Control of the earthquake and wind dynamic response of steel‐framed buildings by using additional braces and/or viscoelastic dampers

The insertion of steel braces equipped with viscoelastic dampers (VEDs) (‘dissipative braces’) is a very effective technique to improve the seismic or wind behaviour of framed buildings. The main purpose of this work is to compare the earthquake and wind dynamic response of steel‐framed buildings with VEDs and achieve optimal properties of dampers and supporting braces. To this end, a numerical investigation is carried out with reference to the steel K‐braced framed structure of a 15‐storey office building, which is designed according to the provisions of Eurocodes 1 and 3, and to four structures derived from the first one by the insertion of additional diagonal braces and/or VEDs. With regard to the VEDs, the following cases are examined: absence of dampers; insertion of dampers supported by the existing K‐braces in each of the structures with or without additional diagonal braces; insertion of dampers supported by additional diagonal braces. Dynamic analyses are carried out in the time domain using a step‐by‐step initial stress‐like iterative procedure. For this purpose, the frame members and the VEDs are idealized, respectively, by a bilinear model, which allows the simulation of the nonlinear behaviour under seismic loads, and a six‐element generalized model, which can be considered as an in‐parallel‐combination of two Maxwell models and one Kelvin model. Artificially generated accelerograms, whose response spectra match those adopted by Eurocode 8 for a medium subsoil class and for different levels of peak ground acceleration, are considered to simulate seismic loads. Along‐wind loads are considered assuming, at each storey, time histories of the wind velocity for a return period T_r=5 years, according to an equivalent spectrum technique. Copyright © 2010 John Wiley & Sons, Ltd.     

SMA-VED混合自复位支撑钢框架地震易损性与风险分析

本文提出了一种新型形状记忆合金（Shape Memory Alloy,SMA）-黏弹性阻尼器（ViscoelasticDamper,VED）自复位支撑,设计了普通预应力筋自复位支撑钢框架与SMA-VED自复位支撑钢框架。采用组合模型以及改进材料模型准确模拟了支撑的力学行为,详细讨论了考虑构件失效的模拟方法,通过试验确定了VED的失效应变范围,最后基于概率统计方法进行了易损性分析以及全周期风险分析。研究发现: SMA-VED自复位支撑可显著提升框架抗震性能;倒塌风险以及残余变形超越概率均显著低于普通预应力筋自复位支撑钢框架,下降比例最高超过50%。预应力筋断裂失效导致框架倒塌风险可提高5倍以上; SMA-VED自复位支撑失效会造成残余变形超越概率有所上升但幅度不大。总体来说,SMA-VED自复位支撑钢框架具备更好的地震鲁棒性。     

Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be modelled by way of a first‐order filter. We use this result to formulate a procedure that calculates the stiffness required by the supporting brace to provide a specified effectiveness of the damping action. The proposed procedure assumes that viscous dampers have been sized in a previous design step based on any optimal methodology in which, as is usually the case, the presence of supporting braces and their dynamic effects were neglected. Firstly considering a one degree‐of‐freedom system, we show that the proposed method ensures a desired level of damper efficiency for all frequencies within a selected bandwidth. Then the analysis is extended to the case of multi‐degree‐of‐freedom systems to show that the design criteria can be applied in a straightforward and successful manner to more complex structures. © 2014 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.     

装设粘弹性阻尼器钢筋混凝土结构抗震实用分析

为了设计装设粘弹性阻尼器受控结构、推进此项技术的工程应用,分别利用粘弹性阻尼器的复刚度模型和有限元模型,编制了振型分解反应谱程序和弹性时程分析程序,并对一装设粘弹性阻尼器的16层钢筋混凝土结构和相应原结构在多遇地震下的响应进行了分析。     

Minimum‐cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting

This paper presents an effective approach for achieving minimum‐cost designs for seismic retrofitting using nonlinear fluid viscous dampers. The damping coefficients of the dampers and the stiffness coefficients of the supporting braces are designed by an optimization algorithm. A realistic retrofitting cost function is minimized subject to constraints on inter‐story drifts at the peripheries of frame structures. The cost function accounts for costs related to both the topology and the sizes of the dampers. The behavior of each damper‐brace element is defined by the Maxwell model, where the force–velocity relation of the nonlinear dampers is formulated with a fractional power law. The optimization problem is first posed and solved as a mixed integer problem. For the reduction of the computational effort required in the optimization, the problem is then reformulated with continuous variables only and solved with a gradient‐based algorithm. Material interpolation techniques, which have been successfully applied in topology optimization and in multi‐material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3‐D irregular frames are presented and discussed. Copyright © 2017 John Wiley & Sons, Ltd.     

