher-mode effect. Numerical studies on shear-type viscoelastically damped building models are conducted to examine the accuracy of the proposed procedures and to investigate the significance of the higher-mode effect on their seismic response. Two damper models are used to estimate the peak damper forces in the proposed procedures. Study results reveal that the higher-mode effect is significant for long-period viscoelastically damped buildings. The higher-mode effect on base shear is less significant than on story acceleration response. Maximum difference of the seismic response usually occurs at the top story. Also, the higher-mode effect may not be reduced by decreasing the damping ratio provided by the viscoelastic dampers. For practical application, it is realized that the linear viscous damping model without considering the higher-mode effect may predict larger damper forces and hence, is on the conservative side. Supported by: Science Council, Chinese Taipei, grant no. 88-2625-2-002-006     

Stochastic seismic response of structures with added viscoelastic dampers modeled by fractional derivative

Viscoelastic dampers, as supplementary energy dissipation devices, have been used in building structures under seismic excitation or wind loads. Different analytical models have been proposed to describe their dynamic force deformation characteristics. Among these analytical models, the fractional derivative models have attracted more attention as they can capture the frequency dependence of the material stiffness and damping properties observed from tests very well. In this paper, a Fourier-transform-based technique is presented to obtain the fractional unit impulse function and the response of structures with added viscoelastic dampers whose force-deformation relationship is described by a fractional derivative model. Then, a Duhamel integral-type expression is suggested for the response analysis of a fractional damped dynamic system subjected to deterministic or random excitation. Through numerical verification, it is shown that viscoelastic dampers are effective in reducing structural responses over a wide frequency range, and the proposed schemes can be used to accurately predict the stochastic seismic response of structures with added viscoelastic dampers described by a Kelvin model with fractional derivative.     

The damped cable system for seismic protection of frame structures — Part II: Design and application

The complementary sections of the studies carried out on the damped cable system, whose experimental and numerical characterization and assessment analyses are described in the companion paper, are presented herein. The first section includes a criterion for a preliminary evaluation of the section area of cables, the second branch stiffness of spring‐dampers and the mutual installation preload, and suggestions for a simplified nonlinear dynamic computation of the damping coefficient of dissipaters. A second section follows, aimed at evaluating the influence of cable layout on damped cable system performance. A numerical enquiry is developed on a four‐story and an eight‐story RC plane frame, to assess their seismic response for several shapes of cables, and determine what geometrical configurations are the best performing ones. In the third section, a demonstrative application of the protective system, represented by the seismic retrofit of a hospital building with RC structure, is offered. The characteristics of the system designed for this case study, including locations, dimensions, layouts, and technical installation details of cables and spring‐dampers, are illustrated, and the improvement of seismic performance as compared with the original conditions, is finally assessed. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental beyond design and residual performances of full-scale viscoelastic dampers and their empirical modeling

Most past researches relevant to viscoelastic (VE) dampers, regardless of analytical and experimental ones, aimed at their design (or pre-damage) performance. In reality, however, under maximum considered or greater shaking caused by earthquakes, the shear deformation of the VE dampers installed in a structure may exceed or is even much larger than their nominal design range, thus leading to damage to the VE material. Under this circumstance, the structural design might become not conservative when the viscoelastically damped structure is a retrofit design or is not a supplemental damping design. Therefore, in this study, the beyond design and residual performances of the full-scale VE dampers after suffering damage are experimentally probed and compared with their design (or pre-damage) performance tested before. To have more engineering sense in practice, some suitable and conservative empirical post-damage models through considering reduction factors in the Kelvin-Voigt model for assessing the beyond design and residual performances of the full-scale VE dampers after suffering damage are recommended.     

台湾某钢框架大楼采用阻尼器补强结构减震效果评析

阻尼器是一种效果良好的减震装置,将阻尼器安装于结构中能够适时为结构体系提供阻尼力,从而减小地震作用对结构的破坏。黏滞阻尼器对振动的反应比较敏感,在结构受到较小振动时就可以发挥其减震效果,其阻尼力会随着振动周期和使用状态温度的不同而变化。当地震发生时,安装在结构中的阻尼器会消减地震作用,降低传导到主结构体系的地震能量,减小结构相对位移。本文介绍了黏滞阻尼器的工作原理和安装有黏滞阻尼器的结构体系的阻尼比的计算方法,对减震结构的减震效果的评析方法做出探讨,并以一安装有黏滞阻尼器的台湾某既有钢框架结构为例,分析了(1)该结构在遭受地震作用时的地震反应;(2)该结构体系在不同地震作用水平时的阻尼比,包括主体结构阻尼比和黏滞阻尼器阻尼比;(3)结构安装黏滞阻尼器后的减震效果。实例对本文的减震评析方法和减震效果进行了说明和分析,计算及分析结果表明利用黏滞阻尼器加固既有结构能够取得较好的减震效果,本文所提减震效果评析方法是一种实用有效的评析方法,对类似工程的减震评析具有一定的参考价值。     

