Bar fracture modeling in progressive collapse analysis of reinforced concrete structures

Reliable evaluation of progressive collapse resistance of structures requires substantiated methods and techniques for analyzing the response of critical elements subjected to large deformations. Steel bar fracture is a significant event that can lead to progressive collapse of reinforced concrete (RC) structures. Given the sudden discontinuity associated with bar fracture, modeling of such an event in a continuum domain analysis is challenging. In this paper a method is proposed for finite element modeling and analysis of RC elements that accounts for bar fracture. It is demonstrated that such a modeling technique is capable of developing catenary action. Analytical results based on the proposed method show good agreement with experimental data. The underlying cause for a drop in beam vertical resisting force following the peak force is identified and explained.     

An improved tie force method for progressive collapse resistance design of reinforced concrete frame structures

Progressive collapse of structures refers to local damage due to occasional and abnormal loads, which in turn leads to the development of a chain reaction mechanism and progressive and catastrophic failure. The tie force (TF) method is one of the major design techniques for resisting progressive collapse, whereby a statically indeterminate structure is designed through a locally simplified determinate structure by assumed failure mode. The method is also adopted by the BS8110-1:1997, Eurocode 1, and DoD 2005. Due to the overly simplified analytical model used in the current practical codes, it is necessary to further investigate the reliability of the code predictions. In this research, a numerical study on two reinforced concrete (RC) frame structures demonstrates that the current TF method is inadequate in increasing the progressive collapse resistance. In view of this, the fundamental principles inherent in the current TF method are examined in some detail. It is found that the current method fails to consider such important factors as load redistribution in three dimensions, dynamic effect, and internal force correction. As such, an improved TF method is proposed in this study. The applicability and reliability of the proposed method is verified through numerical design examples.     

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.     

Progressive collapse performance analysis of precast reinforced concrete structures

In this paper, the progressive collapse performance analysis of precast reinforced concrete (RC) structures is performed. A numerical simulation framework for precast RC structures is developed on the basis of the OpenSEES software, where the fiber frame element is used for beam and column type members and Joint2D element is used for the beam‐to‐column connections. The conjugated material models are then introduced, and a min–max failure criterion is imposed on the original models to reflect the steel fracture and concrete crushing when the structure is undergoing progressive collapse. In addition, to overcome the computational difficulties arisen from progressive collapse behavior, two enhanced nonlinear solutions , that is, the consistent quasi‐Newton algorithm and the explicit KR‐α algorithm, are employed, respectively, for static and dynamic analysis. A 10‐storey prototype precast RC structures is designed to verify the developed numerical framework, and the progressive collapse resisting mechanism of the structures is investigated through both static pushdown analysis and dynamic column‐removal analysis. Finally, influences of some typical parameters in precast RC structures on their progressive collapse performance are studied.     

建筑结构抗连续倒塌的分析方法及控制设计

近年来,随着偶然荷载（地震、撞击、爆炸）的增加,造成了大量的人员和财产的损失。其中由于这种非常规荷载引起的结构连续性倒塌所造成的损失占很大的比例。本文介绍了抗连续性倒塌的研究现状,并对目前几种连续性倒塌的分析方法及控制设计做了全面的总结。     

从汶川地震震害谈建筑结构抗连续倒塌设计方法

在5·12汶川特大地震中,许多建筑物发生了连续倒塌。本文结合该次地震造成的建筑物连续倒塌震害,介绍分析了建筑结构连续倒塌的定义、原因以及抗连续倒塌主要设计方法,并对我国抗连续倒塌设计研究提出建议,为我国深入研究和尽快完善建筑结构抗连续倒塌设计提供参考。     

Numerical studies on the effect of plan irregularities in the progressive collapse of steel structures

