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.     

Hybrid simulation of a zipper‐braced steel frame under earthquake excitation

Hybrid simulation is a testing methodology that combines laboratory and analytical simulation to evaluate seismic response of complex structural framing systems. One or more portions of the structure, which may be difficult to model numerically or have properties that have not been examined before, are tested in one or more laboratories, whereas the remainder of the structure is modeled in software using one or more computers. These separate portions are assembled such that combined dynamic response of the hybrid model to excitation is computed using a time‐stepping procedure. A hybrid simulation conducted to examine the seismic response of a type of steel concentrically braced frame, the suspended‐zipper‐braced frame, is presented. The hybrid simulation testing architecture, hybrid model, test setup, solution algorithm, and the seismic response of the suspended‐zipper‐braced frame hybrid model are discussed. Accuracy of this hybrid simulation is examined by comparing hybrid and computer‐only simulations and the errors are quantified using an energy‐based approach. This comparison indicates that the deployed hybrid simulation method can be used to accurately model the seismic response of a complex structural system such as the zipper‐braced frame. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic performance of hybrid ductile‐rocking braced frame system

A new hybrid ductile‐rocking seismic‐resistant design is proposed which consists of a code‐designed buckling‐restrained braced frame (BRBF) that yields along its height and also partially rocks on its foundation. The goal of this system is to cost‐effectively improve the performance of BRBFs, by reducing drift concentrations and residual deformations, while taking advantage of their large ductility and their reliable limit on seismic forces and accelerations along a building's height. A lock‐up device ensures that the full code‐compliant lateral strength can be achieved after a limited amount of column uplift, and supplemental energy dissipation elements are used to reduce the rocking response. This paper outlines the mechanics of the system and then presents analyses on rocking frames with both ductile and elastic braces in order to highlight the large higher mode demands on elastic rocking frames. A parametric study using nonlinear time‐history analysis of BRBF structures designed according to the proposed procedure for Los Angeles, California is then presented. This study investigates the system's seismic response and the effect of different energy dissipation element properties and allowable base rotation values before the lock‐up is engaged. Finally, the effect of vertical mass modeling on analysis results was investigated. These studies demonstrated that the hybrid ductile‐rocking system can in fact improve the global peak and residual deformation response as well as reduce brace damage. This enhanced performance could eliminate the need for expensive repairs or demolition that are otherwise to be expected for conventional ductile fixed base buildings that sustain severe damage.     

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.     

Steel buckling‐restrained braced frames with single and dual corner gusset connections: seismic tests and analyses

The design of a three‐story buckling‐restrained braced frame (BRBF) with a single‐diagonal sandwiched BRB and corner gusset was evaluated in cyclic tests of a one‐story, one‐bay BRBF subassembly and dynamic analyses of the frame subjected to earthquakes. The test focused on evaluating (1) the seismic performance of a sandwiched BRB installed in a frame, (2) the effects of free‐edge stiffeners and dual gusset configurations on the corner gusset behavior, (3) the frame and brace action forces in the corner gusset, and (4) the failure mode of the BRBF under the maximum considerable earthquake level. The subassembly frame performed well up to a drift of 2.5% with a maximum axial strain of 1.7% in the BRB. Without free‐edge stiffeners, the single corner gusset plate buckled at a significantly lower strength than that predicted by the specificationof American Institute of Steel Construction (2005). The buckling could be eliminated by using dual corner gusset plates similar in size to the single gusset plate. At low drifts, the frame action force on the corner gusset was of the same magnitude as the brace force. At high drifts, however, the frame action force significantly increased and caused weld fractures at column‐to‐gusset edges. Nonlinear time history analyses were performed on the three‐story BRBF to obtain seismic demands under both design and maximum considerable levels of earthquake loading. The analytical results confirmed that the BRB and corner gusset plate achieved peak drift under cyclic loading test. Copyright © 2011 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。     

Analytical prediction of seismic behaviour for concentrically-braced steel systems

