A design procedure for dual eccentrically braced systems: Numerical investigation

The paper investigates the seismic response of dual braced structures constituted by eccentrically braced frames and moment resisting frames. The response of dual braced structures designed according to the procedure described in the companion paper is first examined with the aim of suggesting behaviour factors varying with the mechanical length of the links. A larger set of structures is then designed according to the proposed values of the behaviour factor to validate the expression adopted. The seismic response of these structures is obtained by incremental dynamic analyses with reference to deterministic and random values of strength of steel. To highlight the qualities of the response of these structures the results of the dynamic analyses are compared to those obtained from structures designed according to procedures suggested by codes. A comparison is also carried out with conventional eccentrically braced frames in which the degree of interaction between the eccentrically braced frames and the other parts of the structure is purposely held very low.     

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.     

多高层钢结构的分类及其稳定性设计

提出了与钢结构稳定性计算有关的多高层钢结构的分类 ,由此可以更好地理解钢结构稳定性的计算方法 ,合理选择钢结构稳定计算的图表或公式 ,判断某些钢结构规范稳定性计算条文的合理性。     

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。     

Influence of the link overstrength factor on the seismic behaviour of eccentrically braced frames

The paper investigates the influence of the link overstrength factor on the seismic behaviour of eccentrically braced frames designed in accordance with capacity design principles. To this end, systems characterised by different level number and link length are designed according to the force-based approach, by either static or modal analysis. In order to correctly evaluate the ability of structures to develop global collapse mechanisms characterized by remarkable exploitation of the deformation capacity of links, incremental dynamic analyses are carried out with reference to either deterministic or random values of yield strength. While the first analyses are intended to lead to the conventional evaluation of the seismic response of EBFs, those referred to random values of yield strength are carried out to achieve a more correct verification of the capacity design principles and a deep comprehension of the sensitivity of the structural response to real strength distributions. On the basis of such results, the study also permits a critical analysis of the values of the behaviour factor generally proposed by building codes with reference to this structural typology.     

用附加防屈曲支撑钢筋混凝土框架加固既有钢筋混凝土框架抗震性能试验研究

利用附加防屈曲支撑（BRB）钢筋混凝土框架对既有钢筋混凝土框架结构进行减震加固。设计3榀钢筋混凝土框架,其中2榀为附加设置BRB加固框架的钢筋混凝土框架,另外1榀为纯钢筋混凝土框架以作对比。通过低周反复加载试验,验证所设计的外贴防屈曲支撑钢筋混凝土框架加固既有钢筋混凝土框架的可行性。分析既有及外贴钢筋混凝土框架的开裂、荷载 侧移滞回曲线、骨架曲线、荷载 防屈曲支撑变形曲线,以及等效黏滞阻尼比和等效刚度等特性。结果表明：所设计的附加钢筋混凝土框架、预埋件、连接构造受力可靠,附加设置BRB的钢筋混凝土加固框架具有良好的减震耗能能力;水平荷载-侧移滞回曲线圆润饱满;防屈曲支撑在小层间位移角下可屈服耗能,大位移下不失效,耗能稳定;附加框架能够显著增加既有钢筋混凝土框架结构的阻尼,有效降低地震反应,改善既有框架结构抗震性能。     

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.     

Seismic performance of Y‐type eccentrically braced frames combined with high‐strength steel based on performance‐based seismic design

In the Y‐type eccentrically braced frame structures, the links as fuses are generally located outside the beams; the links can be easily repairable or replaceable after earthquake without obvious damage in the slab and beam. The non‐dissipative member (beams, braces, and columns) in the Y‐type eccentrically braced frames are overestimated designed to ensure adequate plastic deformation of links with dissipating sufficient energy. However, the traditionally code design not only wastes steel but also limits the application of eccentrically braced frames. In this paper, Y‐type eccentrically braced steel frames with high‐strength steel is proposed; links and braces are fabricated with Q345 steel (the nominal yield stress is 345 MPa); the beams and columns are fabricated with high‐strength steel. The usage of high‐strength steel effectively decreases the cross sections of structural members as well as reduces the construction cost. The performance‐based seismic design of eccentrically braced frames was proposed to achieve the ideal failure mode and the same objective. Based on this method, four groups Y‐type eccentrically braced frames of 5‐story, 10‐story, 15‐story, and 20‐story models with ideal failure modes were designed, and each group includes Y‐type eccentrically braced frames with ordinary steel and Y‐type eccentrically braced frames with high‐strength steel. Nonlinear pushover and nonlinear dynamic analyses were performed on all prototypes, and the near‐fault and far‐fault ground motions are considered. The bearing capacity, lateral stiffness, story drift, link rotations, and failure modes were compared. The results indicated that Y‐type eccentrically braced frames with high‐strength steel have a similar bearing capacity to ordinary steel; however, the lateral stiffness of Y‐type eccentrically braced frames with high‐strength steel is smaller. Similar failure modes and story drift distribution of the prototype structures designed using the performance‐based seismic design method are performed under rare earthquake conditions.     

