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.     

Analysis of RC slab–beam–column sub‐assemblages subjected to bidirectional lateral cyclic loading using a new 3D macroelement

An existing two‐dimensional macroelement for reinforced concrete beam–column joints is extended to a three‐dimensional macroelement. The three‐dimensional macroelement for beam–column joints consists of six rigid interface plates and uniaxial springs for concrete, steel, and bond–slip, which model the inside of a beam–column joint. The mechanical models for the materials and the stiffness equation for the springs are also presented. To validate the model, we used test results from three slab–beam–column sub‐assemblages subjected to bi‐lateral cyclic load. It is revealed that the new joint model is capable of capturing the strength of beam–column joints and the bidirectional interaction in joint shear response, including the concentration of damage in the beam–column joint, the pinching nature in hysteretic behavior, the stiffness degradation, and strength deterioration resulting from cyclic and bidirectional loading. Copyright © 2017 John Wiley & Sons, Ltd.     

Cyclic Displacement Model for Reinforced Concrete Columns

Reinforced concrete (RC) structures in low to moderate seismic regions and many older RC structures in high seismic regions include columns with steel reinforcement details not meeting the requirements of modern seismic design codes. These columns typically fail in shear or in a brittle manner and their behavior must be accurately captured when RC structures are modeled and analyzed. The total lateral displacement of a low ductility or shear critical RC column can be represented as the sum of three displacement components: (1) flexural displacement, (2) displacement due to slippage of the reinforcing bars at column ends, and (3) shear displacement. In this study, these three displacement components are separately modeled and then combined together following a proposed procedure based on the expected overall behavior of the column and its failure mechanism. A simplified slip model is proposed. The main objective of this research is to develop an easy-to-apply method to model and capture the cyclic behavior of RC columns considering the shear failure mechanism. The proposed model is validated using the available data from RC column and frame experiments.     

Failure simulation of shear‐critical RC columns with non‐ductile detailing under lateral load

Reinforced concrete columns with non‐ductile detailing typically exhibit a softening behavior characterized by severe degradation when subjected to cyclic lateral loads. Whether the response is brittle or ductile, shear failure occurs with an inclined through crack along which sliding occurs coupled with loss of horizontal and vertical load‐bearing capacity of the member. The rapid loss of resistance after the peak strength is reached is because of one or more of the following local failure mechanisms: brittle failure of poorly confined concrete; buckling of longitudinal reinforcing bars because of lack of adequate transverse reinforcement or following opening of stirrups after spalling of cover concrete; bond failure. In this study, a modeling strategy to build a detailed 3D finite element model capable of capturing all of the above‐mentioned local failure mechanisms is presented. In particular, a steel–concrete interface model for representing the interaction within the member between concrete core, cover and longitudinal and transverse reinforcement is proposed. Comparison with results of an experimental test of a shear‐sensitive column demonstrates the effectiveness of the simulation up to failure of the element. Copyright © 2016 John Wiley & Sons, Ltd.     

Inelastic response analysis of reinforced concrete structures using modified force analogy method

A modified force analogy method (MFAM) is developed to simulate the nonlinear inelastic response of reinforced concrete (RC) structures. Beam–column elements with three different plastic mechanisms are utilized to simulate inelastic response caused by moment and shear force. A multi‐linear hysteretic model is implemented to simulate the nonlinear inelastic response of RC member. The P‐Δ effect of the structure is also addressed in MFAM. Static and dynamic inelastic response of structure, damage condition and failure type for structural element, structural limit state and collapse time can also be simulated using MFAM. Compared with the general algorithm, the MFAM provides less computational time especially in the case of large structural system. It is also easier to be written as computer program. Three test data groups, which include cyclic loading test data of a non‐ductile RC bridge column, a two‐storey RC frame, and dynamic collapse test data of a non‐ductile RC portal frame, are selected to confirm the effectiveness of applying MFAM to simulate the inelastic behaviour of structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of performance of non‐invasive upgrade strategy for beam–column sub‐assemblages of poorly designed structures under seismic type loading

Beam–column sub‐assemblages are the one of the most vulnerable structural elements to the seismic loading and may lead to devastating consequences. In order to improve the performance of the poorly/under‐designed building structures to the critical loading scenarios, introduction of steel bracing at the RC beam–column joint is found to be one of the modern and implementable techniques. In the present work, a diagonal metallic single haunch/bracing system is introduced at the beam–column joints to provide an alternate load path and to protect the joint zone from extensive damage because of brittle shear failure. In this paper, an investigation is reported on the evaluation of tae influence of different parameters, such as angle of inclination, location of bracing and axial stiffness of the single steel bracing on improving the performance through altering the force transfer mechanism. Numerical investigations on the performance of the beam–column sub‐assemblages have been carried out under cyclic loading using non‐linear finite element analysis. Experimentally validated numerical models (both GLD and upgraded specimen) have been further used for evaluating the performance of various upgrade schemes. Cyclic behaviour of reinforcement, concrete modelling based on fracture energy, bond‐slip relations between concrete and steel reinforcement have been incorporated. The study also includes the numerical investigation of crack and failure patterns, ultimate load carrying capacity, load displacement hysteresis, energy dissipation and ductility. The findings of the present study would be helpful to the engineers to develop suitable, feasible and efficient upgrade schemes for poorly designed structures under seismic loading. Copyright © 2016 John Wiley & Sons, Ltd.     

