BRBF response modification factor

In this paper, overstrength, ductility and response modification factor of Buckling Restrained Braced frames were evaluated. To do so, buildings with various stories and different bracing configuration including diagonal, split X, chevron (V and Inverted V) bracings were considered. Static pushover analysis, nonlinear incremental dynamic analysis and linear dynamic analysis have been performed using Opensees software. The effects of some parameters influencing response modification factor, including the height of the building and the type of bracing system, were investigated. In this article seismic response modification factor for each of bracing systems has been determined separately and tentative values of 8.35 and 12 has been suggested for ultimate limit state and allowable stress design methods.     

Bracing systems for seismic retrofitting of steel frames

The present study assesses the seismic performance of steel moment resisting frames (MRFs) retrofitted with different bracing systems. Three structural configurations were utilized: special concentrically braces (SCBFs), buckling-restrained braces (BRBFs) and mega-braces (MBFs). A 9-storey steel perimeter MRF was designed with lateral stiffness insufficient to satisfy code drift limitations in zones with high seismic hazard. The frame was then retrofitted with SCBFs, BRBFs and MBFs. Inelastic time-history analyses were carried out to assess the structural performance under earthquake ground motions. Local (member rotations) and global (interstorey and roof drifts) deformations were employed to compare the inelastic response of the retrofitted frames. It is shown that MBFs are the most cost-effective bracing systems. Maximum storey drifts of MBFs are 70% lower than MRFs and about 50% lower than SCBFs. The lateral drift reductions are, however, function of the characteristics of earthquake ground motions, especially frequency content. Configurations with buckling-restrained mega-braces possess seismic performance marginally superior to MBFs despite their greater weight. The amount of steel for structural elements and their connections in configurations with mega-braces is 20% lower than in SCBFs. This reduces the cost of construction and renders MBFs attractive for seismic retrofitting applications.     

基于屈服点谱法的中心支撑钢框架抗震性态评估

屈服点谱(Yield Point Spectra,YPS)是以位移-加速度表述的反应谱形式。YPS可以用于对现有结构进行抗震评估,确定结构在给定地震作用下的峰值位移和延性。本文按照我国设计规范分别设计了6层、9层、12层3个人字形中心支撑钢框架结构,利用YPS对3个结构进行非线性静力分析,得到结构在设防地震和罕遇地震下的峰值位移和层间位移角,并与SAP2000动力时程分析得到的结果进行对比,评估人字形中心支撑钢框架在设防地震和罕遇地震下的抗震性态,评价了YPS方法用于中心支撑钢框架抗震性态评估的可靠性。     

低延性中心支撑钢框架结构振动台试验

中心支撑钢框架结构是一种典型的双重抗侧力体系,强震作用下支撑失效会引起结构承载力和刚度的折减,支撑失效后,结构剩余部分作为储备体系能够继续承担地震作用。为深入了解低延性中心支撑钢框架结构在地震作用下的非线性反应,研究在支撑失效后结构储备体系的抗震性能,开展了3层中心支撑钢框架结构模型的振动台试验。模型结构为3榀2跨结构,中间榀布置一跨低延性人字形中心支撑(截面宽厚比超出我国规范限值),模型长度缩尺比为1∶6. 5,分别采用硬土、软土场地的地震波单向激励,峰值加速度逐级增加。结构在7度罕遇地震作用下发生底层支撑失效,储备体系避开了硬土场地地震波的卓越周期,加载至超过9度罕遇地震后依然未出现明显损伤。储备体系对软土场地地震波(宁河波)更为敏感,在8度罕遇地震作用下濒临倒塌。结构2、3层支撑始终未发生屈曲和破坏。研究结果表明,当储备体系设计合理时,低延性中心支撑钢框架结构具有良好的抗震性能和抗倒塌能力。     

Progressive collapse analysis of seismically designed steel braced frames

The progressive collapse resistance of seismically designed steel braced frames is investigated using validated computational simulation models. Two types of braced systems are considered: namely, special concentrically braced frames and eccentrically braced frames. The study is conducted on previously designed 10-story prototype buildings by applying the alternate path method. In this methodology, critical columns and adjacent braces, if present, are instantaneously removed from an analysis model and the ability of the model to successfully absorb member loss is investigated. Member removal in this manner is intended to represent a situation where an extreme event or abnormal load destroys the member. The simulation results show that while both systems benefit from placement of the seismically designed frames on the perimeter of the building, the eccentrically braced frame is less vulnerable to progressive collapse than the special concentrically braced frame. Improvement in behavior is due to improved system and member layouts in the former compared to the latter rather than the use of more stringent seismic detailing.     