A seismic retrofit method by connecting viscous dampers for microelectronics factories

The implementation of viscous dampers to microelectronics factories has been previously proved not to affect the micro‐vibration of the factories in operation so that the vibration‐sensitive manufacturing process will not be interfered. Therefore, a seismic retrofit strategy which employs the viscous dampers installed in between the exterior and interior structures of the ‘fab’ structure is proposed in the study. The design formulas corresponding to the proposed retrofit method are derived using the non‐proportional damping theory. Based on the study, it is found that the added damping ratio to the fab structure depends greatly on the frequency ratio of the two structures in addition to the damping coefficients of the added dampers. Outside the bandwidth of the frequency ratio in which the added damping ratio is very sensitive to the variation of the frequency ratio, the added damping ratio can be well captured using the classical damping theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Optimum placement and characteristics of velocity-dependent dampers under seismic excitation

In this study,through novel drift-based equations of motion in the frequency domain,optimum placement and characteristics of linear velocity-dependent dampers are investigated.In this study,the sum of the square of the absolute values of transfer matrix elements for interstory drifts is considered as the optimization index.Optimum placement and characteristics of dampers are simultaneously obtained by minimizing the optimization index through an incremental procedure.In each step of the procedure,a predefined value is considered as the damper characteristic.The optimum story for this increment is selected such that it leads to a minimum value for the optimization index.The procedure is repeated for the next increments until the optimization index meets its target value,which is obtained according to the desired damping ratio for the overall structure.In other words,the desired overall damping ratio is the input to the proposed procedure,and the optimal placement and characteristics of the dampers are its output.It is observed that the optimal placement of a velocitydependent damper depends on the damping coefficient of the added damper,frequency of the excitation,and distribution of the mass,stiffness,and inherent damping of the main structure.     

Response prediction,experimental characterization and P‐spectra design of frames with viscoelastic–plastic dampers

Viscoelastic–plastic (VEP) dampers are hybrid passive damping devices that combine the advantages of viscoelastic and hysteretic damping. This paper first formulates a semi‐analytical procedure for predicting the peak response of nonlinear SDOF systems equipped with VEP dampers, which forms the basis for the generation of Performance Spectra that can then be used for direct performance assessment and optimization of VEP damped structures. This procedure is first verified against extensive nonlinear time‐history analyses based on a Kelvin viscoelastic model of the dampers, and then against a more advanced evolutionary model that is calibrated to characterization tests of VEP damper specimens built from commercially available viscoelastic damping devices, and an adjustable friction device. The results show that the proposed procedure is sufficiently accurate for predicting the response of VEP systems without iterative dynamic analysis for preliminary design purposes. A design method based on the Performance Spectra framework is then proposed for systems equipped with passive VEP dampers and is applied to enhance the seismic response of a six‐storey steel moment frame. The numerical simulation results on the damped structure confirm the use of the Performance Spectra as a convenient and accurate platform for the optimization of VEP systems, particularly during the initial design stage. Copyright © 2016 John Wiley & Sons, Ltd.     

Centrifuge modelling of structures with oil dampers under seismic loading

Experimental research into the seismic performance of buildings with passive oil dampers has so far been restricted to large-scale testing of frames erected on laboratory shaking tables that ignore the foundation soil below. This simplification of the problem falls short of replicating dynamic soil-structure interaction that would occur in the field. This paper presents the first experimental attempt at utilising high gravity dynamic centrifuge testing to replicate the response of a damped building at a reduced model scale. The paper compares the dynamic response of two similar two-degree-of-freedom model sway frames, one control (bare) frame and one frame equipped with miniature oil dampers, both structures founded on shallow raft foundations in dry dense sand. The miniature oil dampers successfully mitigate floor accelerations, drifts, and storey shear forces in the damped frame with minor modification to the frame stiffness. For strong, near resonance motions, global rocking of the undamped frame associated with physical uplifting of the foundation from the soil surface and subsequent yielding of sand beneath has led to floor acceleration levels, which are comparable to those obtained in the damped building fitted with miniature oil dampers. Assessment of the instrumentation installed on the miniature oil dampers reveals a viscoelastic damper behaviour with a dependency on stroke magnitude and on velocity.     

Active viscous damping system for control of MDOF structures

The development and applications of a supplemental viscous damping device with active capacity are described. The system of the dampers defined as active viscous damping system (AVDS) is presented herein. Structural control principles defined here as active control theory (ACT) are used to obtain the control forces at each time step during an excitation. Control of the damping forces is possible due to a mechanical structure of the proposed AVDS and do not require the input of large power and energy. This system can be efficiently used to enhance the damping of a structure without adding in stiffness and strength. The added damping forces can be adjusted in a wide range. Its efficiency is demonstrated by a numerical simulation of a seven‐storey building subjected to earthquakes. The simulation shows that the behaviour of the damped structure with the AVDS is significantly improved compared to that of an uncontrolled system. Moreover, the response is better than that of adding either passive viscous dampers or electrorheological damping devices. Copyright © 2001 John Wiley & Sons, Ltd.     

