Evaluating response modification factors of concentrically braced steel frames

Response modification factor is one of the seismic design parameters to consider nonlinear performance of building structures during strong earthquake. Relying on this, many seismic design codes led to reduce loads. The present paper tries to evaluate the response modification factors of conventional concentric braced frames (CBFs) as well as buckling restrained braced frames (BRBFs). Since, the response modification factor depends on ductility and overstrength, the static nonlinear analysis has been performed on building models including single and double bracing bays, multi-floors and different brace configurations (chevron V, invert V and X bracing). The CBFs and BRBFs values for factors such as ductility, overstrength, force reduction due to ductility and response modification have been assessed for all the buildings. The results showed that the response modification factors for BRBFs were higher than the CBFs one. It was found that the number of bracing bays and height of buildings have had greater effect on the response modification factors.     

Lateral cyclic behavior of zipper braced frames-considering connection details

During Northridge earthquake in USA in 1994, a variety of failures occurred in welded steel connections. Studying these structural failures has led to development of more reliable moment resisting connections and new ways of using braced frames as seismic load resisting systems. This article investigates through numerical simulations, the lateral capacity and seismic behavior of two of these newly-thought braced frames, zipper braced frames and suspended zipper braced frames. The overall seismic behavior of these frames is investigated through displacement-based pushover analyses considering the effect of connection elements such as gusset plate and shear tab. To study the efficiency of these two types of concentrically braced frames, a numerical investigation on their behaviors for low-, mid- and high-rise buildings was conducted. Three zipper braced frames and three suspended zipper braced frames with different number of stories have been modeled using OpenSEES software. For each simulation, frame maximum strength, maximum drift capacity, and weight are determined and compared with each other. It is concluded that connection modeling has significant effects on the lateral behavior of these frames. Furthermore, the suspended zipper braced frames show higher ductility when compared with the ductility of zipper braced frames. Finally, the suspended zipper braced frames are recommended to be used in high-rise buildings, however, for the lowand mid-rise buildings it is recommended to use zipper frames due to economic efficacy.     

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.     

Seismic response of steel braced frames with shape memory alloy braces

In this paper, the seismic performance of steel frames equipped with superelastic SMA braces was investigated. To do so, buildings with various stories and different bracing configurations including diagonal, split X, chevron (V and inverted V) bracings were considered. Nonlinear time history analyses of steel braced frames equipped with SMA subjected to three ground motion records have been performed using OpenSees software. To evaluate the possibility of adopting this innovative bracing system and its efficiency, the dynamic responses of frames with SMA braces were compared to the ones with buckling restrained braces. After comparing the results, one can conclude that using an SMA element is an effective way to improve the dynamic response of structures subjected to earthquake excitations. Implementing the SMA braces can lead to a reduction in residual roof displacement and peak inter-story drift compare to the buckling restrained braced frames.     

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.     

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.     

Seismic design of concentric braced frames

In this paper some modifications to the design procedure, currently implemented in the modern European seismic code for ductile cross concentric braced frames (X-CBFs), are proposed. The code procedure is aimed to obtain a ductile and dissipative ultimate behaviour by imposing that the yielding of diagonal members occurs before the damage and premature failure of beams, columns and connections (capacity design); this approach, involving overstrength requirements and diagonal slenderness limitations, strongly affects the design of CBFs and generally leads to oversized structural solutions, thus suggesting a high weight premium related to the capacity design. The approach proposed by the authors in this paper consists of some modifications to the current design provisions of the European seismic codes, with the major aim of controlling the overstrength requirements to the non-dissipative members of braced frames, thus reducing the associated structural weight premium while preserving a satisfactory inelastic behaviour. In order to assess the reliability of the proposed approach, the results of non-linear FE analyses are presented in the paper with reference to three, and six‐ and nine‐storey buildings, for which different structural solutions are designed according to the current and the proposed approaches.     

Comparative study of special and ordinary braced frames

The collapse probability of ductile and non‐ductile concentrically braced frames was investigated using nonlinear dynamic response analysis. Two buildings with three and nine stories located in Boston and Los Angeles, respectively, were designed and subjected to ground motions from the areas. In Boston area, three‐story and nine‐story buildings were designed as ordinary concentrically braced frame with response modification reduction factor R equal to 3 1/4 to be considered as non‐ductile structural systems; comparatively, in Los Angeles area, three‐story and nine‐story buildings were designed as special concentrically braced frame with response modification reduction factor R equal to 6 to be considered as ductile structural systems. In order to evaluate the performance of ductile and non‐ductile concentrically braced frames in moderate and severe seismic regions, ATC‐63 would be used as reference to assess the seismic behaviors. Evaluation approach recommended by ATC‐63 was adopted, and hundreds of nonlinear dynamic analyses were performed. Through alternating the scale factors of designated ground motions, median of structural collapse intensity was presented for each structure. By observing the results of statistical performance assessment, the seismic performance of the systems was evaluated, and some observations are made based on the study. Copyright © 2012 John Wiley & Sons, Ltd.     

