Progressive collapse resisting capacity of moment frames with viscous dampers

In this paper, the effect of viscous dampers on reducing progressive collapse potential of steel moment frames was evaluated by nonlinear dynamic analysis. Parametric studies were conducted first to evaluate the effects of dampers installed in a steel beam‐column subassembly with varying natural period and yield strength on the reduction of progressive collapse potential. Then 15‐story moment‐resisting frames with three different span lengths were designed with and without viscous dampers, and the effect of viscous dampers was investigated by nonlinear dynamic analysis. According to the parametric study, the vertical displacement generally decreased as the damping ratio of the system increased, and the dampers were effective in both the elastic and the elasto‐plastic systems. It was also observed that the effect of the damper increased as the natural period of the structure increased and the strength ratio decreased. The analysis results of 15‐story analysis model structures showed that the viscous dampers, originally designed to reduce earthquake‐induced vibration, were effective in reducing vertical displacement of the structures caused by sudden removal of a first‐story column, and the effect was more predominant in the structure with longer span length. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

Progressive collapse analysis of concentrically braced frames through EPCA algorithm

This paper introduces a new algorithm, namely the Extended Progressive Collapse Analysis (EPCA) algorithm, whose features, such as potential and capacity of buildings for occurrence of progressive collapse, were investigated. Their failure modes were determined by using pushdown and vertical incremental dynamic analyses. Moreover, by applying this procedure, the element removal impact factor and the most critical locations of such removals were obtained. This algorithm was utilized for progressive collapse analysis of two newly designed concentrically braced frames with different numbers and locations of braced bays in order to quantitatively determine its effect on mitigating progressive collapse. Using this method, the minimum residual capacity and the most critical locations of element loss as well as element removal impact factor for the frames that were studied were determined. Results showed that the frame with two braced bays had more robustness for mitigating progressive collapse, at least to the rate of 17.21% comparing to the frame with three braced bays.     

Progressive collapse resisting capacity of tilted building structures

In this study, the progressive collapse resisting capacities of tilted buildings are evaluated on the basis of arbitrary column removal scenario. As analysis model structures both regular and tilted moment‐resisting frames, structures with outrigger trusses, and tubular/diagrid structures are designed, their progressive collapse resisting capacities are evaluated by nonlinear static and dynamic analyses. It turns out that the tilting of the structures requires increased steel tonnage due to the increased p‐delta effect. In addition in the tilted structures the plastic hinges are more widely distributed throughout the bays and stories when a column is removed from a side or a corner of the structures. With the analysis results, it is concluded that the tilted building structures, once they are properly designed to satisfy a given design code, may have at least an equivalent resisting capacity for progressive collapse caused by sudden loss of a column. Copyright © 2012 John Wiley & Sons, Ltd.     

Progressive collapse resisting capacity of building structures with outrigger trusses

In this paper, the progressive collapse potential of building structures with core and outrigger trusses were evaluated using nonlinear static and dynamic analyses. To this end 36‐storey analysis model structures composed of RC core walls and perimeter frames connected by outrigger trusses at the top were prepared. The static pushdown analysis of the structure with mega‐columns and outrigger trusses showed that the maximum strength reached only about 20% of the load specified in the US General Services Administration guideline when a mega‐column in the first storey was removed. According to dynamic analysis results, the vertical displacement monotonically increased until collapse as a result of buckling of some of outrigger truss members. However the structure with outrigger and belt trusses remained stable after a perimeter column was removed. The stability of the structure with mega‐columns and outrigger trusses could be achieved by redesigning it with additional belt trusses or with moment connections in interior or exterior frames. Based on the analysis results it was concluded that the dynamic amplification factor of 2.0 recommended in the guidelines provided reasonably conservative results. Copyright © 2010 John Wiley & Sons, Ltd.     

