Dynamic collapse analysis for a reinforced concrete frame sustaining shear and axial failures

Shaking table test results from a one‐story, two‐bay reinforced concrete frame sustaining shear and axial failures are compared with nonlinear dynamic analyses using models developed for the collapse assessment of older reinforced concrete buildings. The models provided reasonable estimates of the overall frame response and lateral strength degradation; however, the measured drifts were underestimated by the models. Selected model parameters were varied to investigate the sensitivity of the calculated response to changes in the drift at shear failure, rate of shear strength degradation, and drift at axial failure. For the selected ground motion, the drift at shear failure and rate of shear strength degradation did not have a significant impact on the calculated peak drift. By incorporating shear and axial‐load failure models, the analytical model is shown to be capable of predicting the axial‐load failure for a hypothetical frame with three nonductile columns. Improvements are needed in drift demand estimates from nonlinear dynamic analysis if such analyses are to be used in displacement‐based performance assessments. Copyright © 2008 John Wiley & Sons, Ltd.     

Collapse of a nonductile concrete frame: Shaking table tests

Post‐earthquake reconnaissance has reported the vulnerability of older reinforced concrete (RC) columns lacking details for ductile response. Research was undertaken to investigate the full‐range structural hysteretic behavior of older RC columns. A two‐dimensional specimen frame, composed of nonductile and ductile columns to allow for load redistribution, was subjected to a unidirectional base motion on a shaking table until global collapse was observed. The test demonstrates two types of column failure, including flexure‐shear and pure flexural failure. Test data are compared with various simplified assessment models commonly used by practicing engineers and researchers to identify older buildings that are at high risk of structural collapse during severe earthquake events. Comparison suggests that ASCE/SEI 41‐06 produces very conservative estimates on load–deformation relations of flexure‐shear columns, while the recently proposed ASCE/SEI 41‐06 update imposes significant modifications on the predictive curve, so that improved accuracy has been achieved. Copyright © 2008 John Wiley & Sons, Ltd.     

Curvature ductility of columns and structural displacement ductility in RC frame structures subjected to ground motions

This paper examined the statistical relationship between the curvature ductility demands of columns and the global displacement ductility demands of reinforced concrete (RC) frame structures when subjected to earthquakes. Elements with a designated moment–curvature relationship were adopted for both beam and column elements, and five-story and ten-story RC frame numerical structures were established. Using pushover analysis and earthquake nonlinear dynamic time-history analysis, the maximum global displacement ductility demands of the structure and the maximum curvature ductility demands of the columns were determined. The effects of the spectral acceleration and the strong column factor on ductility demands were analyzed, and the quantitative relationship between the curvature ductility demands of columns and the global displacement ductility demands of frame structures were established. Moreover, the validity of the established relationship was further tested and verified through a real-world application. The results show that the maximum curvature ductility demands of the columns and the maximum displacement ductility demands of the structure were positively associated with the spectral acceleration and negatively associated with the strong column factor. A proposed first-degree linear relationship between curvature ductility of columns and structural displacement ductility in RC frame structures with two parameters was obtained by curve fitting, while considering the effect of the strong column factor. The model was highly correlated with the sampling analysis data. Applying the empirical model established in this study is a simple and effective means to guide the design of ductility and the assessment of RC frame columns.     

Composed analytical models for seismic assessment of reinforced concrete bridge columns

This paper presents general composed analytical models to predict the behavior of reinforced concrete (RC) bridge columns. The analytical models were developed in OpenSees to represent the common hysteretic behavior of RC bridge columns. The proposed composed models can accommodate flexure failure, flexure‐shear failure, and pure shear failure, which are observed in existing RC bridge piers. The accuracy of the models was verified using data from the static cyclic‐loading experiments of 16 single columns and one multi‐column bent and dynamical experiment from two pseudo‐dynamic tests. The results showed that the analytical models could simulate the nonlinear behavior until the post‐failure behavior, including the strength degradation, the buckling of the reinforcement, and the pinching effect. Therefore, a global view of the behavior of reinforcement concrete is prescribed as simply as possible from the academic perspective, and these models are expected to provide sufficient accuracy when applied in engineering practice. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of reinforcement slippage on the non‐linear response under cyclic loadings of RC frame structures

This paper discusses the importance of including the bond‐slip effects in assessing the response under cyclic loads of reinforced concrete frames. The discussion is based on analyses performed using numerical models which are simple, computationally efficient and capable of representing the salient features of reinforced concrete frames under both static and dynamic loads. The numerical models comprise a displacement‐based, reinforced concrete frame element with bond‐slip and a rigid beam column joint element with bond‐slip. Two applications illustrate the model accuracy and show the importance of including bond‐slip. The first application considers a reinforced concrete beam‐column subassemblage experimentally tested under cyclic loads. The second application considers the shaking table test of a two‐story one‐bay reinforced concrete frame In both cases the analytical results correlate well with the experimental results in terms of strength, displacement demands and hysteretic energy dissipation. Furthermore, the paper shows how the analyses that include bond‐slip yield a better correlation with the experimental results with respect to the analyses that assume a perfect bond. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical study of a full‐scale six‐story reinforced concrete wall‐frame structure tested at E‐Defense