Ductility reduction factor and collapse mechanism evaluation of a new steel knee braced frame

In this study, the suitability of a new structural system called the knee braced frames (KBFs) is investigated for seismic resistant steel structures. In these structural systems, ends of beams are connected to columns by hinges (simple connection) instead of rigid connections, and ends of knee braced elements are connected to columns and beams by hinges as well. In the present paper, in addition to a comparison between elastic behaviour and elastic fundamental natural period, the ductility reduction factor and the type of collapse mechanism in steel KBFs and steel moment resisting frames (MRFs) are compared. The study revealed that the stiffness of steel buildings can be increased considerably by applying knee braced elements and the effects of knee braced elements are highly dependent on knee braced configuration. By applying the pushover analysis, it was observed that the type of collapse mechanism of KBFs is very similar to the mechanism of MRFs. Furthermore in most cases, the ductility reduction factor, R_μ, obtained from steel KBFs is greater than the ductility reduction factor obtained for steel MRFs. Based on the similarity between type of collapse mechanism and the proximity of ductility reduction coefficients of the KBFs and MRFs systems, it can be concluded that the new steel knee braced frame systems can be categorised as steel MRFs with rigid connections.     

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.     

Topology optimization and seismic collapse assessment of shape memory alloy (SMA)-braced frames: Effectiveness of Fe-based SMAs

This paper presents a seismic topology optimization study of steel braced frames with shape memory alloy (SMA) braces. Optimal SMA-braced frames (SMA-BFs) with either Fe-based SMA or NiTi braces are determined in a performance-based seismic design context. The topology optimization is performed on 5- and 10-story SMA-BFs considering the placement, length, and cross-sectional area of SMA bracing members. Geometric, strength, and performance-based design constraints are considered in the optimization. The seismic response and collapse safety of topologically optimal SMA-BFs are assessed according to the FEMA P695 methodology. A comparative study on the optimal SMA-BFs is also presented in terms of total relative cost, collapse capacity, and peak and residual story drift. The results demonstrate that Fe-based SMA-BFs exhibit higher collapse capacity and more uniform distribution of lateral displacement over the frame height while being more cost-effective than NiTi braced frames. In addition to a lower unit price compared to NiTi, Fe-based SMAs reduce SMA material usage. In frames with Fe-based SMA braces, the SMA usage is reduced by up to 80%. The results highlight the need for using SMAs with larger recoverable strains.     

防屈曲支撑钢框架结构中被撑柱抗震设计探讨

通过3个算例,对采用人字形和V字形的无粘结内藏钢板支撑剪力墙(即人字形和V字形防屈曲支撑)的防屈曲支撑钢框架结构的抗震性能进行分析。重点考察大震下,支撑的轴力分布和对被撑柱所受轴力的影响。分析表明,采用结构在一阶振型下的支撑轴力分布来设计被撑柱的做法,适用于多层的防屈曲支撑钢框架结构;而对于高层的防屈曲支撑钢框架结构,高振型影响较显著,上述设计方法对被撑柱的设计较保守,有必要考虑高振型参与下的支撑轴力分布来设计被撑柱。     

混凝土框架结构楼梯参与计算的抗震性能研究及建议

通过对某框架结构实际工程的分析计算,得到了楼梯对框架结构抗震性能的影响和楼梯自身的抗震特性。结果表明,地震作用下楼梯参与计算时框架结构整体指标和楼梯周边构件内力变化很大,楼梯自身地震反应强烈。根据分析结果,提出了设计建议。     

梁贯通式支撑钢框架体系的强度折减系数研究

基于强度折减系数的抗震设计方法,将增量动力分析（IDA）和能力谱法（CSM）结合,对典型梁贯通式支撑钢框架结构的强度折减系数进行研究。采用结构试验校准后的有限元分析模型对结构进行分析,得到结构性能点。通过比较按照设防烈度弹性设计的基底剪力Ve和按照小震设计的基底剪力Vd得到强度折减系数R。分析表明：支撑与框架柱的配置比例及布置方式会对此类结构的强度折减系数产生影响;适用于7度设防烈度的典型两层结构两种支撑配置比例（CASE1和CASE2一层与二层支撑配置比例分别为3∶1和2∶1）梁贯通式支撑钢框架结构体系的强度折减系数可分别取为3.02和2.54。最后建议了该新型结构体系考虑强度折减系数并基于我国现行规范进行抗震设计的地震作用取值范围。     

Incremental dynamic analysis of steel braced frames designed based on the first,second and third editions of the Iranian seismic code (standard no. 2800)

Incremental dynamic analysis (IDA) is an emerging method in structural analysis which allows evaluation of seismic capacity and demand of structures through a series of nonlinear dynamic analyses using multiple scaled ground motion records. Seismic behaviour of concentrically braced frames designed based on the first, second and third revisions of the Iranian seismic code, standard no. 2800, has been evaluated through IDA in the present paper. Besides, a brief comparison is made between seismic behaviour of these frames, frames with different heights and different bracing types. Seismic capacity and limit states of such structures have been reviewed through the paper. The IDA results imply that frames designed with the first edition are seriously vulnerable and fail before reaching the acceleration levels predicted in the code. On the other hand, frames designed with the second and third editions, although behaving better, need partial reinforcement in some cases. Other results of this study show that chevron braced frames behave seismically better than X‐braced ones. Copyright © 2009 John Wiley & Sons, Ltd.     

