An efficient three‐dimensional solid finite element dynamic analysis of reinforced concrete structures

Most of the finite element analyses of reinforced concrete structures are restricted to two‐dimensional elements. Three‐dimensional solid elements have rarely been used although nearly all reinforced concrete structures are under a triaxial stress state. In this work, a three‐dimensional solid element based on a smeared fixed crack model that has been used in the past mainly for monotonic static loading analysis is extended to cater for dynamic analysis. The only material parameter that needs to be input for this model is the uniaxial compressive strength of concrete. Steel bars are modelled as uniaxial elements and an embedded formulation allows them to have any orientation inside the concrete elements. The proposed strategy for loading or unloading renders a numerical procedure which is stable and efficient. The whole process is applied to two RC frames and compared against existing experiments in the literature. Results show that the proposed approach may adequately be used to predict the dynamic response of a structure. Copyright © 2005 John Wiley & Sons, Ltd.     

Stiffened steel box columns. Part 1: Cyclic behaviour

This paper aims to study the cyclic inelastic behaviour of stiffened steel box columns failed by local and overall interaction instability under a constant compressive axial force and cyclic lateral loading. Such columns find broad application in steel bridge piers. The columns are of box sections with longitudinal stiffeners. In the analysis, a modified two‐surface plasticity model developed at Nagoya University is employed to model material non‐linearity. For comparison, analyses using classical isotropic‐ and kinematic‐hardening models are also carried out. Hysteretic curves and buckling modes obtained from analysis using the two‐surface model and classical models are compared with experimental results. Moreover, the progression of deformation from occurrence of local buckling to structural failure is discussed in detail. The comparisons show that the use of an accurate plasticity model is quite important in the prediction of both the cyclic inelastic behaviour and failure characteristic of steel box columns failed by coupled local and overall instability. It is found that the modified two‐surface model is a satisfactory model in predicting the cyclic hysteretic behaviour of both the thin‐ and thick‐walled steel box columns. Copyright © 2000 John Wiley & Sons, Ltd.     

Life‐cycle reliability of RC bridge piers under seismic and airborne chloride hazards

Over the last two decades, the probabilistic assessment of reinforced concrete (RC) structures under seismic hazard has been developed rapidly. However, little attention has been devoted to the assessment of the seismic reliability of corroded structures. For the life‐cycle assessment of RC structures in a marine environment and earthquake‐prone regions, the effect of corrosion due to airborne chlorides on the seismic capacity needs to be taken into consideration. Also, the effect of the type of corrosive environment on the seismic capacity of RC structures has to be quantified. In this paper, the evaluation of the displacement ductility capacity based on the buckling model of longitudinal rebars in corroded RC bridge piers is established, and a novel computational procedure to integrate the probabilistic hazard associated with airborne chlorides into life‐cycle seismic reliability assessment of these piers is proposed. The seismic demand depends on the results of seismic hazard assessment, whereas the deterioration of seismic capacity depends on the hazard associated with airborne chlorides. In an illustrative example, an RC bridge pier was modeled as single degree of freedom (SDOF). The longitudinal rebars buckling of this pier was considered as the sole limit state when estimating its failure probability. The findings show that the life‐cycle reliability of RC bridge piers depends on both the seismic and airborne chloride hazards, and that the cumulative‐time failure probabilities of RC bridge piers located in seismic zones can be dramatically affected by the effect of airborne chlorides. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite element analysis of damage and failure of reinforced concrete members under earthquake loading

This paper presents a three‐dimensional analysis framework, based on the explicit finite element method, for the simulation of reinforced concrete components under cyclic static and dynamic loading. A recently developed triaxial constitutive model for concrete is combined with a material model for reinforcing steel which can account for rupture due to low‐cycle fatigue. The reinforcing bars are represented with geometrically nonlinear beam elements to account for buckling of the reinforcement. The strain penetration effect is also accounted for in the models. The modeling scheme is used in a commercial finite element program and validated with the results of experimental static and dynamic tests on reinforced concrete columns and walls. The analyses are supplemented with a parametric study to investigate the impact of several modeling assumptions on the obtained results.     

Towards an optimum model for the response of reinforced concrete beams to cyclic loads

The paper describes the development of a mathematical model to predict the flexural response of reinforced concrete beams to severe cyclic loading. The model is constructed with the aid of System Identification, which permits the coefficients in it to be so tuned as to replicate with the maximum possible accuracy the results of physical experiments. The uniaxial constitutive behaviour of the concrete and steel are considered separately, and they are then combined through a bond-slip relationship to form a global model for the composite material. The cyclic stress-strain law for the steel proves to be critical to the overall accuracy, and a suitable formulation is developed for it. Comparisons between observed and predicted behaviour are presented, both for the steel alone and for the composite material.     