A full‐scale shake table test on a six‐story reinforced concrete wall frame structure was carried out at E‐Defense, the world's largest three‐dimensional earthquake simulation facility, in January 2006. Story collapse induced from shear failure of shear critical members (e.g., short columns and shear walls) was successfully produced in the test. Insights gained into the seismic behavior of a full‐scale specimen subjected to severe earthquake loads are presented in this paper. To reproduce the collapse process of the specimen and evaluate the ability of analytical tools to predict post‐peak behavior, numerical simulation was also conducted, modeling the seismic behavior of each member with different kinds of models, which differ primarily in their ability to simulate strength decay. Simulated results showed good agreement with the strength‐degrading features observed in post‐peak regions where shear failure of members and concentrated deformation occurred in the first story. The simulated results tended to underestimate observed values such as maximum base shear and maximum displacement. The effects of member model characteristics, torsional response, and earthquake load dimensions (i.e., three‐dimensional effects) on the collapse process of the specimen were also investigated through comprehensive dynamic analyses, which highlighted the following seismic characteristics of the full‐scale specimen: (i) a model that is incapable of simulating a specimen's strength deterioration is inadequate to simulate the post‐peak behavior of the specimen; (ii) the torsional response generated from uniaxial eccentricity in the longitudinal direction was more significant in the elastic range than in the inelastic range; and (iii) three‐dimensional earthquake loads (X–Y–Z axes) generated larger maximum displacement than any other loading cases such as two‐dimensional (X–Y or Y–Z axes) or one‐dimensional (Y axis only) excitation. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of gravity framing on the overstrength and collapse capacity of steel frame buildings with perimeter special moment frames

This paper investigates the effect of the gravity framing system on the overstrength and collapse risk of steel frame buildings with perimeter special moment frames (SMFs) designed in North America. A nonlinear analytical model that simulates the pinched hysteretic response of typical shear tab connections is calibrated with past experimental data. The proposed modeling approach is implemented into nonlinear analytical models of archetype steel buildings with different heights. It is found that when the gravity framing is considered as part of the analytical model, the overall base shear strength of steel frame buildings with perimeter SMFs could be 50% larger than that of the bare SMFs. This is attributed to the gravity framing as well as the composite action provided by the concrete slab. The same analytical models (i) achieve a static overstrength factor, Ω_s larger than 3.0 and (ii) pass the collapse risk evaluation criteria by FEMA P695 regardless of the assigned total system uncertainty. However, when more precise collapse metrics are considered for collapse risk assessment of steel frame buildings with perimeter SMFs, a tolerable probability of collapse is only achieved in a return period of 50 years when the perimeter SMFs of mid‐rise steel buildings are designed with a strong‐column/weak‐beam ratio larger than 1.5. The concept of the dynamic overstrength, Ω_d is introduced that captures the inelastic force redistribution due to dynamic loading. Steel frame buildings with perimeter SMFs achieve a Ω_d > 3 regardless if the gravity framing is considered as part of the nonlinear analytical model representation. Copyright © 2014 John Wiley & Sons, Ltd.     

Inelastic displacement demand of bridge columns considering shear–flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi‐directional seismic shakings. The inelastic displacement of columns can be increased by shear–flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full‐size columns subject to a suite of near‐fault ground motions. A coupled hysteretic model is used to simulate the shear‐flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post‐yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure‐to‐pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Implications of seismic pounding on the longitudinal response of multi-span bridges-an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach, Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is essential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Seismic hybrid simulation of a nonductile RC building with severe damage to multiple columns

Reinforced concrete frame structures built prior to the mid‐1970s are susceptible to brittle column failure under seismic action, potentially leading to progressive collapse of the structure. The behavior of columns susceptible to brittle shear‐axial failure has been studied previously but rarely has the interaction between damaged columns and the surrounding three‐dimensional structure been investigated experimentally and at full scale. In this study, as the second in a series of hybrid simulations, two full‐scale reinforced concrete columns of a representative pre‐1970s structure were tested at the Multi‐axial Full‐scale Substructure Testing and Simulation (MUST‐SIM) laboratory. Through the use of hybrid simulation, the interaction of the columns with the surrounding structure is studied under a severe seismic motion including vertical excitation. The computational model representing the remainder of the representative 10‐story structure is created in the computer program OpenSees. During the hybrid simulation, both physical specimens experience significant loss of shear and axial strength, and the effects of these failures on the surrounding system are described. The three‐dimensional computational model in OpenSees allowed for analytical flexural‐axial failure of a third column in the structure to occur. The effects of these multiple failures on the response of a full structural system under seismic action are quantified, and the progressive collapse resistance mechanisms are discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic loss estimation of non‐ductile reinforced concrete buildings