This paper presents an analytical model for the inelastic response analysis of braced steel structures. A model is first presented for the behaviour of steel struts subjected to cyclic axial load, which combines the analytical formulation of plastic hinge behaviour with empirical formulas developed on the basis of experimental data. The brace is modelled as a pin-ended member, with a plastic hinge located at the midspan. Braces, with other end conditions, are handled using the effective length concept. Step-wise regression analysis is employed, to approximate the plastic conditions for the steel UC section. Verification of the brace model is performed on the basis of quasi-static analyses of individual struts and a one-bay one-storey X-braced steel frame. The comparison of analytical and experimental data has confirmed that the proposed brace model is able to accurately simulate the cyclic inelastic behaviour of steel braces and braced systems. A series of dynamic analyses has been performed on two-storey V- and X-braced frames to study the influence of brace slenderness ratio on the inelastic response, and to look at the redistribution of forces in the post-buckling range of behaviour of CBFs. Recommendations have been made as to the estimation of maximum storey drifts for concentrically-braced steel frames in major seismic event. © 1997 John Wiley & Sons, Ltd.     

A model to simulate special concentrically braced frames beyond brace fracture

Special concentrically braced frames (SCBFs) are commonly used as the lateral‐load resisting system in buildings. SCBFs primarily sustain large deformation demands through inelastic action in the brace, including compression buckling and tension yielding; secondary yielding may occur in the gusset plate and framing elements. The preferred failure mode is brace fracture. Yielding, buckling, and fracture behavior results in highly nonlinear behavior and accurate analytical modeling of these frames is required. Prior research has shown that continuum models are capable of this level of simulation. However, those models are not suitable for structural engineering practice. To enable the use of accurate yet practical nonlinear models, a research study was undertaken to investigate modeling parameters for line‐element models, which is a more practical modeling approach. This portion of the study focused on methods to predict brace fracture. A fracture modeling approach simulated the nonlinear, cyclic response of SCBFs by correlating onset of fracture to the maximum strain range in the brace. The model accounts for important brace design parameters including slenderness, compactness, and yield strength. Fracture data from over 40 tests was used to calibrate the model and included single‐brace component, single story frame, and full‐scale multistory frame specimens. The proposed fracture model is more accurate and simpler than other, previously proposed models. As a result, the proposed model is an ideal candidate for practical performance simulation of SCBFs. Copyright © 2012 John Wiley & Sons, Ltd.     

屈曲约束支撑钢框架结构影响因素的静力弹塑性分析

为检验抗侧刚度比和支撑布置方式等因素对具有不同总层数的屈曲约束支撑钢框架的抗震性能影响,借助SAP2000软件,探讨6层、12层、18层屈曲约束支撑钢框架结构在抗侧刚度比分别为1、2、3、4、5共五种工况及倒V型和单斜向两种支撑布置方式下的抗震性能。结果表明,屈曲约束支撑钢框架结构基底剪力-顶点位移曲线呈典型的双线性特征;随抗侧刚度比的增大,结构的层间位移角总体上呈降低趋势,基底剪力及支撑轴力增大,顶点水平位移变小,框架所分担的剪力降低;倒V型布置支撑较单斜向布置具有略大的基底剪力、谱加速度,较小的顶点位移、层位移、层间剪力和框架剪力分担率。分析表明,总体上来看,倒V型布置较单斜向布置时支撑框架结构具有略优的抗震性能;抗侧刚度比较支撑布置方式对支撑框架结构抗震性能的影响更为显著。     

Effect of non‐moment braced frame seismic deformations on buckling‐restrained brace end connection behavior: Theoretical analysis and subassemblage tests

In‐plane buckling‐restrained brace (BRB) end rotation induced by frame action is a commonly observed phenomenon in buckling‐restrained braced frames (BRBFs). However, its effect on BRB end connection behavior has not yet been clear. In this study, four BRB end deformation modes for quick determination of end rotational demand are proposed for non‐moment BRBF considering different BRB arrangements, installing story of BRBs, and boundary condition of corner gussets connected with column base. Key factors affecting BRB end rotation and flexural moments are examined theoretically by parametric analysis. Subassemblage tests of seven BRB specimens under horizontal cyclic loading were conducted by adopting two loading frames to impose the expected BRB end deformations. It shows that BRB end rotation subjected BRB ends to significant flexural moments, leading to premature yielding of BRB ends or even tendency of end zone buckling. The deformation modes, the flexural rigidity of BRB ends, and the initial geometric imperfections of BRBs were found to have significant influence on BRB end connection behavior. The triggering moment induced by BRB end rotation was the main contributor to end flexural moment. However, the moment amplification effect induced by flexure of BRB end zones became prominent especially for small flexural rigidity of BRB ends. Implications and future research needs for design of BRB end connections are provided finally based on the theoretical and experimental results. Copyright © 2015 John Wiley & Sons, Ltd.     