Progressive collapse resisting capacity of tube‐type structures

In this study, the progressive collapse potential of tube‐type buildings, such as diagrid and tubular structures, composed of lateral load‐resisting perimeter frames and internal pin‐connected gravity frames, was evaluated by nonlinear static and dynamic analyses. To this end, 36‐ and 54‐storey structures were designed as analysis models and progressive collapse analyses were carried out by removing first‐storey columns. According to the analysis results, the progressive collapse of tube‐type analysis model buildings occurred when perimeter columns corresponding to more than 11% of all member cross‐sectional areas were removed from one side of the structures. When the diagonals located around a corner were removed, the ratio was reduced to 8%. It was observed that the corner columns in the diagrid system helped prevent the propagation of member failure all around the perimeter. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of system reliability‐based assessment for collapse fragility of braced moment‐resisting frames

This paper presents a system reliability‐based framework for collapse fragility assessment of steel braced moment‐resisting frames (BMRFs). The conditional failure of intermediate events is calculated, considering two important features in the design of BMRFs: (i) different failure scenarios (FSs) with multiple sequences of components failure formation and (ii) structural reliability analysis based on the failure propagation from components to system. The system collapse reliability‐based assessment of BMRFs is developed with an efficient algorithm using the Monte Carlo simulation procedure incorporated into a nonlinear finite element (FE) analysis program. An appropriate nonlinear FE model of such systems is demonstrated, and the probability of various predefined components' failure over the most likely FSs in the presence of both epistemic and inherent uncertainties is calculated. Then, a system‐simulated reliability index (SSRI) is computed by lower and upper bounds in the probability of BMRF system collapse. Finally, fragility curves based on the SSRI is compared with the ones from incremental dynamic analysis, and later, the outcomes from multiple FSs are compared with the codified main collapse criterion. For the BMRFs analyzed herein, it is shown that the existing allowable story drift for the collapse limit state is conservative, and a new criterion is appraised. Copyright © 2015 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.     

The collapse behaviour of braced steel frames exposed to fire

Progressive collapse mechanisms of braced two-dimensional steel-framed structures, subjected to fire heating, are investigated using a robust static–dynamic procedure developed by the authors. 20 cases have been analysed to provide a comprehensive view of the mechanisms of progressive collapse for these frames, with different bracing systems under different fire conditions. The influences of stiffness and strength of the bracing systems are also analysed. The results indicate that the pull-in of columns is one of the main factors which generate progressive collapse. Horizontal “hat truss” bracing systems have limited capacity to avoid pull-in of columns supporting the heated floor, although they can directly redistribute the vertical load lost by buckling columns to adjacent columns. On the other hand, vertical bracing systems have the effect, not only of increasing the lateral restraint of the frame, which reduces the pull-in of the columns, but also of effectively preventing the collapse progressing from local to global. Stronger vertical bracing systems can redistribute load from a buckled column to its surrounding structural members. Frames with a combined hat and vertical bracing system can be designed to enhance the capability of the frame as much as possible to prevent progressive collapse when a heated column buckles.     

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.     

Progressive collapse design of seismic steel frames using structural optimization

This paper uses structural optimization techniques to cost-effectively design seismic steel moment frames with enhanced resistance to progressive collapse, which is triggered by the sudden removal of critical columns. The potential for progressive collapse is assessed using the alternate path method with each of the three analysis procedures (i.e., linear static, nonlinear static, and nonlinear dynamic), as provided in the United States Department of Defense United Facilities Criteria (UFC) Design of Buildings to Resist Progressive Collapse. As a numerical example, member sizes of a two-dimensional, nine-story, three-bay regular steel immediate moment frame are optimally determined such that the total steel weight is minimized while the design satisfies both AISC seismic provisions and UFC progressive collapse requirements. Optimization results for the example frame reveal that the traditional minimum weight seismic design, which does not explicitly consider progressive collapse, fails to meet the UFC alternate path criteria associated with any analysis procedure. Progressive collapse design optimization using the linear static procedure produces the most conservative and consequently heaviest design against progressive collapse. In contrast, the more accurate nonlinear static and dynamic procedures lead to more economical designs with UFC-acceptable resistance to progressive collapse, at the expenses of considerable modeling and computing efforts.     