Identification of the hysteretic behaviour of a partial‐strength steel–concrete moment‐resisting frame structure subject to pseudodynamic tests

In low‐rise steel‐concrete composite structures, moment‐resisting frames can be designed to develop a ductile response in beam‐to‐column joints and column bases by activating flexural yielding of beams and end plates, shear yielding of column web panel zones and yielding of anchors. To evaluate the performance of these components under differing earthquake intensities, a series of pseudodynamic, quasistatic cyclic and vibration tests were carried out on a two‐storey two‐bay moment resisting structure. The performance‐based seismic design and control of these structures requires that stiffness degradation, strength deterioration and slip are properly modelled. In this context, compact hysteretic models can play a key role and must therefore be striven for. Nonetheless, relevant techniques, like nonlinear system identification, are far from representing standard and reliable tools for the dynamic characterization of full‐scale structural systems. With this objective in mind, we present a restoring force surface‐based technique applied to pseudodynamic test data, in view of the nonlinear identification of multistorey frames. The technique is developed by means of a parametric approach, where a time‐variant stiffness operator is coupled to a modified Bouc–Wen model that allows both for slip and for degradation in stiffness. Strength deterioration is indirectly taken into account too. We also show how model‐based parameters can be correlated to the damage process progressively observed both in the structure and in its components. Finally, the predictive capabilities of the identified model are highlighted. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental and analytical studies on earthquake resisting behaviour of confined concrete block masonry structures

To improve the seismic performance of masonry structures, confined masonry that improves the seismic resistance of masonry structures by the confining effect of surrounding bond beams and tie columns is constructed. This study investigated the earthquake resisting behaviour of confined masonry structures that are being studied and constructed in China. The structural system consists of unreinforced block masonry walls with surrounding reinforced concrete bond beams and tie columns. The characteristics of the structure include: (1) damage to blocks is reduced and brittle failure is avoided by the comparatively lower strength of the joint mortar than that of the blocks, (2) the masonry walls and surrounding reinforced concrete bond beams and tie columns are securely jointed by the shear keys of the tie columns. In this study, wall specimens made of concrete blocks were tested under a cyclic lateral load and simulated by a rigid body spring model that models non‐linear behaviour by rigid bodies and boundary springs. The results of studies outline the resisting mechanism, indicating that a rigid body spring model is considered appropriate for analysing this type of structure. Copyright © 2006 John Wiley & Sons, Ltd.     

Modeling RC column flexural failure modes under intensive seismic loading

The aim of this work is to model beam‐column behavior in a computationally effective manner, revealing reliably the overall response of reinforced concrete members subjected to intensive seismic loading. In this respect, plasticity and damage are considered in the predominant longitudinal direction, allowing for fiber finite element modeling, while in addition the effect of inelastic buckling of longitudinal rebars, which becomes essential at later stages of intensive cyclic loading, is incorporated. Α smooth plasticity‐damage model is developed for concrete, accounting for unilateral compressive and tensile behavior, nonlinear unloading and crack closure phenomena. This is used to address concrete core crushing and spalling, which triggers the inelastic buckling of longitudinal rebars. For this reason, a uniaxial local stress‐strain constitutive relation for steel rebars is developed, which is based on a combined nonlinear kinematic and isotropic hardening law. The proposed constitutive model is validated on the basis of existing experimental data and the formulation of the buckling model for a single rebar is developed. The cross section of rebar is discretized into fibers, each one following the derived stress‐strain uniaxial law. The buckling curve is determined analytically, while equilibrium is imposed at the deformed configuration. The proposed models for concrete and rebars are embedded into a properly adjusted fiber beam‐column element of reinforced concrete members and the proposed formulation is verified with existing experimental data under intensive cyclic loading.     