This research examines the effect of plan irregularities on the progressive collapse of four steel structures located in regions with different seismic activity. The plans of the first and second structure are irregular, whilst those of the third and fourth structures are regular. The collapse patterns of the four buildings are examined and compared under seven loading scenarios using non-linear dynamic and static analyses. In the non-linear dynamic analyses, node displacements above the removed columns and the additional force on the columns adjacent to them are discussed. Furthermore, the strength and capacities of the columns are compared to determine their susceptibility to collapse. In the non-linear static analyses, the pushdown curve and yield load factor of the structures are obtained after column removal. The results indicate that an irregular structure designed in site class C seismic zone, collapses in most of the column-removal scenarios. Moreover, when comparing regular and irregular structures designed in site class E seismic zone, the demand force to capacity ratio (D/C) of the columns in the irregular structures is on average between 1.5 and 2 times that of the regular ones.     

机械铰的量化准则及其在倒塌分析中的应用

为了评估建筑结构的抗倒塌能力,在机械铰理论的基础上,提出了机械铰的量化准则,进行了框架节点的数值模拟,并与节点的试验结果进行对比和验证,最后建立了基于机械铰的结构倒塌判定准则,并对某二层钢筋混凝土框架结构进行了倒塌分析。研究结果表明,相比于塑性铰的倒塌判定准则,基于机械铰的倒塌判定准则更接近于结构的真实倒塌极限,可以更真实地模拟结构的抗倒塌能力。     

基于性能设计方法在超限高层抗连续倒塌设计应用

我国抗震设计规范提出"小震不坏、中震可修、大震不倒"的设防目标,其中,"中震可修、大震不倒"的第二、第三水准设防目标,主要是采用经验调整系数及构造加强措施来实现,缺乏定量的计算分析。本文应用基于性能抗震设计的方法,采用静力非线性有限元倒塌计算原理,分析框架结构在大震作用下的破坏机理,对结构"大震不倒"进行定量分析,确保结构实现抗倒塌的设计目标。并结合一个超限高层实例,验证倒塌计算结果与振动台实验结果的相符性。     

Investigation of the influence of design and material parameters in the progressive collapse analysis of RC structures

This contribution deals with the modelling of reinforced concrete (RC) structures in the context of progressive collapse simulations. One-dimensional nonlinear constitutive laws are used to model the material response of concrete and steel. These constitutive equations are introduced in a layered beam approach, in order to derive physically motivated relationships between generalised stresses and strains at the sectional level. This formulation is used in dynamic progressive collapse simulations to study the structural response of a multi-storey planar frame subjected to a sudden column loss (in the impulsive loading range). Thanks to the versatility of the proposed methodology, various analyses are conducted for varying structural design options and material parameters, as well as progressive collapse modelling options. In particular, the effect of the reinforcement ratio on the structural behaviour is investigated. Regarding the material modelling aspects, the influence of distinct behavioural parameters can be evaluated, such as the ultimate strain in steel and concrete or the potential material strain rate effects on the structural response. Finally, the influence of the column removal time in the sudden column loss approach can also be assessed. Significant differences are observed in terms of progressive failure patterns for the considered parametric variations.     

钢筋混凝土单向梁板子结构抗连续倒塌试验研究

梁和板组成的楼盖系统是框架结构的主要抗连续倒塌构件。为了分析各类结构参数对钢筋混凝土楼盖系统抗连续倒塌性能的影响,该文首先根据《混凝土结构设计规范》GB 50010—2010设计制作了8个钢筋混凝土单向梁板子结构缩尺试件,这些试件具有不同的截面尺寸和配筋率。然后通过竖向加载试验研究这些试件在中柱破坏后的材料变形/损伤和抗连续倒塌承载力。试验结果表明：带楼板的子结构试件的承载能力明显高于相同截面的梁试件的承载能力;试件在梁机制阶段的承载能力主要由截面尺寸和钢筋面积所决定,而悬链线机制阶段的承载能力主要由截面中连续钢筋面积所决定;楼板的宽度、厚度和板内配筋以及梁高对梁机制下的承载力有较大的提高,其中板宽在大于一定值后影响变得不显著;只有楼板宽度和楼板配筋率对悬链线机制下的承载力有显著影响;梁内抗震配筋对缩尺试件在两个阶段的抗连续倒塌承载力影响都不大。     