Non‐ductile reinforced concrete buildings represent a prevalent construction type found in many parts of the world. Due to the seismic vulnerability of such buildings, in areas of high seismic activity non‐ductile reinforced concrete buildings pose a significant threat to the safety of the occupants and damage to such structures can result in large financial losses. This paper introduces advanced analytical models that can be used to simulate the nonlinear dynamic response of these structural systems, including collapse. The state‐of‐the‐art loss simulation procedure developed for new buildings is extended to estimate the expected losses of existing non‐ductile concrete buildings considering their vulnerability to collapse. Three criteria for collapse, namely first component failure, side‐sway collapse, and gravity‐load collapse, are considered in determining the probability of collapse and the assessment of financial losses. A detailed example is presented using a seven‐story non‐ductile reinforced concrete frame building located in the Los Angeles, California. Copyright © 2012 John Wiley & Sons, Ltd.     

Near‐collapse response of existing RC building under severe pulse‐type ground motion using hybrid simulation

Column shear‐axial failure is a complex response, which lends itself to physical experimentation. Reinforced concrete structures built prior to the mid‐1970s are particularly susceptible to such failure. Shear‐axial column failure has been examined and studied at the element level, but current rehabilitation practice equates such a column failure with structural collapse, neglecting the collapse resistance of the full structural system following column failure. This system‐level response can prevent a column failure from leading to progressive collapse of the entire structure. In this study, a hybrid simulation was conducted on a representative pre‐1970s reinforced concrete frame structure under severe seismic ground motion, in which three full‐scale reinforced concrete columns were tested at the University of Illinois at Urbana Champaign. The analytical portion of the model was represented in the computer program OpenSees. Failure occurred in multiple physical specimens as a result of the ground motion, and the hybrid nature of the test allowed for observation of the system‐level response of the tested columns and the remaining structural system. The behavior of the system accounting for multiple column shear‐axial failure is discussed and characterized. Copyright © 2016 John Wiley & Sons, Ltd.     

Implications of seismic pounding on the longitudinal response of multi-span bridges - an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach. Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is cssential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Torsional response of nonductile structures with soft‐first‐storey

In this paper, torsional response of nonductile structures with soft‐first‐storey subjected to bidirectional ground motions is studied using a simplified two‐storey model with two‐way eccentricities. The stiffness ratio of second storey to first storey is varied to create different levels of soft‐first‐storey effect, while the stiffness eccentricity is varied to create torsional effects. Different overstrength ratios are used in the simplified models to study the response of structure with different structural capacity. Hysteretic model with strength deterioration and stiffness degradation properties is used to capture the deterioration of element stiffness and strength. Ductility capacity of 2.0 is used as the models are for nonductile structures. In general, displacement amplification of irregular model with respect to regular model increases as stiffness ratio increases, while no consistent trend of changes in displacement amplification is found with increase in stiffness eccentricity. It is found that the displacement amplification due to only soft‐first‐storey effect can be conservatively taken as 1.5. Coupling of torsional and soft‐first‐storey effects is more significant in affecting the displacement amplification of elements at flexible side. The trend of changes in displacement amplification of elastic system is similar to that of inelastic system. The displacement amplification of elements at the flexible side is larger than that at the stiff side. The elements at the flexible side in the direction of shorter uncoupled lateral period have larger displacement response than those in the orthogonal direction. Ductility demand–capacity curves subsequently constructed can be used to approximately assess the seismic performance of existing structures and as guidelines for designing structures in Singapore to withstand the maximum credible earthquake considering the coupling of torsional and soft‐first‐storey effects. Copyright © 2014 John Wiley & Sons, Ltd.     

采用纤维模型的钢管混凝土框架-中心支撑结构抗连续倒塌非线性分析

为研究不同形式的中心支撑对钢管混凝土结构抗连续倒塌性能的影响,基于纤维梁模型建立5种钢管混凝土框架-中心支撑结构数值模型,在合理选取钢材和混凝土材料本构模型的基础上,计算不同失效工况下结构的抗连续倒塌非线性动力响应,通过非线性静力加载获得结构的整体刚度和极限承载力。研究结果表明：设置中心支撑均可以提高结构的整体刚度和抗倒塌承载能力,其中对边柱失效工况的提升效果好于中柱失效工况;设置中心支撑提供了新的荷载传递路径,可以有效减小失效柱相邻构件的分配内力;X型支撑在不同失效工况下都能显著提升框架刚度和承载能力,降低失效节点的竖向位移,反斜支撑框架表现出更好的延性和极限承载能力,研究结果可为建筑结构抗连续倒塌设计提供参考。     