消能支撑框架结构的非线性分析

本文介绍了六榀钢筋混凝土支撑框架模型（两榀为普通支撑框架，另四榀为消能支撑框架）在低周反复荷载作用下的工作性能和试验结果；编制了非线性程序，对试验模型进行了计算分析，计算结果和试验实测值符合较好；另外还计算了两榀足尺消能支撑框架结构，研究不同的消能器滑移荷载对结构抗震能力的影响，结果表明消能支撑框架结构具有良好、稳定的抗震性能。     

不同支撑形式高强钢组合偏心支撑抗震性能研究

耗能梁段作为偏心支撑结构的耗能元件,在大震作用下通过弹塑性变形吸收地震能量,保护主体结构处于弹性受力状态。现行规范基于强度的设计理论,为了保证耗能梁段进入塑性或破坏,梁柱构件需要进行放大内力设计,导致截面过大,而且基于强度的设计方法很难保证结构的整体破坏状态。目前,抗震设计越来越重视基于性能的设计思想,该方法能够评估结构的弹塑性反应。对于高强钢组合偏心支撑,其中耗能梁段和支撑采用Q345钢,框架梁柱采用Q460或者Q690高强度钢材,高强钢不仅带来良好的经济效益,而且能够推广高强钢在抗震设防区的应用。利用基于性能设计方法设计了4种不同形式的高强钢组合偏心支撑钢框架,包括K形、Y形、V形和D形,考虑4层、8层、12层和16层的影响。通过Pushover分析和非线性时程分析评估该结构的抗震性能,研究结果表明:4种形式的高强钢组合偏心支撑钢框架具有类似的抗震性能,在罕遇地震作用下,几乎所有耗能梁段均参与耗能,而且层间侧移与耗能梁段转角沿高度分布较为均匀。其中:D形偏心支撑具有最大的抗侧刚度,但延性较差,而Y形偏心支撑的抗侧刚度最弱,但延性最佳。     

Seismic design and test of gusset connections for buckling‐restrained braced frames

The corner gusset plates in a steel braced frame can be subjected to forces not only from the brace but also from the effects of the frame actions. In this study, several finite element models are constructed to analyze the gusset‐to‐beam and gusset‐to‐column interface forces. It is found that the frame actions affect the gusset interface force distributions significantly. A simplified strut model to represent the gusset plate is adopted to evaluate the frame action forces. In addition, the generalized uniform force method is adopted as it provides more freedom for designers to configure the gusset plate shapes than using the uniform force method. In this paper, a performance‐based design method is proposed. The gusset interface force demands take into account the combined effect of the brace maximum axial force capacity and the peak beam shear possibly developed in the frame. The specimen design and key results of a series of full‐scale three‐story buckling‐restrained braced frame (BRBF) hybrid tests are discussed. The gusset interface cracks observed at inter‐story drift greater than 0.03 radians can be well predicted by using the proposed design method. The BRBF tests and analyses confirm that the proposed design method is reasonable. The effectiveness of varying the width of gusset edge stiffeners in reducing the gusset tip stress concentrations is also investigated. This paper concludes with recommendations for the seismic design of BRBF corner gusset plates. Copyright © 2013 John Wiley & Sons, Ltd.     

Using model error in response history analysis to evaluate component calibration methods

This research is part of a larger effort to better understand and quantify the epistemic model uncertainty in dynamic response-history simulations. This paper focuses on how calibration methods influence model uncertainty. Structural models in earthquake engineering are typically built up from independently calibrated component models. During component calibration, engineers often use experimental component response under quasi-static loading to find parameters that minimize the error in structural response under dynamic loading. Since the calibration and the simulation environments are different, if a calibration method wants to provide optimal parameters for simulation, it has to focus on features of the component response that are important from the perspective of global structural behavior. Relevance describes how efficiently a calibration method can focus on such important features. A framework of virtual experiments and a methodology is proposed to evaluate the influence of calibration relevance on model error in simulations. The evaluation is demonstrated through a case study with buckling-restrained braced frames (BRBF). Two calibration methods are compared in the case study. The first, highly relevant calibration method is based on stiffness and hardening characteristics of braces; the second, less relevant calibration method is based on the axial force response of braces. The highly relevant calibration method consistently identified the preferable parameter sets. In contrast, the less relevant calibration method showed poor to mediocre performance. The framework and methodology presented here are not limited to BRBF. They have the potential to facilitate and systematize the improvement of component-model calibration methods for any structural system.     

