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 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.     

Seismic collapse analysis of high‐rise reinforced concrete frames under long‐period ground motions

Structural damages associated with buckling of longitudinal reinforcing steel and crushing of concrete induce strength and stiffness degradation in reinforced concrete (RC) beams and columns. This paper presents a numerical investigation on earthquake‐induced damages and collapse of typical high‐rise RC buildings model incorporating strength degradation (SD) effects. In a simple finite‐element analysis program with the generalized stress fiber discretization, hysteretic constitutive models primarily dominate the inelastic behavior. Buckling of reinforcing steel and crushing of confined concrete are taken into accounted to the stress–strain relationship of fiber elements. The SD effect in components with small hoop ratio tends to amplify the seismic responses high‐rise RC moment‐resisting frames when the intensity of ground motions exceeds the design level. Buckling of steel rebar and crushing of concrete should be fully considered together with the P‐Δ effect for collapse simulations.     

Seismic assessment of steel frames with the endurance time method

In the endurance time (ET) method, structures are subjected to a specially designed intensifying ground acceleration function and their performance is judged based on their response at various excitation levels. A range of equivalent intensities can be covered in a single numerical or experimental simulation, thus significantly reducing the computational demand as compared to full nonlinear response-history analyses. The applied excitation intensity at various times has been correlated with those of the scaled ground motions. Response spectra of seven ground motions on stiff soil were used to produce intensifying acceleration functions that at each time window produce a response spectrum that is compatible with the template spectrum and proportionally scale up with time. The drift ratios and plastic hinge rotations compare well with those from ground motions in steel frames with various numbers of stories and bays. The locations of plastic hinges are also predicted quite satisfactorily by ET analysis. The sensitivity of the results to the selection of a particular set of ground motions is also studied.     

Assessment of progressive collapse-resisting capacity of steel moment frames

In this study the progressive collapse-resisting capacity of steel moment resisting frames was investigated using alternate path methods recommended in the GSA and DoD guidelines. The linear static and nonlinear dynamic analysis procedures were carried out for comparison. It was observed that, compared with the linear analysis results, the nonlinear dynamic analysis provided larger structural responses and the results varied more significantly depending on the variables such as applied load, location of column removal, or number of building story. However the linear procedure provided more conservative decision for progressive collapse potential of model structures. As the nonlinear dynamic analysis for progressive collapse analysis does not require modeling of complicated hysteretic behavior, it may be used as more precise and practical tool for evaluation of progressive collapse potential of building structures.     

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.     

不同弯矩增大系数钢筋混凝土框架结构地震易损性分析

设计3个不同柱端弯矩增大系数的钢筋混凝土框架结构模型,考虑结构材料、荷载及地震动参数的随机性,分别对其进行随机增量动力分析（IDA）,以地震峰值加速度（a _pg）作为地震动强度指标,结构的顶点最大位移角θ_max作为结构的反应参数,得到各结构模型的IDA曲线。在IDA分析的基础上,对各结构模型进行地震需求概率分析,通过定义4个抗震性能水平,对各模型进行随机pushover分析,确定各性能水平的限值,分别对各结构模型进行易损性分析,得出各结构的地震易损性曲线。计算分析结果表明：弯矩增大系数的取值对结构的易损性有一定的影响,其取值越大时,结构在地震作用下倒塌的概率越小;在一定的范围内(0.2g≤a _pg≤1.0g),当结构的塑性程度发展越大时,提高弯矩增大系数对结构抗震性能的贡献越明显;建议规范修订时可适当增加柱端弯矩增大系数的取值。     

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.     

Direct displacement‐based design of steel‐braced reinforced concrete frames

This study investigates a direct displacement‐based design procedure for dual system structures composed of reinforced concrete frames and steel bracings. In this procedure, in order to establish the design displacement profile before any analysis, strength proportions between bracings and frames are assigned. By using the displacement profile and damping characteristics of the structural components, the structure can be represented as an equivalent single‐degree‐of‐freedom system. The effective period and secant stiffness of the structure are then calculated, and finally, after the base shear was computed, the design process can be implemented. Structures with 4, 8 and 12 stories have been designed using this methodology, and in order to validate it, seven accelerograms have been used for nonlinear time‐history analysis of the above structures. The results demonstrate the efficiency of this procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Application of endurance time method in seismic assessment of steel frames