A distributed parameter model of a frame pin‐supported wall structure

Many reinforced‐concrete frames collapse via a soft‐story mechanism during severe earthquakes. Such collapses are mainly attributed to concentrated deformation in a soft story. Deformation control is thus important in preventing collapse. The frame pin‐supported wall structure is a type of rocking structure that releases constraints at the bottom of the wall. Previous research has obtained good results for the deformation control of this type of structure. However, the interior forces and strength demands of the pin‐supported wall have not been systematically explored. In this paper, a distributed parameter model is developed to investigate the strength demand of the wall in a frame pin‐supported wall structure. In the model, the pin‐supported wall is simplified as a bending beam and the frame is simplified as a shear beam. The two beams are joined by distributed shear connectors, so that the shear force can be transferred at any location on the interface. The model can be solved using differential equations based on equilibrium and compatibility. The accuracy of the model is verified using SAP2000 (Computers and Structures Inc., Berkeley, CA, USA). Displacement distribution of the structure and distributions of the moment and shear force within the pin‐supported wall are obtained for two typical external force profiles. It is found that the pin‐supported wall can effectively reduce the drift concentration factor. Distributions of the displacement, moment, and shear force are closely correlated with the relative stiffness of the wall and frame. Finally, recommendations on the stiffness and strength of a pin‐supported wall are made. Copyright © 2015 John Wiley & Sons, Ltd.     

R.C.框架结构的振动台试验和面向设计的时程分析方法

钢筋混凝土框架结构的弹塑性时程反应分析是抗震设计规范所要求的一项重要内容,但目前还滑有比较简单实用肯计算可靠的方法。本文进行了两个六层钢筋混凝土框架结构模型的地震模拟震动台试验,通过分析试验模型的自振特性、变形形式、加速度反应、位移反应和破坏开矿以及钢筋混凝土框架结构的实际震害,建立了面向设计的钢筋混凝土框架结构弹塑性里程反应分析的计算方法。在这一方法中,对钢筋混凝土框架整体结构采用层间剪切模型,     

A novel structural detailing for the improvement of seismic and progressive collapse performances of RC frames

Earthquake-induced building collapse and progressive collapse due to accidental local failure of vertical components are the two most common failure modes of reinforced concrete (RC) frame structures. Conventional design methods usually focus on the design requirements of a specific hazard but neglect the interactions between different designs. For example, the progressive collapse design of an RC frame often yields increased reinforcement and flexural strength of the beams. As a result, the seismic design principle of “strong-column-weak-beam” may be violated, which may lead to unfavorable failure modes and weaken the seismic performance. To avoid these adverse effects of the progressive collapse design on the seismic resistance of RC frames, a novel structural detailing is proposed in this study. The proposed detailing technique intends to concurrently improve the seismic and progressive collapse performances of an RC frame by changing the layout of the newly added longitudinal reinforcement against progressive collapse without introducing any additional reinforcement. A six-story RC frame is used as the prototype building for this investigation. Both cyclic and progressive collapse tests are conducted to validate the performance of the proposed structural detailing. Based on the experimental results, detailed finite element (FE) models of the RC frame with different reinforcement layouts are established. The seismic and progressive collapse resistances of different models are compared based on the incremental dynamic analysis (IDA) and nonlinear dynamic alternate path (AP) methods, respectively. The results indicate that the proposed structural detailing can effectively resolve the conflict between the seismic and progressive collapse designs.     

Practice‐oriented probabilistic seismic performance assessment of infilled frames with consideration of shear failure of columns

The objective of the study presented in this paper is to investigate the effects of masonry infills on the shear demand and failure of columns for the case when reinforced concrete frames with such infills are modeled by means of simplified nonlinear models that are not capable of the direct simulation of these effects. It is shown that an approximate simulation of the shear failure of columns can be achieved through an iterative procedure that involves pushover analysis, post‐processing of the analysis results using limit‐state checks of the components, and model adaptation if shear failure of columns is detected. The fragility parameters and the mean annual frequency of limit‐state exceedance are computed on the basis of nonlinear dynamic analysis by using an equivalent SDOF model. The proposed methodology is demonstrated by means of two examples. It was shown that the strength of the four‐story and seven‐story buildings and their deformation capacity are significantly overestimated if column shear failure due to the effects of masonry infills is neglected, whereas the mean annual frequency of limit‐state exceedance for the analyzed limit states is significantly larger than that estimated for the case if the shear failure of columns is neglected. Copyright © 2012 John Wiley & Sons, Ltd.