Effects of brace stiffness on performance of structures with supplemental Maxwell model‐based brace–damper systems

Shear‐type buildings with Maxwell model‐based brace–damper systems are studied in this paper with a primary emphasis on the effects of brace stiffness. A single‐story building with a viscous damper installed on top of a Chevron‐brace is first investigated. Closed‐form solutions are derived for the simple structure, relating the brace stiffness and damper coefficient to the targeted reduction in response displacement or acceleration. For a given brace stiffness, the solution is minimized to give a set of formulae that will allow the optimal damper coefficient to be determined, assuring the desired performance. The model is subsequently extended to multistory buildings with viscous dampers installed on top of Chevron‐braces. For a targeted reduction in the mean square of the interstory drift, floor acceleration or base shear force, the minimum brace stiffness and optimal damper coefficients are obtained through an iterative procedure. The response reduction, which signifies the improved performance, is achieved by a combination of brace stiffness and viscous damper coefficients, unlike conventional approaches where damper coefficients are typically optimized independent of brace stiffnesses. Characteristics of multi‐degree‐of‐freedom systems are studied using a 2‐story and a 10‐story buildings where the effects of brace stiffness on the overall performance of the building can be quantified. Copyright © 2010 John Wiley & Sons, Ltd.     

Buckling‐restrained brace using steel mortar planks; performance evaluation as a hysteretic damper

The authors developed a buckling‐restrained brace that enables increased design freedom at both ends of the core plate and strict quality control while providing stable hysteresis characteristics even under high strains. The buckling‐restrained brace can be formed by welding a core plate covered with unbonded material to a pair of mortar‐filled channel steels (steel mortar planks) as a restraining part. The use of this approach enables visual confirmation of the status of the mortar filling and also facilitates standardizing structural members and member‐by‐member quality control. Specimens of a buckling‐restrained brace with different steel mortar plank heights are fabricated to adjust the restraining force, along with specimens with different core plate width‐to‐thickness ratios. The tests were conducted to reveal the hysteretic characteristics of the braces, as well as their cumulative plastic strain energy, elastoplastic properties, and stiffening properties. A performance evaluation formula as well as a buckling‐restrained brace design method using the test results is proposed. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic performance and new design procedure for chevron‐braced frames

The paper is concerned with the seismic design of steel‐braced frames in which the braces are configured in a chevron pattern. According to EuroCode 8 (EC8), the behaviour factor q, which allows for the trade‐off between the strength and ductility, is set at 2.5 for chevron‐braced frames, while 6.5 is assigned for most ductile steel moment‐resisting frames. Strength deterioration in post‐buckling regime varies with the brace's slenderness, but EC8 adopts a unique q value irrespective of the brace slenderness. The study focuses on reevaluation of the q value adequate for the seismic design of chevron‐braced frames. The present EC8 method for the calculation of brace strength supplies significantly different elastic stiffnesses and actual strengths for different values of brace slenderness. A new method to estimate the strength of a chevron brace pair is proposed, in which the yield strength (for the brace in tension) and the post‐buckling strength (for the brace in compression) are considered. The new method ensures an identical elastic stiffness and a similar strength regardless of the brace slenderness. The advantage of the proposed method over the conventional EC8 method is demonstrated for the capacity of the proposed method to control the maximum inter‐storey drift. The q values adequate for the chevron‐braced frames are examined in reference to the maximum inter‐storey drifts sustained by most ductile moment‐resisting frames. When the proposed method is employed for strength calculation, the q value of 3.5 is found to be reasonable. It is notable that the proposed method does not require larger cross‐sections for the braces compared to the cross‐sections required for the present EC8 method. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic retrofitting of reinforced concrete frame structures using GFRP-tube-confined-concrete composite braces