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.     

Multi-Index Seismic Capacity Evaluation of Buckling-Restrained Braced Frames

The seismic capacity of a structure is determined by the performance index that reaches its ultimate bearing or deformation capacity first. This paper presents a multi-index seismic capacity evaluation method for accurately evaluating the seismic capacity of a structure. The normalized response curves of several indices are concurrently plotted to form a multi-index seismic capacity evaluation figure, in which the seismic capacity and demand values that correspond to various indices can be determined by vertical and horizontal threshold lines. Based on an incremental dynamic analysis (IDA), a 6-story buckling-restrained braced frame (BRBF) and a series of comparable 6-story steel frames are analyzed using the proposed method to verify the method and investigate the seismic behavior of BRBFs. The results show that the seismic performance of buckling-restrained braces is not the only factor that determines the seismic capacity of BRBFs and indicate that the multi-index seismic capacity evaluation method can effectively identify the critical index of a structure and the weakest links that restrict the structural seismic capacity.     

Incremental dynamic analysis of steel frames equipped with NiTi shape memory alloy braces

This paper determines the seismic performance of four‐storey concentrically braced frames equipped with either steel buckling‐restrained braces or buckling‐restrained superelastic shape memory alloy (SMA) braces through incremental dynamic analysis. The incremental dynamic analysis technique is used to examine the behaviour of four‐storey braced frames with four different bracing configurations (including diagonal, split‐X, chevron‐V and inverted‐V) under 20 different ground motion records. The study reveals a satisfactory performance at the design intensity level for both types of braced frames. The results show that the SMA braces lead to a uniform distribution of inelastic response over the height of the buildings, as well as mitigating seismic response in terms of maximum inter‐storey drift and residual roof displacement. By comparing the responses of SMA and buckling‐restrained braced frames under higher intensities of earthquake loading, it is found that the SMA braces can be more beneficial especially under severe ground motion excitations. Copyright © 2014 John Wiley & Sons, Ltd.     

The seismic behaviour of steel moment-resisting frames with stiffening braces

The present paper deals with the seismic behaviour of steel structures which are designed in the attempt of exploiting the dual characteristics of moment resisting frames (MRFs) and concentrically braced frames (CBFs) as lateral force resisting systems. Three prototype frames are studied within the context of Eurocode 8 (EC8) provisions; these are MRFs which are traditionally designed, against ultimate seismic actions (ULS), without checking serviceability limit state rules (SLS-interstory drift limits). To fulfill these requirements concentrical braces are inserted in the frames, which are not considered in the collapse resistance of the structural system. The non-linear behaviour of these systems under ultimate seismic environment is studied and compared to the one of the unbraced MRFs. The influence of second order effects is also investigated.     

柱轴压比对我国RC框架结构抗地震倒塌能力的影响

首先用纤维模型和美国ATC-63委员会推荐的IDA方法,对按照我国现行抗震规范设计的24个钢筋混凝土框架结构(7度设防,跨度、层高、层数不同)的抗地震倒塌能力进行了分析,发现框架柱轴压比是影响框架结构抗地震倒塌能力的最主要因素,轴压比和结构的倒塌储备系数CMR具有一定的线性负相关关系,现行规范轴压比限值偏高是导致框架结构抗地震倒塌能力不足的主要原因。通过改变框架柱截面尺寸调整轴压比后的进一步分析表明,控制轴压比可有效改善框架结构的抗地震倒塌能力。     

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.     