钢筋混凝土框架结构抗震与抗连续倒塌的比较

从钢筋混凝土结构受力机制和倒塌破坏准则两方面,对抗震与抗连续倒塌的区别进行了分析与比较,结果表明：抗倒塌不同于抗震,结构抗震设计的有益作用并不能取代抗倒塌设计。     

Experimental investigation of asymmetrical reinforced concrete spatial frame substructures against progressive collapse under different column removal scenarios

The progressive collapse resistance design approach is generally applied in the context of a “column‐removal” scenario to assess the structural vulnerability to progressive collapse. To obtain a better understanding of the complex progressive collapse resistance of 3D asymmetrical column‐beam‐slab systems, five one‐third scale 2 × 2 bay asymmetrical reinforced concrete (RC) spatial frame substructure specimens were tested to analyze their collapse mechanisms under five different column removal scenarios, namely, an interior column removal scenario (INT), an exterior column removal scenario in the asymmetrical direction (EXT‐X), an exterior column removal scenario in the symmetrical direction (EXT‐Y), a corner column removal scenario at the long bay (COR‐L), and a corner column removal scenario at the short bay (COR‐S), which are among the most critical scenarios for analyzing structural resistance against progressive collapse. The test results showed that INT had the highest progressive collapse resistance capacity among the scenario substructures and exhibited two progressive collapse‐resisting mechanism stages: a primary mechanism stage (beam and compressive membrane mechanism) under small deformations and a secondary mechanism stage (catenary and tensile membrane mechanism) under large deformations in both the X‐direction and the Y‐direction. In EXT‐X and EXT‐Y, the collapse resistance was mainly provided by the double‐span beam at both the primary mechanism stage and the secondary mechanism stage. In COR‐L and COR‐S, the tensile membrane mechanism could not be mobilized, as the single‐span beams in both the X‐direction and the Y‐direction behaved like cantilevers. Additionally, the asymmetrical span design reduced the resistance of the structure against progressive collapse.     

钢筋混凝土框架抗倒塌与抗震设计的对比分析

以一栋六层框架结构为例,对其抗倒塌设计与抗震设计的结果进行了分析,研究结果表明,抗倒塌设计不同于抗震设计,并提出抗倒塌设计的一些措施,为将来工程抗倒塌设计和相关方面的设计提供了参考依据。     

Effect of retrofit strategies on mitigating progressive collapse of steel frame structures

In this study, the effect of three retrofit strategies on enhancing the response of existing steel moment resisting frames designed for gravity loads is investigated using Alternate Path Methods (APM) recommended in the General Services Administration (GSA) and the Department of Defense (DoD) guidelines for resisting progressive collapse. The response is evaluated using 3-D nonlinear dynamic analysis. The studied models represent 6-bay by 3-bay 18-storey steel frames that are damaged by being subjected to six scenarios of sudden removal of one column in the ground floor. Four buildings with bay spans of 5.0 m, 6.0 m, 7.5 m, and 9.0 m were studied. The response of the damaged frames is evaluated when retrofitted using three approaches, namely, increasing the strength of the beams, increasing the stiffness of the beams, and increasing both strength and stiffness of the beams.The objective of this paper is to assess effectiveness of the studied retrofit strategies by evaluating the enhancement in three performance indicators which are chord rotation, tie forces, and displacement ductility demand for the beams of the studied building after being retrofitted.     

The influence of joints and composite floor slabs on effective tying of steel structures in preventing progressive collapse

The event of the terrorist attack on 11th September 2001 in the USA has attracted increasing attention of researchers and engineers on progressive collapse of structures. It has gradually become a general practice for engineers to consider progressive collapse resistance in their design. In this paper, progressive collapse of steel frames with composite floor slabs is simulated by the finite element method. The numerical results are compared with test results. The influence of the joints and the concrete slabs on the effective tying of steel beams is investigated through parametric studies. From the analysis, methods of preventing progressive collapse that can be considered in design and when retrofitting existing structures are proposed. The results show that retrofitting a structure with pre-stressed steel cables and an increase of crack resistance in the concrete near joints can effectively improve effective tying of a structure, which results in an enhanced structural capacity in preventing progressive collapse.     