This paper presents a new type of structural bracing intended for seismic retrofitting use in framed structures. This special composite brace,termed glass-fiber-reinforced-polymer(GFRP)-tube-confined-concrete composite brace,is comprised of concrete confined by a GFRP tube and an inner steel core for energy dissipation.Together with a contribution from the GFRP-tube confined concrete,the composite brace shows a substantially increased stiffness to control story drift, which is often a preferred feature in seismic retrofitting.An analysis model is established and implemented in a general finite element analysis program-OpenSees,for simulating the load-displacement behavior of the composite brace.Using this model,a parametric study of the hysteretic behavior(energy dissipation,stiffness,ductility and strength)of the composite brace was conducted under static cyclic loading and it was found that the area ratio of steel core to concrete has the greatest influence among all the parameters considered.To demonstrate the application of the composite brace in seismic retrofitting, a three-story nonductile reinforced concrete(RC)frame structure was retrofitted with the composite braces.Pushover analysis and nonlinear time-history analyses of the retrofitted RC frame structure was performed by employing a suite of 20 strong ground motion earthquake records.The analysis results show that the composite braces can effectively reduce the peak seismic responses of the RC frame structure without significantly increasing the base shear demand.     

Influence of gusset plate connections and braces on the seismic performance of X‐braced frames

Braced frames are one of the most economical and efficient seismic resisting systems yet few full‐scale tests exist. A recent research project, funded by the National Science Foundation (NSF), seeks to fill this gap by developing high‐resolution data of improved seismic resisting braced frame systems. As part of this study, three full‐scale, two‐story concentrically braced frames in the multi‐story X‐braced configuration were tested. The experiments examined all levels of system performance, up to and including fracture of multiple braces in the frame. Although the past research suggests very limited ductility of SCBFs with HSS rectangular tubes for braces recent one‐story tests with improved gusset plate designs suggest otherwise. The frame designs used AISC SCBF standards and two of these frames designs also employed new concepts developed for gusset plate connection design. Two specimens employed HSS rectangular tubes for bracing, and the third specimen had wide flange braces. Two specimens had rectangular gusset plates and the third had tapered gusset plates. The HSS tubes achieved multiple cycles at maximum story drift ratios greater than 2% before brace fracture with the improved connection design methods. Frames with wide flange braces achieved multiple cycles at maximum story drift greater than 2.5% before brace fracture. Inelastic deformation was distributed between the two stories with the multi‐story X‐brace configuration and top story loading. Copyright © 2010 John Wiley & Sons, Ltd.     

Seismic performance of chevron-configured special concentrically braced frames with yielding beams

Current seismic design requirements for special concentrically braced frames (SCBFs) in chevron configurations require that the beams supporting the braces be designed to resist the demands resulting from the simultaneous yielding of the tension brace and degraded, post-buckling strength of the compression brace. Recent research, including large-scale experiments and detailed finite-element analyses, has demonstrated that limited beam yielding is not detrimental to chevron braced frame behavior and actually increases the story drift at which the braces fracture. These findings have resulted in new expressions for computing beam demands in chevron SCBFs that reduce the demand in the tension brace to be equal to the expected compressive capacity at buckling of the compression brace. In turn, the resultant force on the beam is reduced as is the required size of the beam. Further study was undertaken to investigate the seismic performance of buildings with SCBFs, including chevron SCBFs with and without yielding beams and X-braced frames. Prototype three- and nine-story braced frames were designed using all three framing systems, that is, chevron, chevron with yielding beams, and X SCBFs, resulting in six building frames. The nonlinear dynamic response was studied for ground motions simulating two different seismic hazard levels. The results were used to characterize the seismic performance in terms of the probability of salient damage states including brace fracture, beam vertical deformation, and collapse. The results demonstrate that the seismic performance of chevron SCBFs with limited beam yielding performs as well as or better than the conventionally designed chevron and X SCBFs.     

Subassemblage cyclic loading test of RC frame with buckling restrained braces in zigzag configuration

A new buckling restrained braced frame system is proposed for reinforced concrete building structures, which is featured by the zigzag configuration of the braces and the corresponding connection details. The connection details tend to separate the vertical and horizontal components of force imposed by the braces to be resisted by independent structural components to make the behavior of the connection easier to estimate and control. The performance of the brace connection details was evaluated through cyclic load testing on 1/2‐scale subassemblies of the proposed system, each of which consisted of a reinforced concrete part and a set of buckling restrained braces. To simplify the test control, the specimens were rotated 90° in the test and were loaded by two displacement controlled actuators. The test results show that the normal and the shear resistance of the gusset plate connection are essentially independent of each other. However, the rotation of the gusset plate with respect to the beam‐to‐column joint may result in nonuniform force distribution of the anchor bolts, the primary resistance for tensile force. At the same time, such rotation may also subject the concrete corbels, the primary shear resistance, to unfavorable tensile force. In addition, it is also confirmed that the buckling restrained braces performed well in the proposed system. Copyright © 2012 John Wiley & Sons, Ltd.     