锈蚀钢筋混凝土圆柱抗震性能的试验研究

对不同锈蚀程度的钢筋混凝土圆柱进行低周反复试验,研究了不同轴压比下的钢筋锈蚀率对钢筋混凝土圆柱滞回曲线、骨架曲线、刚度、延性及耗能能力的影响;给出了试件累积耗能、屈服荷载、极限荷载、荷载最大值和位移延性系数与钢筋锈蚀率和轴压比的关系。研究表明,随着钢筋锈蚀率和轴压比的增大,试件的滞回曲线趋于干瘪,骨架曲线下降段变陡,试件的刚度、延性和耗能能力减小。     

A new modelling strategy for the behaviour of shear walls under dynamic loading

A new simplified modelling strategy to simulate the non‐linear behaviour of reinforced concrete shear walls under dynamic loading is presented. The equivalent reinforced concrete (ERC) model is derived from the framework method and uses lattice meshes for concrete and reinforcement bars and uniaxial constitutive laws based on continuum damage mechanics and plasticity. Results show the capacity of the model to analyse structures having different slenderness and boundary conditions. For low reinforcement ratios however, results are sensitive to the angle formed by the diagonals of the concrete lattice and the horizontal bars. The method is compared with the shear multi‐layered beam model that uses Timoshenko multi‐layered 2D beam elements and biaxial constitutive laws. Comparisons for both models with experimental results of two research programs (one organized by NUPEC and the other by COGEMA and EDF) are provided. ERC is a simplified method that intends to save computer time and allows parametrical studies. Copyright © 2002 John Wiley & Sons, Ltd.     

A distributed shear and flexural flexibility model with shear–flexure interaction for R/C members subjected to seismic loading

A beam–column‐type finite element for seismic assessment of reinforced concrete (R/C) frame structures is presented. This finite element consists of two interacting, distributed flexibility sub‐elements representing inelastic flexural and shear response. Following this formulation, the proposed model is able to capture spread of flexural yielding, as well as spread of shear cracking, in R/C members. The model accounts for shear strength degradation with inelastic curvature demand, as well as coupling between inelastic flexural and shear deformations after flexural yielding, observed in many experimental studies. An empirical relationship is proposed for evaluating the average shear distortion of R/C columns at the onset of stirrup yielding. The proposed numerical model is validated against experimental results involving R/C columns subjected to cyclic loading. It is shown that the model can predict well the hysteretic response of R/C columns with different failure modes, i.e. flexure‐critical elements, elements failing in shear after flexural yielding, and shear‐critical R/C members. Copyright © 2008 John Wiley & Sons, Ltd.     

Fiber-based hysteretic model for simulating strength and stiffness deterioration of steel hollow structural section columns under cyclic loading

An efficient component model has been developed that captures strength and stiffness deterioration of steel hollow structural section (HSS) columns. The proposed model consists of two fiber-based segments at a member's ends along with an elastic segment in between. The fibers exhibit nonlinear uniaxial stress–strain behavior, which is explicitly defined by uniaxial monotonic tensile and cyclic round coupon tests. The postbuckling behavior of an HSS column is traced through a proposed uniaxial effective stress–strain constitutive formulation, which includes a softening branch in compression and an energy-based deterioration rule to trace the influence of cyclic deterioration in the inelastic cyclic straining. These may be inferred by uniaxial stub-column tests. The component model captures the coupling between the column axial force and flexural demands. Consistent model parameters for a number of steel materials used in the steel construction in North America and Japan are proposed along with the associated model calibration process. The efficiency of the proposed model in predicting the hysteretic behavior of HSS columns is demonstrated by comparisons with physical steel column tests subjected to various loading histories, including representative ones of ratcheting prior to earthquake-induced collapse. The proposed model is implemented in an open-source finite element software for nonlinear response history analysis of frame structures. The effectiveness of the proposed model in simulating dynamic instability of steel frame buildings is demonstrated through nonlinear response simulations of a four-story steel frame building, which was tested at full-scale through collapse. Limitations as well as suggestions for future work are discussed.     

FRP（钢绞线）加筋混凝土梁正截面受弯承载力计算

纤维增强复合筋、不锈钢绞线等高强材料作为混凝土梁的受力筋可以充分发挥强度高、耐腐蚀性能好等优点,在土木工程中得到了广泛应用。为了分析此类高强材料加筋混凝土梁的受弯性能,在平截面假定基础上,对混凝土和受力纵筋分别采用混凝土Hongnestad模型和线弹性模型,通过平衡条件,推导了FRP（钢绞线）加筋混凝土梁受弯承载力的计算公式,并与国内外82根简支梁的试验结果进行了对比。研究结果表明：加筋混凝土梁抗弯强度试验值与理论值之比的平均值为1.07,标准差为0.14。建议公式可以较好地计算FRP（钢绞线）加筋混凝土梁的受弯承载力。实际工程构件抗弯截面设计时,建议安全配筋率取1.4倍平衡配筋率,设计截面弯矩取0.625倍理论受弯承载力,以使构件具有足够安全储备。     

Experimental evaluation of rectangular reinforced concrete column behaviour under biaxial cyclic loading

The cyclic behaviour of reinforced concrete columns has been the subject of many experimental studies in recent years. However, most of these studies have focused on the unidirectional loading of columns with square cross‐sections under constant axial loading conditions. In the present study, four types of full‐scale quadrangular building columns were tested under different types of loading, including uniaxial and biaxial loading conditions. The first two specimens of each column type were independently cyclically tested in the strong and weak directions. Bidirectional tests using different loading paths were performed on the other column specimens. All columns were tested under constant axial loading conditions. In this paper, the experimental results are presented, and the global behaviour of tested columns is discussed, particularly focusing on the stiffness and strength degradation because of the increasing cyclic demand. Finally, the deformation‐based performance limits proposed in Part 3 of Eurocode 8 were calculated and compared with the experimental results. Copyright © 2012 John Wiley & Sons, Ltd.     