Y型偏心支撑钢框架受力性能有限元分析

建立了四种Y型偏心支撑钢框架有限元模型,对平面模型框架和三种空间模型框架进行了单向加载和循环加载试验,并对比分析了模型框架的屈服强度、极限承载力、侧向刚度、延性和耗能能力等方面的受力性能差异,得到的结果为工程设计提供了参考。     

A balanced design procedure for special concentrically braced frame connections

Concentrically braced frames (CBFs) are stiff, strong structures that are suitable for resisting large lateral loads. Special CBFs (SCBF) are used for seismic design and are designed and detailed to sustain relatively large inelastic deformations without significant deterioration in resistance. Current AISC Seismic Design Provisions aim to ensure the brace sustains the required inelastic action, but recent research showed that current SCBF design requirements lead to variable seismic performance, unintended failure modes, and limited deformation capacity. To improve the seismic response of SCBFs, a balanced design procedure was proposed. The premise of the design methodology is to balance the primary yield mechanism, brace buckling and yielding, with other, complementary ductile yielding mechanisms, such as gusset plate yielding. This balance process maximizes ductile yielding in the frame thereby maximizing the drift capacity of the frame. Further, the undesirable failure modes are balanced with the yield mechanisms and the preferred failure mode, brace fracture, to ensure that the frame fails in the desired manner. To achieve the objectives of the design methodology namely maximum drift capacity, and adherence to a desired yield and failure hierarchy, rational resistance checks and appropriate balance factors (β factors) are used to balance each yield mechanism and failure mode. These factors were developed, validated, and refined using the measured results from an extensive test program. An SCBF connection design example to illustrate the application of the balanced design method and to demonstrate differences from the current AISC design method is presented in an appendix.     

An investigation on the accuracy of pushover analysis for estimating the seismic deformation of braced steel frames

This paper investigates the potentialities of the pushover analysis to estimate the seismic deformation demands of concentrically braced steel frames. Reliability of the pushover analysis has been verified by conducting nonlinear dynamic analysis on 5, 10 and 15 story frames subjected to 15 synthetic earthquake records representing a design spectrum. It is shown that pushover analysis with predetermined lateral load pattern provides questionable estimates of inter-story drift. To overcome this inadequacy, a simplified analytical model for seismic response prediction of concentrically braced frames is proposed. In this approach, a multistory frame is reduced to an equivalent shear-building model by performing a pushover analysis. A conventional shear-building model has been modified by introducing supplementary springs to account for flexural displacements in addition to shear displacements. It is shown that modified shear-building models have a better estimation of the nonlinear dynamic response of real framed structures compared to nonlinear static procedures.     

Cost-benefit evaluation of self-centring concentrically braced frames considering uncertainties

Self-centring concentrically braced frame (SC-CBF) systems have been developed to reduce post-earthquake damages in braced frames. However, due to special details required by the SC-CBF system, the construction cost of an SC-CBF is expected to be higher than that of a conventional CBF. In this study, the seismic performance and economic effectiveness of two prototype buildings utilising SC-CBFs are assessed and compared with buildings utilising conventional CBFs by evaluating the annual probabilities of exceeding various damage levels, expected annual losses, life cycle costs (under seismic hazard) and economic benefit of using SC-CBFs considering prevailing uncertainties. The results of this study show that the SC-CBF buildings have lower drift-related losses but higher acceleration-related losses. The SC-CBF is found to be beneficial for the 6-storey configuration, but not for the 10-storey configuration. For the 6-storey buildings studied here, if the construction cost of the SC-CBF is assumed to be twice that of the CBF, the pay-off time is expected to be 12 to 21 years, with a probability of 68%, considering the uncertainties in the demand, capacity, loss parameters and initial construction costs. Finally, appropriate probabilistic engineering demand parameter model formulation is critical for generating accurate loss analysis results.     

