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 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.     

A design procedure for suspended zipper‐braced frames in the framework of Eurocode 8

In the recent past, suspended zipper‐braced frames were proposed to avoid one‐storey collapse mechanisms and dynamic instability under severe ground motions. In this paper, the design procedure suggested by Yang et al. is first slightly modified to conform to the design approach and capacity design rules stipulated in Eurocode 8 for concentrically braced frames. The procedure is applied to a set of suspended zipper‐braced frames with different number of storeys and founded on either soft or rock soil. The structural response of these frames is analysed to highlight qualities and deficiencies and to assess the critics reported by other researchers with regard to the design procedure by Yang et al. Then, improvements are proposed to this procedure to enhance the energy dissipation of the chevron braces and the response of the structural system as well. The effectiveness of the design proposals is evaluated by incremental dynamic analysis on structures with different geometric properties, gravity loads and soil of foundation. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

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.     

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。     

Proposal of design rules for ductile X-CBFS in the framework of EUROCODE 8

Cross concentrically braced frames (X-CBFs) are commonly used as primary seismic resisting system, owing to their large lateral stiffness, simplicity of design, and relatively low constructional cost. Current EN 1998-1 provides design rules theoretically aiming at developing ductile global plastic mechanism, namely enforcing plastic deformations in the diagonal members, while the remaining structural members and connections should elastically behave. However, as widely demonstrated by many existing studies, the design and the corresponding seismic performance of EC8-compliant X-CBFs are generally affected by several criticisms, eg, difficulties in sizing of diagonal members, massive and non-economical structures, and poor seismic behavior. In light of these considerations, the research activity presented in this paper is addressed to revise the design rules and requirements given EN 1998-1 for X-CBFs to simplify the design process and to improve the ductility and the dissipative capacity of this structural system. Hence, design rules are proposed for the next version of EN 1998-1 and numerically validated by means of nonlinear dynamic analyses.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.     

Fundamental periods of steel concentrically braced frames designed to Eurocode 8

A two‐phase research program has been undertaken to investigate fundamental natural periods of concentrically braced frames (CBFs) designed according to Eurocode 8 (EC8). In the first phase of the program, over 83,700 buildings were designed, and the accuracy of the lower bound expressions given in well‐known design specifications was evaluated. The results indicated that the lower bound expressions given in EC8 and National Building Code of Canada (NBCC) are acceptable. Although all structures had periods longer than the ones estimated by the EC8 expression, a few structures had shorter periods than the ones estimated by the NBCC expression. In general, the lower bound expressions given in EC8 and NBCC were found to provide over conservative estimates for most cases. In the second phase of the program, a simple hand method was developed to estimate the fundamental natural periods of CBFs designed to EC8. This method requires the use of inelastic top story drift ratio as a parameter to quantify stiffness characteristics. The drift ratios were extracted from the design pool developed as a part of the first phase and represented by simple mathematical relationships. Evaluation of the proposed method indicated that the method is accurate in providing estimates of the fundamental period. To safeguard against providing unconservative estimates, the method was modified to arrive at a new lower bound expression, which significantly improves the estimates compared with the ones provided by the existing expressions. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic buckling of braces in concentrically braced frames

Axially loaded members might experience compressive forces above their static buckling capacity because of dynamic buckling under rapid shortening. Although the subject is studied in the context of engineering mechanics, it has not been thoroughly investigated in the field of earthquake engineering. Such dynamic overshoots in the compressive capacity can also be observed for braces of concentrically braced frames (CBFs) during earthquakes. Consequently, a comprehensive investigation is conducted in this study regarding the effects of dynamic buckling of braces on the seismic behavior of steel CBFs. After providing a theoretical background, recent dynamic experiments on braces and CBFs are simulated and discussed to investigate the occurrence of dynamic overshoot during these tests. Eight archetype CBFs are then designed, modeled, and subjected to a large set of ground motions to provide a quantified insight on the frequency and anticipated level of dynamic overshoot in the compressive capacity of braces during earthquakes. Results of a total of 1600 nonlinear time history analyses revealed that dynamic overshoots occur frequently in braces and affect the behavior of CBFs notably. Considerable increases are recorded in forces transmitted to other members of CBFs as a consequence of such dynamic overshoots. Importance of incorporating these dynamic overshoots in the capacity design procedure of columns, beams, and gusset plates is highlighted. Furthermore, results of a parametric study are presented and summarized in the form of a simple formula that can be used as a guide for estimating the level of dynamic overshoot.     