Numerical and experimental investigations on inelastic cyclic performance of mid‐span gusset plate connections

The design and detailing of gusset plate connections greatly influence the seismic performance of a special concentrically braced frame (SCBF). Recently, a balanced design approach has been proposed in order to develop significant inelastic deformation from multiple yield mechanisms and to delay the failure of connections of SCBF system. Although extensive studies have been conducted on the corner gusset plate connections of SCBFs, research on the detailing of mid‐span beam gusset plates is rather limited. This study aims at investigating the required free length for the detailing of the mid‐span gusset plates with different brace slenderness ratios. A nonlinear finite element analysis has been conducted for a braced frame with 4 different values of linear clearance in the mid‐span gusset plates and 2 values of brace slenderness ratios. In all simulation models, the corner gusset plates have been designed using balanced design approach and detailed using an elliptical clearance of 8 times the gusset plate thickness. An experimental study has also been conducted on 2 gusset plate sub‐assemblages having similar brace slenderness ratio but with 2 different values of linear clearance in the middle gusset plates. The lateral drift capacity corresponding to the brace fracture and the level of damage are found to be dependent on the detailing of the gusset plates. Based on the results of numerical and experimental studies, the required free length has been recommended for the detailing of middle gusset plates of SCBFs of different brace slenderness ratios.     

A unified approach for the design of high ductility steel frames with concentric braces in the framework of Eurocode 8

Eurocode 8 (EC8) stipulates design methods for frames with diagonal braces and for chevron braced frames, which differ as regards the numerical model adopted, the value of the behavior factor q and the estimation of the lateral strength provided by braces. Instead, in this paper, the use of the same design method is suggested for both types of concentrically braced frames. The design method is a generalization of the one proposed for chevron braced frames in a previous study. A numerical investigation is conducted to assess the reliability of this design method. A set of concentrically braced frames is designed according to the EC8 and proposed design methods. The seismic response of these frames is determined by nonlinear dynamic analysis. Finally, it is demonstrated that the proposed design method is equivalent to those provided by EC8, because it can ensure the same level of structural safety which would be expected when using EC8. Copyright © 2013 John Wiley & Sons, Ltd.     

Modified seismic design of concentrically braced frames considering flexural demand on columns

Special concentrically braced frames (SCBFs) are considered as one of the most economical and effective lateral force‐resisting systems in structures located in the regions of high seismicity. Steel braces in a braced frame undergo large axial deformations in tension and compression to dissipate the seismic energy. However, past studies have shown that SCBFs exhibit the soft‐story hinge mechanisms and unpredictable failure patterns under earthquake loading conditions. These inelastic responses along with the use of continuous structural sections as columns over consecutive floors induce flexural demand that is not considered in the current design practice. In this study, the evaluation of seismic performance of nine SCBFs designed as per the current practice has been carried out for three different story heights (i.e., three‐story, six‐story, and nine‐story) and three types of brace configurations (namely, chevron, split X, and single X). Three additional design techniques are also explored based on (i) the inclusion of column moments in the design; (ii) the theory of formation of plastic hinges; and (iii) the design of braces considering the forces computed at their post‐buckled stages. Nonlinear dynamic analyses of these study frames have been evaluated numerically using a computer software Perform‐3D for a suite of 40 ground motions representing the design basis earthquake and maximum considered earthquake hazard levels. Analyses results showed that the SCBFs designed as per the modified procedures achieved the desired performance objectives without the formation of soft‐story mechanism. Copyright © 2017 John Wiley & Sons, Ltd.     

Probabilistic seismic performance evaluation of SMA-braced steel frames considering SMA brace failure

This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.     

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.