地震作用下钢筋混凝土框架结构连续倒塌极限状态可靠度分析

将结构连续倒塌的全概率方法应用于地震作用下的结构整体连续倒塌极限状态可靠度分析,采用构件可靠度方法对结构进行地震作用下最可能失效构件的识别,基于改进点估计法的随机Pushdown方法和随机竖向增量动力分析(竖向IDA)方法,进行完好和损伤结构的概率抗竖向连续倒塌能力分析及参数灵敏度分析。采用整体可靠度方法,分析了损伤结构的竖向连续倒塌条件失效概率。基于系统可靠度理论和全概率方法,分析了RC框架结构发生侧向增量倒塌以及构件地震损伤引起的结构竖向连续倒塌的联合失效概率。分析结果表明,按照我国现行规范设计的钢筋混凝土框架结构具有良好的抗连续倒塌能力。     

Stochastic seismic collapse and reliability assessment of high‐rise reinforced concrete structures

To provide knowledge beyond the conventional engineering insights, attention in this work is focused on a comprehensive framework for the stochastic seismic collapse analysis and reliability assessment of large complex reinforced concrete (RC) structures. Three key notions are emphasized: the refined finite element modeling and analysis approach towards structural collapse, a physical random ground motion model, and an energy‐based structural collapse criterion. First, the softening of concrete material, which substantially contributes to the collapse of RC structures, is modeled by the stochastic damage constitutive model. Second, the physical random ground motion model is introduced to quantitatively describe the stochastic properties of the earthquake ground motions. And then the collapse‐resistance performance of a certain RC structure can be systematically evaluated on the basis of the probability density evolution method combining with the proposed structural collapse criterion. Numerical results regarding a prototype RC frame‐shear wall structure indicate that the randomness from ground motions dramatically affects the collapse behaviors of the structure and even leads to entirely different collapse modes. The proposed methodology is applicable in better understanding of the anti‐collapse design and collapse prediction of large complex RC buildings.     

考虑悬链线效应的钢筋混凝土框架结构抗连续倒塌能力分析

为了研究悬链线效应对钢筋混凝土（RC）框架结构抗连续倒塌能力的影响,基于OpenSees建立可以考虑悬链线效应的RC框架宏模型,通过两个RC框架子结构在移除中柱后的竖向承载力试验结果对比,验证了所采用宏模型的合理性,并研究了悬链线效应对RC框架子结构抗连续倒塌能力的影响。分别采用备用荷载路径法中的非线性静力方法和非线性动力方法对1栋10层RC框架结构进行抗连续倒塌能力分析,研究悬链线效应对RC框架整体结构抗连续倒塌能力的影响。结果表明：不考虑悬链线效应的影响将低估RC框架结构的抗连续倒塌能力;在移除底层中柱情况下,不考虑悬链线效应分析得到的荷载放大系数最大值小于2.0,而考虑悬链线效应分析得到的荷载放大系数最大值则超过2.0。     

Simplified nonlinear progressive collapse analysis of welded steel moment frames

In this study, two nonlinear analysis methods are proposed that can be used for a simplified but accurate evaluation of progressive collapse potential in welded steel moment frames. To this end, the load-resisting mechanism of the column-removed double-span beams in welded steel moment frames was first investigated based on material and geometric nonlinear parametric finite element analysis. A simplified tri-linear model for the vertical resistance versus chord rotation relationship of the double-span beams was developed. The application of the developed model to energy-based nonlinear static progressive collapse analysis was then proposed. The relationship between the gravity loading and the maximum dynamic chord rotation or the concept of collapse spectrum was also established for a quick assessment of the maximum deformation demands.