Damage mechanics applied to performance‐based design of reinforced concrete columns

Performance‐based design methodology is based on reaching performance objectives that are associated to certain damage conditions. These performance objectives are related to the seismic hazard and to the performance levels. In actual application, reliable tools are required for capturing the evolution of the damage condition as well as for measuring and locating it. Moreover, it is essential to accurately establish the relationship between the damage and the performance levels. This paper shows the application of damage mechanics to performance‐based design. A layered damage mechanics‐based finite element program is presented with a discussion on modeling for prediction of the response of normal‐strength and high‐strength concrete columns subjected to cyclic flexural loading and various axial load levels. The damage indices derived from these analyses were used to elaborate several damage charts expressed as a function of drift and displacement ductility. This makes it possible to establish a relationship between the damage state and the performance levels. Results have demonstrated the ability of the damage mechanics modeling to accurately predict the behavior of the specimens tested. Copyright © 2017 John Wiley & Sons, Ltd.     

An efficient fiber beam-column element considering flexure–shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures

In this paper, a fiber beam-column element considering flexure–shear interaction and bond-slip effect is developed for cyclic analysis of reinforced concrete (RC) structures. The element is based on conventional displacement-based Timoshenko beam theory, where the transverse shear deformation is included, and adopts the fiber model to describe the section force–deformation behavior. In the fiber model, shear deformation is assumed to be uniformly distributed along the section and is only resisted by concrete, thus the multi-dimensional concrete damage model is used for concrete fibers and therefore flexure–shear interaction is reflected naturally at the material level. Meanwhile, to account for the significant bond-slip effect at critical regions, the anchorage slip of bars at these regions is analytically derived. Then it is used to modify the uniaxial stress–strain model for steel fibers by assuming that the total strain can be treated as the sum of the bar deformation and anchorage slip, therefore the bond-slip effect is implicitly but simply represented. To validate the proposed element, a series of RC member and structure tests under cyclic loading are simulated. The results indicate that the proposed element can predict cyclic responses of RC structures, and can be used as a reliable tool for analysis of RC structures.     

Modelling damage potential of high‐frequency ground motions

Damage to building structures due to underground blast‐induced ground motions is a primary concern in the corresponding determination of the safe inhabited building distance (IBD). Because of the high‐frequency nature of this category of ground motions and especially the presence of significant vertical component, the characteristics of structural response and damage differ from those under seismic type low‐frequency ground motions. This paper presents a numerical investigation aimed at evaluating reinforced concrete (RC) structure damage generated by underground blast‐induced ground excitation. In the numerical model, two damage indices are proposed to model reinforced concrete failure. A fracture indicator is defined to track the cracking status of concrete from micro‐ to macrolevel; the development of a plastic hinge due to reinforcement yielding is monitored by a plastic indicator; while the global damage of the entire structure is correlated to structural stiffness degradation represented by its natural frequency reduction. The proposed damage indices are calibrated by a shaking table test on a 1: 5‐scale frame model. They are then applied to analyse the structural damage to typical low‐ to high‐rise RC frames under blast‐induced ground motions. Results demonstrate a distinctive pattern of structural damage and it is shown that the conventional damage assessment methods adopted in seismic analysis are not applicable here. It is also found that the existing code regulation on allowable peak particle velocity of blast‐induced ground motions concerning major structural damage is very conservative for modern RC structures. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

橡胶集料风积沙混凝土柱抗震性能试验研究

为研究橡胶集料风积沙混凝土柱的抗震性能,制作了4根相同尺寸的混凝土柱试件,其中包括普通混凝土柱、风积沙混凝土柱、橡胶集料混凝土柱和橡胶集料风积沙混凝土柱。通过低周反复荷载试验,分析各试件的破坏现象、滞回曲线、骨架曲线、刚度退化和延性等抗震性能指标。在试验的基础上,根据能量耗散原理建立累积损伤评价模型,并对结构进行了累积损伤分析。研究结果表明:10%橡胶集料的掺入能够改善混凝土柱的变形能力,但混凝土柱的承载力有所降低;30%风积沙的掺入可以改善混凝土柱的抗震性能;橡胶集料风积沙混凝土柱具有较好的滞回性能,且耗能能力和延性性能明显高于其余试件,柱的抗震性能得到提高;通过累积损伤分析表明:适量掺入橡胶集料和风积沙的可以有效减缓试件的损伤,且该累积损伤模型能够较好的反映出各试件的损伤程度。     

Cyclic analysis and capacity prediction of concrete‐filled steel box columns

Concrete‐filled steel columns have been widely used in civil and architectural constructions throughout the world in recent years. This study is concerned with the cyclic elastoplastic analysis and capacity prediction of concrete‐filled steel columns having thick‐ and thin‐walled stiffened box‐shaped sections. An analytical procedure for determining the ultimate state of the concrete‐filled steel column is proposed based on the fiber analysis technique. Strength and ductility predictions are made by means of a new failure criterion. This is proposed based on the average failure strain of concrete and steel at critical regions. A recently developed monotonic stress–strain relation for confined concrete is modified so that it can be used in the analysis of thin‐ or thick‐walled section columns with stiffeners. A simple cyclic rule is introduced into this model in order to be used in cyclic analysis. Material non‐linearity of steel is represented by the modified two surface model developed at Nagoya University. The predictions are then compared with the existing experimental results and found to exhibit satisfactory agreement. Both small‐ and large‐scaled columns are considered in the comparisons. Copyright © 2001 John Wiley & Sons, Ltd.     