偏心支撑钢框架的设计

简述了偏心支撑钢框架结构的工作原理及特点,介绍了偏心支撑钢框架的设计计算方法,其中重点介绍了各杆件的内力计算：耗能梁段设计、非耗能梁段设计、支撑设计和框架柱设计,为工程设计人员提供了指导。     

Recent research on eccentrically braced frames

Recent research developments on eccentrically braced steel frames for seismic design are reviewed. The emphasis is placed on the design of links, which are short sections of beams between columns and braces, and similar elements at eccentric joints. The review includes some highlights of the latest experiments with one-third scale models employing different eccentric bracing schemes, an updated classification of links, and special design requirements for different types of links. Some results are given on recent cyclic tests of full-size links.     

屈曲约束支撑混凝土框架结构地震反应折减系数研究

提出了一种运用静力推覆和FEMA440等效线性法求解结构体系地震反应折减系数的直接方法,运用此方法分析了按同一剪重比设计的3层、6层、9层的屈曲约束支撑混凝土框架地震反应折减系数,并用时程分析对结果加以验证。结果表明：运用此方法求解R值能够避免了繁琐的试算过程,具有足够的精度和保证率,屈曲约束支撑混凝土框架R值相比普通混凝土框架有明显提高。     

Design and seismic response of tall chevron panel buckling‐restrained braced steel frames

The numerical analysis of the seismic performance for tall chevron panel buckling‐restrained braced steel frames (PBRBFs) under small and strong earthquake excitations has been carried out to investigate a capacity design procedure for chevron PBRBFs and to examine the effects of axial strength distribution of braces along the height of buildings, vertical supports of braces for the braced beams and the overstrength of braces on the seismic response of PBRBFs. It revealed that the chevron braces that remained elastic can actually provide the vertical supports for the braced beams. Under severe earthquake excitations, the vertical supports deteriorated greatly after braces yielding. The PBRBFs designed by omitting vertical supports of braces for the braced beams and considering the overstrength of braces exhibited superior performance with smaller plastic deformations for braced beams and reduction in ductility demands for panel buckling‐restrained braces (PBRBs) as compared with the others. The distribution of yielding for PBRBs in 10‐story buildings verified that the participation from the higher modes is not very remarkable and that the capacity design based on the first‐mode response can be considered for multistory PBRBFs. Moreover, on the basis of the analysis results of the 30‐story PBRBF, the participation of the higher modes should be taken into account for high‐rise PBRBFs. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic response of stainless steel braced frames

The present paper investigates the feasibility of the application of stainless steel (SS) in the seismic design of braced frames, either concentrically (CBFs) or eccentrically (EBFs) braced. A sample of regular multi-storey CBFs and EBFs was designed in compliance with modern seismic standards based on capacity-design rules. The results of pushover and inelastic response history analyses demonstrate that systems employing SSs exhibit enhanced plastic deformations and excellent energy absorbing capacity with respect to mild steel braced frames. The augmented strain hardening of SS, which is nearly twice that of carbon steels, is beneficial to prevent local buckling in steel members, especially those subjected to high axial compression. The performed analyses also demonstrate that in CBFs with SS braces and columns the increase in overstrength is about 40% with respect to the configuration in mild steel. For EBFs, the use of SS in the diagonals or in braces and links increases the global overstrength of the lateral resisting system by 20%. When the EBFs employ braces and columns in SS the increase can be as high as 50%.     

Equivalent viscous damping in direct displacement‐based design of steel braced reinforced concrete frames

Performance‐based design method, particularly direct displacement‐based design (DDBD) method, has been widely used for seismic design of structures. Estimation of equivalent viscous damping factor used to characterize the substitute structure for different structural systems is a dominant parameter in this design methodology. In this paper, results of experimental and numerical investigations performed for estimating the equivalent viscous damping in DDBD procedure of two lateral resistance systems, moment frames and braced moment frames, are presented. For these investigations, cyclic loading tests are conducted on scaled moment resisting frames with and without bracing. The experimental results are also used to calibrate full‐scale numerical models. A numerical investigation is then conducted on a set of analytical moment resisting frames with and without bracing. The equivalent viscous damping and ductility of each analytical model are calculated from hysteretic responses. On the basis of analytical results, new equations are proposed for equivalent viscous damping as a function of ductility for reinforced concrete and steel braced reinforced concrete frames. As a result, the new equation is used in direct displacement‐based design of a steel braced reinforced concrete frame. Copyright © 2012 John Wiley & Sons, Ltd.     