Seismic eccentrically braced frames

This paper provides an overview of the behavior and design of seismic-resistant eccentrically braced frames (EBFs). Basic characteristics of EBFs are first discussed. The important effects of link length on the performance of EBFs are reviewed. The capacity design concept for EGFs is then addressed. The paper addresses several design issues that appear to have been inadequately considered either in current practice or in the emerging seismic code provisions. Some important observations are provided from pseudodynamic tests of large EBFs and experimental studies of EBF subassemblages with link-to-box column connections conducted recently. Future research needs are discussed.     

Effect of inverted-V bracing on retrofitting against progressive collapse of steel moment resisting frames

The effect of inverted-V bracing on enhancing progressive collapse resistance of steel Moment Resisting Frames (MRF) were investigated in this study. A series of nonlinear static and dynamic analyses were performed to determine the resistance of four generic MRFs retrofitted by ten inverted-V bracing element. These structures were subjected to an exterior column loss and had a different number of stories and span lengths in order to study the effect of these variations on the structural response. Both force-controlled and deformation-controlled actions were implemented to determine if the column loss would lead to a failure progression. Results showed that structural configuration affects the structural resistance against failure progression and hence the appropriate brace element to retrofit it. Also, it was shown that for the studied 4-story frames, by increasing the span length by 20%, the structural resistance decreases by 42% on average. Finally, it was observed that by decreasing the span length, the Dynamic Increase Factor (DIF) suggested by the UFC, will lead to underestimating the required cross-sectional area of the brace for strengthening the unbraced structures.     

Successive collapse potential of eccentric braced frames in comparison with buckling-restrained braces in eccentric configurations

In the present research, the successive collapse potential of eccentric braced frames (EBF) in comparison with bucklingrestrained braces in eccentric configurations (BRBF-E) has been studied. Initially, five-story EBF and BRBF-E were analyzed and designed according to the guidelines of the American Institute of Steel Construction (AISC). Subsequently, the nonlinear dynamic analysis based on Unified Facilities Criteria (UFC) guidelines was used. The Alternate Path Method was used in the mentioned structures with various cases for removed columns. Both critical cases and successive collapse potential through values such as Impact Factor for columns, the end point vertical displacement of removed column and Demand-Capacity Ratio for link beams have been specified. The results indicate that removing edge columns caused further critical situation in EBF and BRBF-E compared to the other cases. The results elaborated that the BRBF-E has higher vulnerability than EBF. Furthermore, additional analysis were undertaken to establish the lateral stability of the removed columns. The results of the lateral stability analysis in one of the cases confirmed that the analyzed parameters were increased.     

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.     

On the plastic analysis of concentrically braced frames with shear panel,obtaining predetermined collapse mechanism

Conventional design methods do not ensure that the desired collapse mechanism is developed at target displacement. In this paper, a case study is presented to analyze concentrically braced frames with steel shear panel (CBFSP). Also, extensive investigation in the failure modes are made, to have the global yielding mode at the final state. For this purpose, each of one‐story, three‐story, six‐story and nine‐story CBFSP models were decomposed into three parts where the members' closed‐form equations of internal forces were identified and superimposed. On the basis of the kinematic theorem of plastic collapse, the possible mechanisms and the related energy equations were defined to estimate the lateral load multiplier. First, the shear panels, columns, vertical and horizontal boundary elements were designed using the values of internal forces and seismic loads. Next, sections of the beams and braces were selected by constraining, where the mechanism equilibrium curve of the desired mechanism had to be placed below the others within the admissible roof displacement. Finally, for assessment of the precision of the method, results of the pushover analysis of the finite element models were compared with the theoretical ones. The findings show that, despite more effort for design, the investigated method is reliable and satisfactory. Copyright © 2014 John Wiley & Sons, Ltd.     

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。     

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.     

Buckling of frames braced by flexural bracing

This paper investigates the buckling of multistory frames braced by vertical beams. The sectional properties of the frames and the bracing beam are assumed to vary linearly along the height; the axial forces in the columns and the bracing beam are also assumed to linearly change along the height. A relationship between the buckling load and the bracing rigidity is established. The threshold rigidity for the vertical bracing beam which is just enough to make the frames buckle in a non-sway mode is obtained. The result may be used as a rational basis for classifying sway frames and non-sway frames after taking the influence of initial imperfections and lateral loads into account.