A noniterative design procedure for supplemental brace–damper systems in single‐degree‐of‐freedom systems

In this paper, a method for designing supplemental brace–damper systems in single‐degree‐of‐freedom (SDOF) structures is presented. We include the effects of the supporting brace stiffness in the dynamic response by using a viscoelastic Maxwell model. On the basis of the study of an SDOF under ground excitation, we propose a noniterative design procedure for simultaneously specifying both the damper and the brace while assuring a desired structural performance. It is shown that to increase the damper size beyond the value delivered by the proposed criteria will not provide any improvement but actually worsen the structural response. The design method presented here shows excellent agreement with the FEMA 273 design approach but offers solutions closer to optimality. Copyright © 2013 John Wiley & Sons, Ltd.     

Structural vibration passive control and economic analysis of a high-rise building in Beijing

Performance analysis of the Pangu Plaza under earthquake and wind loads is described in this paper.The plaza is a 39-story steel high-rise building,191 m high,located in Beijing close to the 2008 Olympic main stadium.It has both fluid viscous dampers(FVDs) and buckling restrained braces or unbonded brace(BRB or UBB) installed.A repeated iteration procedure in its design and analysis was adopted for optimization.Results from the seismic response analysis in the horizontal and vertical directions show that th...     

Shake table testing and numerical simulation of a self‐centering energy dissipative braced frame

The self‐centering energy dissipative (SCED) brace is a new steel bracing member that provides both damping to the structure and a re‐centering capability. The goal of this study was to confirm the behavior of SCED braces within complete structural systems and to confirm the ability to model these systems with both a state‐of‐the‐art computer model as well as a simplified model that would be useful to practicing engineers. To these ends, a three‐story SCED‐braced frame was designed and constructed for testing on a shake table. Two concurrent computer models of the entire frame were constructed: one using the opensees nonlinear dynamic modeling software, and a simplified model using the commercial structural analysis software sap2000 . The frame specimen was subjected to 12 significant earthquakes without any adjustment or modification between the tests. The SCED braces prevented residual drifts in the frame, as designed, and did not show any significant degradation due to wear. Both numerical models were able to predict the drifts, story shears, and column forces well. Peak story accelerations were overestimated in the models; this effect was found to be caused by the absence of transitions at stiffness changes in the hysteretic model of the braces. Copyright © 2013 John Wiley & Sons, Ltd.     

Retrofit of reinforced concrete frames with buckling‐restrained braces

Damage to buildings observed in recent earthquakes suggests that many old reinforced concrete structures may be vulnerable to the effects of severe earthquakes. One suitable seismic retrofit solution is the installation of steel braces to increase the strength and ductility of a building. Steel bracings have some compelling advantages such as their comparatively low weight, their suitability for prefabrication, and the possibility of openings for utilities, access, and light. The braces are typically connected to steel frames that are fixed to the concrete structure using post‐installed concrete anchors along the perimeter. However, these framed steel braces are not without some disadvantages such as heavier steel usage and greater difficulties during the installation. Therefore, braces without steel frames appear to be an attractive alternative. In this study, braces were connected to gussets furnished with anchor brackets, which were fixed by means of a few post‐installed concrete anchors. The clear structural system and the increased utilization of the anchors allowed the anchorage to be designed precisely and economically. The use of buckling‐restrained braces (BRBs) provides additional benefits in comparison with conventional braces. BRBs improve the energy dissipation efficiency and allow the limitation of the brace force to be taken up by the highly stressed anchorage. Cyclic loading tests were conducted to investigate the seismic performance of BRBs connected with post‐installed anchors used to retrofit reinforced concrete frames. The tests showed that the proposed design method is feasible and increases strength as well as ductility to an adequate seismic performance level. Copyright © 2014 John Wiley & Sons, Ltd.     