Seismic reliability of traditional and innovative concentrically braced frames

Structural engineering problems are always affected by many sources of uncertainty, such as aleatory of material properties, applied loads and earthquake intensity, therefore, seismic assessment of structures should be based on probabilistic methods. Since PBSD (Performance‐based Seismic Design) philosophy was formulated, many researches have been conducted in this field in order to develop simple and accurate procedures for evaluating structural reliability. An important contribution has been provided by Jalayer and Cornell, who have developed a closed‐form expression to evaluate the mean annual frequency of exceeding a defined limit state. In this paper, by assuming the record‐to‐record variability as the only source of uncertainty, the seismic reliability of concentrically braced frames designed according to traditional and innovative methodologies is investigated, and a comparison between their performances is presented. In particular, two design methodologies have been applied: Eurocode 8 provisions and a new design methodology based on a rigorous application of ‘capacity design’ criteria. The innovative reduced section solution strategy, based on the reduction of cross sections at bracing member ends, has also been analysed. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic retrofitting of braced frame buildings by RC rocking walls and viscous dampers

A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.     

Development of a ten-element hybrid simulation platform and an adjustable yielding brace for performance evaluation of multi-story braced frames subjected to earthquakes

This paper presents a ten-element hybrid (experimental-numerical) simulation platform, referred to as UT10, which was developed for running hybrid simulations of braced frames with up to ten large-capacity physical brace specimens. This paper presents the details of the development of different components of UT10 and an adjustable yielding brace (AYB) specimen, which was designed to perform hybrid simulations with UT10. As the first application of UT10, a five-story buckling-restrained braced frame and a special concentrically braced frame (BRBF and SCBF) were designed and tested with AYB specimens and buckling specimens representing the braces. Cyclic tests of the AYB, one- and three-element hybrid simulations of the BRBF, and four-element hybrid simulations of the SCBF inside the UT10 confirmed the functionality of UT10 for running hybrid simulations on multiple specimens. The tests also indicated that AYB was capable of producing a stable hysteretic response with characteristics similar to BRBs. Comparison of the results of the hybrid simulations of the BRBF and SCBF with their fully numerical models showed that the modeling inaccuracies of the yielding braces could potentially affect the global response of the multi-story braced frames further emphasizing the need for experimental calibration or hybrid simulation for achieving more accurate response predictions. UT10 provides a simple and reconfigurable platform that can be used to achieve a realistic understanding of the seismic response of multi-story frames with yielding braces, distinguish their modeling limitations, and improve different modeling techniques available for their seismic response prediction.     

直接基于位移设计的高强钢组合K形偏心支撑钢框架的抗震性能研究

K形高强钢组合偏心支撑(K-HSS-EBF)是指耗能连梁和支撑采用Q345钢,而框架梁、框架柱采用高强度钢(如Q460)。为研究其在罕遇地震作用下的抗震性能,在试验研究的基础上,采用直接基于位移的抗震设计方法设计了5层、8层和12层算例,分别进行静力推覆分析和动力弹塑性分析,研究高强钢组合偏心支撑钢框架在罕遇地震作用下层间侧移分布和破坏模式。研究结果表明:直接基于位移的抗震设计方法设计的算例在罕遇地震作用下,结构的层间侧移满足我国现行抗震规范的要求,结构呈理想的渐进式梁铰屈服机构,并证明该设计方法的合理性和可靠性。     

Evaluation of the response modification coefficient and collapse potential of special concentrically braced frames