Progressive collapse resisting capacity of braced frames

In this study, the progressive collapse potential of braced frames was investigated using nonlinear static and dynamic analyses. Eight different bracing types were considered and their performances were compared with those of a special moment‐resisting frame designed with the same design load. According to the pushdown analysis results, most braced frames designed per current design codes satisfied the design guidelines for progressive collapse initiated by loss of a first story interior column; however, most model structures showed brittle failure mode caused by buckling of braces and columns. Among the braced frames considered, the inverted‐V type braced frames showed superior ductile behaviour during progressive collapse. The nonlinear dynamic analysis results showed that all the braced structures remained in stable condition after sudden removal of a column, and their deflections were less than that of the moment‐resisting frame. Copyright © 2009 John Wiley & Sons, Ltd.     

A comparison of dynamic nonlinear behavior of ordinary and buckling restrained braced frames subjected to strong ground motion

In this paper nonlinear dynamic analyses of 4‐ to 12‐story frames with two types of bracing behavior are performed. In the first series of analyses, the bracing post‐buckling behavior is modeled using a Jain‐phenomenological model. In this model bracing buckled against compressive loading and yielded when subjected to tensile loading. In the second series, buckling restrained brace frames subjected to strong ground motion have been analyzed using elements with a bilinear behavior. The results in terms of story drifts, story shears, story shear versus drift hysteresis behavior and plastic hinge locations were compared. By comparing the response of the frame with the buckling restrained brace and the ordinary brace, better performance was observed for the buckling restrained braced frames. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessment of eccentrically braced frames strength against progressive collapse

One of the most important and effective factors of structural strength against the risk of progressive collapse is the type of lateral load bearing system of a building. In this research, strength of dual steel moment frames equipped with a variety of eccentric bracings against progressive collapse was evaluated by using nonlinear static alternate path method. 6-floored building samples were designed with steel frame using a dual steel moment system together with 3 different types of bracing, including inverted eccentrically V-shaped bracing (chevron bracing), eccentrically V-shaped bracing and eccentrically X-shaped bracing, each with two different kinds of arrangement of bracings in the structural plan, in form of alternate and neighbor. The effects of sudden removal of columns on different floors of these buildings were examined. These studies showed that dual steel moment frames equipped with eccentric bracings generally exhibited desirable strength against progressive collapse. A change in the type of bracing resulted in significant changes in the system capacity in the progressive collapse. Among the different types of braces assessed, chevron type eccentrically brace showed higher strength against progressive collapse. Also, that alternate arrangement of bracings in structure plan demonstrated better performance than neighboring arrangement.     

高强钢组合K形偏心支撑框架结构振动台试验研究

为研究高强钢组合K形偏心支撑框架的抗震性能,推动高强钢在我国建筑领域的应用,对一个单跨两榀三层高强钢组合K形偏心支撑钢框架进行缩尺比例为1/2的振动台试验,得到不同工况下的自振频率、阻尼比、加速度反应、位移反应及耗能梁段的应变。研究表明：随地震波峰值加速度的增大,结构的自振频率降低,阻尼比增大,加速度反应增大,动力放大系数减小。按照动力相似关系推导出原型结构的地震反应,多遇地震作用下结构最大层间位移角为1/1667,罕遇地震作用下结构最大层间位移角为1/237,均满足抗震规范变形验算的规定。综上,高强钢组合K形偏心支撑框架具有良好的抗震性能,满足“三水准”抗震设防准则。     

Seismic behaviour of eccentrically braced frames

In the past, the analysis of the seismic behaviour of eccentrically braced frames designed in fulfilment of capacity design principles has highlighted the significant role of the link overstrength factor. The link overstrength factor is, however, unable to explain many seismic responses because it is defined on the basis of the sole elastic behaviour of structures. To achieve thorough comprehension of the seismic behaviour of eccentrically braced systems, a new parameter, called damage distribution capacity factor, is defined here. The proposed parameter is calculated on the basis of the inelastic structural behaviour and is intended to evaluate the effect of premature yielding of links on the ability of structures to develop significant inelastic behaviour of all links prior to link failure. The paper discusses the distribution of the damage distribution capacity factor in eccentrically braced structures designed in accordance with capacity design principles and the influence of this parameter on the seismic response of structures. Finally, an analytical relation is defined between overstrength factor of links, damage distribution capacity factor and plastic rotation of links to obtain quantitative evaluation of the structural damage of eccentrically braced structures upon first failure of links.