Probabilistic seismic demand analysis of controlled steel moment‐resisting frame structures

This paper describes a proposed methodology, referred to as probabilistic seismic control analysis, for the development of probabilistic seismic demand curves for structures with supplemental control devices. The resulting curves may be used to determine the probability that any response measure, whether for a structure or control device, exceeds a pre‐determined allowable limit. This procedure couples conventional probabilistic seismic hazard analysis with non‐linear dynamic structural analyses to provide system specific information. This method is performed by evaluating the performance of specific controlled systems under seismic excitations using the SAC Phase II structures for the Los Angeles region, and three different control‐systems: (i) base isolation; (ii) linear viscous brace dampers; and (iii) active tendon braces. The use of a probabilistic format allows for consideration of structural response over a range of seismic hazards. The resulting annual hazard curves provide a basis for comparison between the different control strategies. Results for these curves indicate that no single control strategy is the most effective at all hazard levels. For example, at low return periods the viscous system has the lowest drift demands. However, at higher return periods, the isolation system becomes the most effective strategy. Copyright © 2002 John Wiley & Sons, Ltd.     

带耗能腋撑竖向不规则短肢剪力墙结构减震性能分析

在不影响建筑使用空间前提下,提出在抗侧构件不连续处设置耗能腋撑以改善竖向不规则结构抗震性能。以底部大空间短肢剪力墙结构为研究对象,利用大型通用有限元程序ETABS研究耗能器类型与场地土对耗能腋撑工作性能和竖向不规则结构受力性能的影响。研究表明,黏滞型耗能腋撑对文中分析模型各楼层地震反应有较好的控制效果,对转换层处层间位移角与层剪力最大值减幅最大,分别为40.14%和15.66%,对顶层加速度与基底剪力峰值的最大减幅分别为16.06%和23.57%,黏滞型耗能腋撑最大能耗散输入结构能量的42%,而黏弹型耗能腋撑对结构的控制效果不理想;当地震震级较大、震中距较小时,耗能腋撑对坚硬与软弱场地土的模型结构控制作用相差不大,减震位移比在转换层处达到最小值0.76;随着震级减小或震中距增大,耗能腋撑对该模型结构的控制作用随场地土变硬而逐渐增强,其减震位移比介于0.68～0.74之间。     

Optimal seismic design of moment‐resisting steel frames with hysteretic passive devices

The effectiveness of hysteretic passive devices to protect and mitigate the response of a structure under seismic loading is well established by both analytical and experimental research. Nevertheless, a systematic and well‐established methodology for the topological distribution and size of these devices in order to achieve a desired structural response performance does not exist. In this paper, a computational framework is proposed for the optimal distribution and design of yielding metallic buckling restrained braces (BRB) and/or friction dampers within steel moment‐resisting frames (MRF) for a given seismic environment. A Genetic Algorithm (GA) is used to solve the resulting discrete optimization problem. Specific examples involving two three‐story, four‐bay steel MRFs and a six‐story, three‐bay steel MRF retrofitted with yielding and/or friction braces are considered. The seismic environment consists of four synthetic ground motions representative of the west coast of the United States with 5% probability of exceedance in 50 years. Non‐linear time‐history analyses are employed to evaluate the potential designs. As a result of the evolutionary process, the optimal placement, strength and size of the dampers are obtained throughout the height of the steel MRF. Furthermore, the developed computational approach for seismic design based upon GAs provides an attractive procedure for design of MRFs with hysteretic passive dampers. Copyright © 2009 John Wiley & Sons, Ltd.     

建筑结构的屈曲约束支撑对其抗震加固性能的影响

当前方法采用伸臂桁架加固建筑结构时,未考虑建筑结构的屈曲约束支撑力的影响,伸臂桁架与建筑结构的连接不牢固,导致其对建筑结构的抗震加固性能较差。故此,深入分析建筑结构的屈曲约束支撑对其抗震加固性能的影响,设计建筑结构抗震加固方案,利用高强螺栓节点经由连接钢板实现屈曲约束支撑与建筑结构的铰接固定。分别从支撑变形同建筑结构层间位移的关系、建筑结构支撑承载力、多遇地震影响下屈曲约束支撑框架的位移验算,以及罕遇地震影响下屈曲约束支撑的弹塑性位移验算方面,分析屈曲约束支撑对建筑结构抗震加固性能影响。经实验分析得出,建筑结构加入屈曲约束支撑后第一扭转周期同第一平动周期的比值降低0.14,X、Y两个方向的砌体墙同建筑结构的刚度比值降低6.9、8.0,最大顶点位移值降低15.4 mm、29.3 mm,抗震加固性能大大提高。