In this paper, application of a new dynamic procedure called Endurance Time (ET) method in seismic analysis of steel frames is explained. In this method, structures are subjected to gradually intensifying ground shaking and their performance is assessed based on their response considering relevant design criteria at each intensity level. By considerably reducing the number of time history analyses for assessment of structural response at different intensities, this procedure tends to pave a way for practical performance based design of structures. The accuracy of ET method in predicting the response of structures in linear and nonlinear analysis is investigated by considering a set of steel frames. Different material models consisting of elastic-perfectly plastic, stiffness degrading and strength deteriorating models are considered. Application of ET method in assessment of frames that incorporate fluid viscous dampers as seismic mitigation devices is also demonstrated. It is shown that ET analysis can estimate the results of full response history analysis with reasonable accuracy at different excitation levels. ET analysis results are also shown to be reasonably consistent for different material models. Specific issues that should be considered for a successful ET analysis, including the potential loss of accuracy at highly nonlinear excitation levels are discussed. Capability of ET method in predicting collapse capacity of the studied frames is discussed.     

Seismic performance assessment of masonry infill reinforced concrete buildings in Eastern Canada

In Eastern Canada, most of moment resisting reinforced concrete frames with unreinforced masonry infill (MI-MRF) buildings were constructed between 1915 and 1960. These pre-code structures, in terms of seismic requirements, are considered vulnerable to earthquake due to insufficient ductility and resistance. The goal of this study is to provide a quantitative assessment of their seismic performance using fragility functions. Fragility functions represent the probability of damage that corresponds to a specific seismic intensity measure (e.g. peak ground acceleration at the site). Based on a structural characterisation study on existing buildings in Québec region, a case study three storey–three bay MI-MRF was selected as representative for mid-rise buildings. Pushover analyses were conducted on a nonlinear model of the infill frame to obtain the corresponding lateral load-deformation capacity curve. The nonlinear behaviour of the reinforced concrete beams and columns was modelled with concentrated plastic hinges at members’ ends and a modified strut-and-tie model was used for the infill to account for multiple failure modes. A simplified probabilistic nonlinear static procedure was applied to obtain the seismic demand model at increasing levels of seismic intensity. Fragility functions were then developed using an experiment-based damage model that correlate the extent of damage to the displacement demand. Damage assessment using the developed functions was conducted for an earthquake scenario compatible with the design-level seismic hazard in Quebec City with a 2% and 10% probability of exceedance in 50 years. The developed functions and methodology are particularly useful in probability-based seismic loss assessment and in planning mitigation solutions.     

Seismic fragility assessment of a tall reinforced concrete chimney

In China, a considerable proportion of reinforced concrete (RC) industrial chimneys in operation was designed and constructed in accordance with less rigorous outdated seismic criteria during the end of 19th and early 20th century. However, few research works have been reported till date on a realistic overall assessment of the seismic performance of these existing aging RC chimney structures. Therefore, in this study, fragilities of existing RC chimney were studied. For this purpose, an existing 240 m tall RC chimney was selected and structurally modeled with a lumped mass beam (stick) model by means of the OpenSees analysis program. In order to capture the uncertainties in ground motion realizations, a series of 21 ground motions are selected from the Next Generation Attenuation database as the input motions. To develop the analytical fragility curves, nonlinear incremental dynamic analysis of the studied RC chimney was then carried out using the selected input motions, which were normalized to different excitation levels. The section curvature ductility ratio was considered as the damage index. Based on material strain and sectional analysis, four limit states (LSs) were defined for five damage state. The seismic responses of the all sections were utilized to evaluate the likelihood of exceeding the LSs. Then the peak ground acceleration (PGA)‐based seismic fragility curves of the structure were constructed assuming a lognormal distribution. Finally, under the light of these fragility curves, the damage risks in existing RC chimney were discussed. The analytical results indicated that for design level earthquake of PGA = 0.1 g (g is the gravitational acceleration) and the maximum considered earthquake of PGA = 0.22 g, the probabilities of exceeding the light damage state were around 1.5% and 44%, respectively, while the exceedance probabilities corresponding to moderate, extensive and complete damage states were approximately zero in both cases. On the other hand, fragility analysis revealed that the RC chimney structure had considerable ductility capacity and was capable to withstand a strong earthquake with some structural damages. Copyright © 2014 John Wiley & Sons, Ltd.     