Dynamic characteristics and seismic response of adjacent buildings linked by discrete dampers

Coupling adjacent buildings using discrete viscoelastic dampers for control of response to low and moderate seismic events is investigated in this paper. The complex modal superposition method is first used to determine dynamic characteristics, mainly modal damping ratio and modal frequency, of damper-linked linear adjacent buildings for practical use. Random seismic response of linear adjacent buildings linked by dampers is then determined by a combination of the complex modal superposition method and the pseudo-excitation method. This combined method can effectively and accurately determine random seismic response of non-classically damped systems in the frequency domain. Parametric studies are finally performed to identify optimal parameters of viscoelastic dampers for achieving the maximum modal damping ratio or the maximum response reduction of adjacent buildings. It is demonstrated that using discrete viscoelastic dampers of proper parameters to link adjacent buildings can reduce random seismic responses significantly. Copyright © 1999 John Wiley & Sons Ltd.     

The damped cable system for seismic protection of frame structures — Part I: General concepts,testing and modeling

Research studies on the damped cable system (DCS) for seismic protection of frame structures are presented in this paper and the accompanying one. This technology includes prestressed steel cables linked to pressurized fluid viscous spring‐dampers fixed to the foundation at their lower ends, and to the top floor, or one of the upper floors, at their upper ends. The cables have sliding contacts with the floor slabs, to which they are joined by steel deviators. The general characteristics of the system, as well as of the constituting spring‐dampers and cables, are initially discussed. The results of a laboratory testing campaign developed on a DCS prototype are examined, and transferred into the formulation of the finite element model of the system, conceived to be easily generated by commercial structural analysis programs. A second dynamic experimental investigation follows, concerning a pilot installation of the system on a full‐scale mock‐up building. The benefits of the protective technology are evaluated in terms of maximum displacements and accelerations, as well as of equivalent viscous damping coefficient and MDOF transmissibility ratio. Further sections of the study, including a preliminary sizing criterion of DCS, additional numerical enquiries aimed at optimizing its geometrical layout, and the application to a real case study building, are offered in the companion paper. Copyright © 2011 John Wiley & Sons, Ltd.     

铅—橡胶阻尼器的试验研究

通过4种外径相同但铅芯直接不同的8个铅－橡胶阻尼器的低周往复水平荷载试验，研究影响铅－橡胶阻尼器性能的主要因素，得到了这种阻尼器的初始刚度，屈服刚度和等效阻尼比的变化规律。试验结果还表明，铅－橡胶阻尼器即使在很小的剪切变形下也具有较高的耗能能力。     

Damping characteristics of friction damped braced frame and its effectiveness in the mega-sub controlled structure system

Based on energy dissipation and structural control principle, a new structural configuration, called the mega- sub controlled structure (MSCS) with friction damped braces (FDBs), is first presented. Meanwhile, to calculate the damping coefficient in the slipping state a new analytical method is proposed. The damping characteristics of one-storey friction damped braced frame (FDBF) are investigated, and the influence of the structural parameters on the energy dissipation and the practical engineering design are discussed. The nonlinear dynamic equations and the analytical model of the MSCS with FDBs are established. Three building structures with different structural configurations, which were designed with reference to the conventional mega-sub structures such as used in Tokyo City Hall, are comparatively investigated. The results illustrate that the structure presented in the paper has excellent dynamic properties and satisfactory control effectiveness.     

Seismic response of steel frame structures with added viscoelastic dampers

The feasibility of using viscoelastic (VE) dampers to mitigate earthquake-induced structural response is studied in this paper. The properties of VE dampers are briefly described. A procedure for evaluating the VE damping effect when added to a structure is proposed in which the damping effect of VE dampers is incorporated into modal damping ratios through an energy approach. Computer simulation of the damped response of a multi-storey steel frame structure shows significant reduction in floor displacement levels.     

隔震结构中非经典阻尼影响及最佳阻尼比分析

本文采用双自由度非比例阻尼振动模型描述基础隔震体系,用拉普拉斯变换方法获得其地震时域响应的近似解析解,借助于应谱理论分析了非比例阻尼对隔震体系中的上部结构层间最大剪力及隔震层最大位移等响应值的影响,探寻了隔震系统最佳阻尼比的取值范围。     

菱形开洞软钢阻尼器及其在结构减震中的模拟分析

提出了菱形开洞加劲软钢阻尼器及其在整体结构中的数值模拟方法,并据此对菱形开洞软钢阻尼器的循环加载试验以及安装阻尼器的钢框架结构的震动台试验进行了模拟分析。验证了使用AN-SYS有限元程序进行数值模拟分析的可行性和准确性,同时证明了菱形开洞软钢阻尼器具有良好的滞回性能,在整体结构中能够达到较好的减震效果。