Special concentrically braced frames (SCBFs) are commonly used for seismic design of buildings. Their large elastic stiffness and strength efficiently sustains the seismic demands during smaller, more frequent earthquakes. During large, infrequent earthquakes, SCBFs exhibit highly nonlinear behavior due to brace buckling and yielding and the inelastic behavior induced by secondary deformation of the framing system. These response modes reduce the system demands relative to an elastic system without supplemental damping using a response modification coefficient, commonly termed the R factor. More recently, procedures put forth in FEMAP695 have been made to quantify the R factor through a formalized procedure that accounts for collapse potential. The primary objective of the research in this paper was to evaluate the approach for SCBFs. An improved model for SCBFs that permits simulation of brace fracture was used to conduct response history analyses. A series of three‐story, nine‐story and 20‐story SCBFs were designed and evaluated. Initially, the FEMAP695 method was conducted to estimate collapse and the corresponding R factor. An alternate procedure for scaling the multiple acceleration records to the seismic design hazard was also evaluated. The results show significant variation between the two methods. Of the three variations of buildings studied, the largest vulnerability was identified for the three‐story building. To achieve a consistent margin of safety against collapse, a significantly lower R factor is required for the low‐rise SCBFs (three‐story), whereas the mid‐rise and high‐rise SCBFs (nine‐story and 20‐story) may continue to use the current value of 6, as provided in ASCE‐07. Copyright © 2013 John Wiley & Sons, Ltd.     

基于中美抗震设计规范的双向水平地震效应组合方法的有效性评估

在地震来临时,一般假设建筑结构同时受到两个正交水平方向分量与一个竖向分量的地震动作用。双向水平地震效应组合方法用于估计两个正交水平分量地震动同时作用时结构的内力效应。本文主要对我国与美国抗震设计规范中规定使用的平方和开平方根（SRSS）方法与百分比组合方法的有效性进行了评估。首先,对比了我国与美国规范在考虑双向水平地震效应时的适用情况及相关规定上的异同。以一4层中心支撑-框架结构为工程案例,考虑两国规范在适用情况上的规定,设置了三个结构布置方案。对三个结构布置方案建立有限元模型,选取22组地震动,开展了动力时程分析。提出了针对SRSS方法与百分比组合方法的评估指标,基于时程分析结果,发展了双向水平地震效应组合的概率性评估方法。评估结果表明:SRSS方法与百分比组合方法用于平面扭转不规则结构的设计较为保守。在简化组合规则的适用条件上,美国规范对平面扭转不规则结构不进行考虑有一定的合理性。建议我国规范对中心支撑-框架结构中含双向受压柱的设计要求考虑双向水平地震效应组合。     

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.     

Theory of plastic mechanism control for MRF–CBF dual systems and its validation

In this paper the theory of plastic mechanism control is presented for moment resisting frame–concentrically braced frames dual systems, i.e. for structural systems combined by moment resisting frames and concentrically braced frames. It is aimed at the design of structures failing in global mode, i.e. whose collapse mechanism is characterised by the yielding of all the tensile diagonals and the occurrence of buckling in the compressed ones, and by plastic hinge formation at all the beam ends and at the base of first storey columns. The proposed methodology is based on the application of the kinematic theorem of plastic collapse, by imposing that the global mechanism equilibrium curve has to lie below all the other equilibrium curves corresponding to undesired mechanisms. The practical application of the design methodology is illustrated by means of a worked example. In addition, the results of a non-linear static pushover and dynamic analyses of the designed structure are also discussed in order to demonstrate the effectiveness of the proposed design procedure.     

Probabilistic estimate of seismic response design values of RC frames

Probabilistically controlled design values of the nonlinear seismic response of reinforced concrete frames are obtained using a method previously proposed by the authors. The method allows to calculate conservative design values characterized by a predefined non‐exceedance probability, using a limited number of spectrum‐fitting generated accelerograms. Herein the method is applied to elastic‐strain hardening single degree of freedom systems representative of RC framed structures and is then assessed with reference to four reinforced concrete model frames designed according to EC8. The frames are characterized by different natural periods and aspect ratios. The results, compared with those obtained applying current EC8 recommendations, show the effectiveness of the proposed method. EC8 provides for design values of the seismic response of a structure with a nonlinear behavior computed as the mean value of the responses to seven accelerograms or as the maximum value of the responses to three accelerograms. These two criteria lead to design values characterized by very different and uncontrolled non‐exceedance probability levels, while the proposed method allows the analyst to directly control the non‐exceedance probability level of the calculated design values. Copyright © 2009 John Wiley & Sons, Ltd.