An investigation on the interaction of moment‐resisting frames and shear walls in RC dual systems using endurance time method

Reinforced concrete (RC) dual systems are composed of RC moment‐resisting frames (MRFs) and RC shear walls, where MRFs are barely designed to handle gravity loads. Investigations have demonstrated that shear walls exert negative effects on the upper part of MRFs. In this paper, the interaction of shear walls and MRFs is inspected using endurance time (ET) method. ET is a dynamic time history‐based pushover procedure in which structures are exposed to a set of predefined intensifying ET acceleration functions. In this method, seismic performance of the considered structure is assessed based on earthquake return periods; during which, required predefined seismic performance objectives are fulfilled. In this study, several buildings with RC dual systems were designed based on the conventional codes. Next, their nonlinear duplicates were generated for the application of the ET analysis. It was revealed that shear wall elements impose considerable rotational demands—exceeding the criteria established by ASCE41‐13—on the beams and columns, especially those located on the upper parts of the buildings. This paper puts forth and reviews certain methods to cushion the negative effects brought about by RC shear walls, along with a detailed discussion on their merits and demerits.     

单跨混凝土框架倒塌机理分析

以一单跨混凝土框架为例,采用Pushover方法分析了其倒塌机理,结合已往地震中该类建筑的破坏特征,研究了现浇板及结构地坪的影响,并简单介绍了目前针对该类建筑的几种常用加固方法,以指导工程实践。     

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。     

Seismic fragility curves for mid-rise reinforced concrete frames in Kingdom of Saudi Arabia

This article is concerned with the development of seismic fragility curves for typical mid-rise plane reinforced concrete moment-resisting frames in Kingdom of Saudi Arabia (KSA), which is considered as low-seismicity area. Two structural models; four- and eight-storey moment-resisting frames were considered. Three cities with different seismic intensities, Abha, Jazan and Al-Sharaf, were selected to cover various values of mapped spectral accelerations in KSA. The 0.2-s spectral accelerations range from 0.21 to 0.66 g, while the 1.0-s spectral accelerations range from 0.061 to 0.23 g. The structural models were designed under dead, live and seismic loads of these cities according to the Saudi Building Code. Incremental dynamic analysis was performed under 12 ground motions using SeismoStruct. Five performance levels, namely, operational, immediate occupancy, damage control, life safety and collapse prevention were considered and monitored in the analysis. Fragility curves were developed for the structural models of the three cities considering the five selected performance levels.     

浅埋地下结构耐震时程分析法最优持时研究

为研究持时对地下结构耐震时程分析结果的影响,选取II类和III类工程场地中典型的两层三跨地铁车站为原型,以基岩场地地震动均值反应谱为目标谱,构造了6种典型持时的耐震加速度时程曲线作为输入。通过将耐震分析结果与增量动力分析基准结果对比表明,耐震加速度时程曲线的持时对分析结果影响显著。根据目标时间点与地震动能量指标阿里亚斯强度值的变化规律,给出了最优目标时间点的确定公式并进行验证。由研究结果可知,对于II和III类工程场地,耐震时程曲线较优持时分别为30s和45s;给出的目标时间点的确定公式对上述两类场地中的地下结构抗震性能评价具有一定适用性,当构造的耐震时程曲线在目标时间区段内的能量值与实际地震动的能量值较为接近时,耐震时程分析结果最为精确。     

Collapse safety margin-oriented seismic retrofit strategy for corroded reinforced concrete frames using fibre reinforced plastics

Considering residual service life, this paper presents a collapse safety margin-oriented seismic retrofit strategy for corroded reinforced concrete (RC) frames using fibre reinforced plastics (FRP). With the assumed uniform corrosion model, corrosion-induced initial damage combined with subsequent earthquake-induced damage is identified by the multi-mode-based global damage model developed previously. The collapse-level earthquake intensity determined by incremental dynamic analyses (IDA) with the damage model and the maximum considered earthquake (MCE)-level intensity considering residual service life are combined to generate the time-variant collapse safety margin assessment of corroded RC structures. Based on this assessment, the collapse safety margin-oriented FRP seismic retrofit strategy is proposed and demonstrated on a 4-storey frame. The damage model originally developed for earthquake scenarios has also exhibited its rationality for characterising corrosion-induced initial damage and its influence on coupled damage development with subsequent earthquake excitation. Seismic retrofitting with FRP composites should consider the effects of the corrosion development stage, target collapse safety margin and residual service life. FRP retrofits can cause decreases in the MCE-level collapse probability and increases in the collapse resistance of corroded RC structures. Retrofitting carried out at different times achieves different efficiencies and different time-variant collapse safety margins within the residual service life.