新型梁柱节点高层钢结构抗震性能研究

结构的抗震设计一般有两类途径:主动控制和被动控制。主动控制系统复杂且成本偏高,普通的被动控制抗震结构强震后修复困难。针对上述问题,本文提出了一种新型转动摩擦耗能梁-柱节点,并基于SAP2000对采用新型梁柱耗能节点的X形支撑钢框架体系和普通X形支撑钢框架体系进行了罕遇地震作用下的时程分析,结果表明采用了该新型梁-柱耗能节点的X形支撑钢框架体系具有更好的抗震性能。     

支撑—异形柱钢框架结构的静力弹塑性分析

简述了Push-over方法的基本原理,并运用ETABS对柱截面积相同、柱形(H形柱,异形柱)不同的支撑—钢框架结构进行弹塑性分析,发现了支撑—异形柱钢框架结构抗震性能优于纯钢框架结构,支撑—异形柱钢框架较支撑—H形柱钢框架弱侧抗侧能力更好等优点。     

Behavior and design of reinforced concrete frames retrofitted with steel bracing against progressive collapse

Steel bracing is able to improve progressive collapse resistance of reinforced concrete (RC) frames, but the bracing design is typically based on seismic retrofitting or lateral stability. There is no approach for design of steel bracing against progressive collapse. To this end, a retrofitting approach with steel braces is proposed based on analysis of macro finite element (FE) models with fiber beam elements. The FE models were initially validated through the experimental results of a braced frame and then used to investigate the effects of pertinent parameters on the progressive collapse resistance of planar frames. The results suggest the braces should be placed at the top story. Thereafter, macro FE models are built to investigate the dynamic responses of the three‐dimensional prototype RC frames under different column removal scenarios (CRS) and show the necessity of retrofitting. Accordingly, the design approach of steel bracing is proposed with incremental dynamic analysis (IDA) and assuming independent contribution of braces and frames to resistance. Finally, the fragility analysis of the frames under a corner‐penultimate‐exterior CRS is conducted through IDA and Monte Carlo simulation, and the results confirm the validity of the proposed design approach for retrofitting RC frames.     

考虑结构不确定性的地震倒塌易损性分析

传统的地震倒塌易损性分析中通常只考虑地震动不确定性的影响。在结构临近倒塌时,通常处于高度非线性状态,会出现结构不确定性与地震动不确定性的耦合放大现象。针对这一问题,将平均值一次二阶矩方法（MVFOSM）与逐步增量动力分析（IDA）相结合,提出了一种可以考虑结构不确定性的基于MVFOSM的随机IDA方法。以五层三跨钢筋混凝土框架结构为例,采用基于MVFOSM的随机IDA方法对其进行了地震倒塌易损性分析,并利用“龙卷风图”方法对结构抗地震倒塌能力的灵敏度进行了分析。研究表明：结构不确定性的存在使得结构抗地震倒塌能力的对数标准差增加了70%,因此有必要在地震倒塌易损性分析中考虑结构不确定性的影响。     

丙类与乙类设防RC框架结构抗地震倒塌能力对比

按照GB 50011-2001《建筑抗震设计规范》6～8.5度的丙类与乙类设防要求分别设计了10个典型RC框架结构算例,采用基于动力增量时程分析(IDA)地震倒塌易损性分析方法得到了各算例结构在遭遇罕遇地震和特大地震时的倒塌率,据此对不同设防烈度的丙类和乙类RC框架结构的抗地震倒塌能力进行了评价分析。研究指出,结构的抗倒塌能力需根据结构的绝对抗震能力和相对地震动强度来进行评价。分析结果表明,对于6～7.5度抗震设防的结构,因其绝对抗震能力偏低,抗震设防烈度仅由丙类提高到乙类,其在遭遇特大地震时的抗地震倒塌能力仍较差,需采取进一步的措施增强其抗震能力。     

Seismic capacity assessment of postmainshock damaged containment structures using nonlinear incremental dynamic analysis

This paper investigates the structural performance and seismic capacity of the postmainshock damaged containment structure through the incremental dynamic analysis (IDA). To evaluate the seismic capacity with minimum uncertainty, the damage measure (DM) and intensity measure (IM) for IDA curves are selected in term of the coefficient of variation. The IDA using mainshock records is implemented to examine the seismic damage process of a containment structure and determine key damage states. The static cyclic loading analysis and aftershock IDA are also conducted on mainshock‐damaged containment structures to investigate the effect of initial damage states on the dynamic characteristics of structures. Finally, based on IDA results, limit states of a containment structure are defined using a generalized multidimensional limit‐state function that allows considering the dependence between the mainshock‐damaged level and residual seismic capacity. These proposed bidimensional limit‐state functions can be used in the fragility analysis and risk assessment of containment structures under mainshock–aftershock, which can improve the accuracy of seismic assessment.