Three‐dimensional beam‐truss model for reinforced concrete walls and slabs – part 1: modeling approach,validation, and parametric study for individual reinforced concrete walls

A three‐dimensional beam‐truss model for reinforced concrete (RC) walls developed by the first two authors in a previous study is modified to better represent the flexure–shear interaction and more accurately capture diagonal shear failures under static cyclic or dynamic loading. The modifications pertain to the element formulations and the determination of the inclination angle of the diagonal elements. The modified beam‐truss model is validated using the experimental test data of eight RC walls subjected to static cyclic loading, including two non‐planar RC walls under multiaxial cyclic loading. Five of the walls considered experienced diagonal shear failure after reaching their flexural strength, while the other three walls had a flexure‐dominated response. The numerically computed lateral force–lateral displacement and strain contours are compared with the experimentally recorded response and damage patterns for the walls. The effects of different model parameters on the computed results are examined by means of parametric analyses. Extension of the model to simulate RC slabs and coupled RC walls is presented in a companion paper. Copyright © 2016 John Wiley & Sons, Ltd.     

往复荷载作用下锈蚀钢筋混凝土柱黏结滑移模型及数值模拟研究

为实现地震作用下锈蚀钢筋混凝土柱精细化数值模拟分析,基于已有研究成果建立往复荷载作用下锈蚀钢筋与混凝土间的黏结滑移本构模型:结合课题组前期试验结果,采用ABAQUS有限元分析软件对建立的黏结滑移本构模型进行有效性验证,通过对数值计算结果与试验结果之间误差分析,进一步对黏结滑移模型中的摩擦黏结应力系数和退化系数进行修正,最终建立更为合理的锈蚀钢筋与混凝土间黏结滑移本构模型。通过数值计算结果与试验结果的再次比较,验证修正后黏结滑移本构模型的有效性。结果表明:修正后的锈蚀钢筋与混凝土间黏结滑移模型可更好地反映往复荷载作用下锈蚀钢筋混凝土柱的滞回性能。该成果可为地震作用下锈蚀钢筋混凝土结构的数值分析计算提供理论参考。     

Cyclic behavior of precast segmental concrete bridge columns with high performance or conventional steel reinforcing bars as energy dissipation bars

The cyclic behavior of precast segmental concrete bridge columns with high performance (HP) steel reinforcing bars and that with conventional steel reinforcing bars as energy dissipation (ED) bars were investigated. The HP steel reinforcing bars are characterized by higher strength, greater ductility, and superior corrosion resistance compared with the conventional steel reinforcing bars. Three large‐scale columns were tested. One was designed with the HP ED bars and two with the conventional ED bars. The HP ED bars were fully bonded to the concrete. The conventional ED bars were fully bonded to the concrete for one column, whereas unbonded for a length to delay fracture of the bars and to increase energy dissipation for the other column. Test results showed that the column with the HP ED bars had greater drift capacity, higher lateral strength, and larger energy dissipation than that with fully bonded conventional ED bars. The column with unbonded conventional ED bars achieved the same drift capacity and similar energy dissipation capacity as that with the HP ED bars. All the three columns showed good self‐centering capability with residual drifts not greater than 0.4% drift. An analytical model referred to as joint bar‐slip rotation method for pushover analysis of segmental columns with ED bars is proposed. The model calculates joint rotation from the slip of the ED bars from two sides of the joint. Good agreement was found between analytical predictions and the envelope responses of the three columns. Copyright © 2010 John Wiley & Sons, Ltd.     

An experimental and numerical investigation on the cyclic response of a portal frame pier belonging to an old reinforced concrete viaduct

This paper deals with the assessment of the seismic response of a portal frame pier belonging to an old reinforced concrete viaduct. A series of tests, consisting of cyclically imposed displacements, were carried out on three 1:4 scale mock‐ups. The objective of the experimental campaign is twofold: (1) identification and evaluation of the local failure mechanisms and (2) calibration of a numerical model including all observed nonlinear phenomena. The experimental results show that the shear strength of the transverse beam and of the beam–column joints characterizes the post‐elastic behavior of the piers. Other phenomena, like bond‐slip and buckling of the longitudinal bars of the columns, typical of old reinforced concrete structures have also been observed. Finally, a numerical model, built in OpenSEES, was calibrated to reproduce in a satisfactory way the experimental results and to provide a reliable tool for the evaluation of the seismic response of the pier. Copyright © 2011 John Wiley & Sons, Ltd.