Fundamental periods of steel eccentrically braced frames

This paper describes formulation of a hand method that can be used to estimate the computed fundamental periods of vibration of building structures in general and steel eccentrically braced frames (EBFs) in particular. The developed method uses the Rayleigh's method as a basis and utilizes the roof drift ratio (RD_R) under seismic forces as a parameter. To obtain RD_R, more than 4000 EBFs were designed by considering the seismic hazard, number of stories, braced bay width and link length to bay width ratio as prime variables. A model was developed to estimate RD_R, which depends on the rigid plastic deformation mechanism for a typical EBF. The method was verified using design data produced as a part of this work as well as data published in literature. The verifications indicate that the proposed formulation is capable of providing acceptable estimates of the computed period. When compared with existing empirical period–height relationships, the proposed formulation offers closer estimates with reduced scatter. The method was further refined to derive new period–height relationships for two different seismicity regions. The accuracy of the relationship for high seismic regions was verified using measured periods of EBF buildings. Copyright © 2014 John Wiley & Sons, Ltd.     

钢框架抗震改造的支撑系统研究

评估了采用不同支撑系统改造的抗弯钢框架的抗震性能。共采用3种结构形式:中心支撑框架、防屈曲支撑框架、巨型支撑框架。设计了一横向刚度不足的9层钢框架,满足规范对高地震灾害区域结构的侧移要求。用中心支撑、防屈曲支撑和巨型支撑改造框架。进行非弹性时程分析,评估地震作用下的结构性能。以局部变形(杆件转角)和整体变形(层间及屋顶侧移)为参数,比较改造框架非弹性性能的不同。结果表明:巨型支撑框架是最有效率的支撑系统,其最大层间侧移比抗弯框架低70%,比中心支撑框架低50%。侧移的减小量与地震特性有关,尤其是频率。防屈曲支撑的抗震性能仅稍优于巨型支撑框架,但其总质量更大。巨型支撑框架的杆件和节点用钢量比同心支撑框架低20%,既可降低费用又具有抗震优势。     

Y型偏心支撑钢框架倒塌储备能力分析

为了评估Y型偏心支撑钢框架结构的倒塌储备能力,提出了一种针对于Y型偏心支撑钢框架结构的倒塌判定标准,并利用这个标准对不同设防烈度和不同层数的4个算例进行了IDA分析,得到了4个算例的倒塌储备系数和倒塌概率曲线.分析结果表明：相同条件按9度设计的Y型偏心支撑结构比按8度（0.2g）设计的结构倒塌储备能力弱,且层数越高其倒塌储备能力越弱.     

Stochastic optimisation of buckling restrained braced frames under seismic loading

A stochastic optimisation procedure is proposed for the design of low- and mid-rise buckling restrained braced frames subject to seismic loading. The seismic excitation is represented as a zero-mean nonstationary filtered white noise. The Bouc–Wen model is chosen to represent the hysteretic behaviour of the buckling restrained braces. The equivalent linearisation method is employed to determine the second-order statistics of structural responses from the non-linear system. Three seismic intensity levels are considered in this study, which are associated to earthquakes with different probability of occurrence during the building’s lifecycle. It was observed that the optimal design that minimises the maximum ductility demand produces a more uniform distribution of energy dissipation and avoids soft-storey mechanisms; therefore, this design objective is considered to be a more reasonable optimisation objective for the design of buckling restrained braced frames. For higher rise structures, buckling restrained braces may experience over-dimensioning in the top stories, which means that dissipation will not occur. Thus, an upper bound constraint for the stiffness design of the buckling restrained braces is taken into account.     

钢框架抗震改造的支撑系统研究

评估了不同支撑系统改造的抗弯钢框架的抗震性能。采用3种结构形式:中心支撑框架、防屈曲支撑框架和巨型支撑框架。设计了一横向刚度不足的9层钢框架,满足规范对高地震灾害区域结构的侧移要求。用中心支撑、防屈曲支撑和巨型支撑改造框架,进行非弹性时程分析,评估地震作用下的结构性能。以局部变形(杆件转角)和整体变形(层间及屋顶侧移)为参数,比较改造框架非弹性性能的不同。结果表明:巨型支撑框架是最有效率的支撑系统,其最大层间侧移比抗弯框架低70%,比中心支撑框架低50%。侧移的减小量与地震特性有关,尤其是频率。防屈曲支撑的抗震性能仅稍优于巨型支撑框架,但其总质量更大。巨型支撑框架的杆件和节点用钢量比中心支撑框架低20%,既降低了费用又体现了抗震优势。