GFRP筋混凝土梁耐火性能的试验研究

进行了4根GFRP筋混凝土简支梁在ISO834标准升温曲线下的火灾实验,试件依据ACI440.1R-06进行截面设计,分别考虑了不同荷载比、保护层厚度、端部锚固方式对梁耐火性能的影响。试验结果表明,GFRP筋混凝土梁在火灾中的裂纹开展深度较传统的钢筋混凝土结构明显偏大。由于GFRP筋横向膨胀大更易造成梁底混凝土的开裂与剥落,建议在满足纵筋锚固性能要求的前提下,尽量减少端部J型锚固筋。GFRP筋在高温下的材料性能衰减严重,合理的设计保护层厚度和限制GFRP筋的使用内力,可使GFRP筋混凝土梁的耐火性能满足实际工程的需要。     

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Evaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.     

FIBRE BEAM–COLUMN MODEL FOR NON-LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION

This paper presents a fibre beam–column element for the non-linear static and dynamic analysis of reinforced concrete frames. It is assumed that plane sections remain plane and normal to the longitudinal axis. The effects of shear and bond-slip are, thus, presently neglected. The non-linear hysteretic behaviour of the element derives from the constitutive relations of concrete and reinforcing steel fibres into which each section is divided. The element formulation is flexibility-based and relies on force interpolation functions that strictly satisfy the equilibrium of bending moments and axial force along the element. Since the element does not make use of displacement interpolation functions, an iterative algorithm is needed for the determination of the resisting forces during the element state determination. The proposed algorithm is accurate and stable, even in the presence of strength loss, and is, thus, capable of tracing very well the highly non-linear behaviour of R/C members under cyclic load combinations of bending moment and axial force.     

Reinforced concrete hysteresis model based on the damage concept

Reinforced concrete members subjected to cyclic inelastic deformation may exhibit both stiffness and strength degradation, depending on the maximum amplitude and the number of cycles experienced by the member. Many of the currently available models do not simulate the cycle-dependent stiffness loss often observed during the experiments. An analytical model based on a damage parameter which is a function of the cumulative cyclic inelastic deformation is proposed. A small-scale reinforced concrete beam–column joint was constructed and subjected to cyclic loading to calibrate the damage parameter. The model is able to approximate the complete hysteretic response and is simple to implement. The sensitivity of the analytical model was examined by comparing the model with several experimental results.     

Static inelastic analysis of RC shear walls

A macro-model of a reinforced concrete (RC) shear wall is developed for static inelastic analysis. The model is composed of RC column elements and RC membrane elements. The column elements are used to model the boundary zone and the membrane elements are used to model the wall panel. Various types of constitutive relationships of concrete could be adopted for the two kinds of elements. To perform analysis, the wall is divided into layers along its height. Two adjacent layers are connected with a rigid beam. There are only three unknown displacement components for each layer. A method called single degree of freedom compensation is adopted to solve the peak value of the capacity curve. The post-peak stage analysis is performed using a forced iteration approach. The macro-model developed in the study and the complete process analysis methodology are verified by the experimental and static inelastic analytical results of four RC shear wall specimens. Supported by: National Natural Science Foundation of China, Grant number 59895410     

Performance of composite steel/concrete members under earthquake loading. Part I: Analytical model

This paper presents an advanced non-linear model developed for the analysis of composite steel/concrete frame structures subjected to cyclic and dynamic loads. The formulation consists of beam-column cubic finite elements accounting for geometric non-linearities and material inelasticity. The non-linear cyclic concrete model considers confinement effects and the constitutive relationship for steel includes the effect of local buckling and variable amplitude cyclic degradation. The model is calibrated and compared with experimental data from cyclic and pseudo-dynamic tests conducted by the writers on a new ductile partially-encased composite beam-column. The accuracy and efficiency of the developed model are demonstrated through the correlation between the experimental results and analytical simulations. In a companion paper, the model is used to conduct parametric studies leading to important conclusions for ductility-based earthquake-resistant design.     

A regularized fiber element model for reinforced concrete shear walls

Reinforced concrete shear walls are used because they provide high lateral stiffness and resistance to extreme seismic loads. However, with the increase in building height, these walls have become slenderer and hence responsible of carrying larger axial and shear loads. Because 2D/3D finite element inelastic models for walls are still complex and computationally demanding, simplified but accurate and efficient fiber element models are necessary to quickly assess the expected seismic performance of these buildings. A classic fiber element model is modified herein to produce objective results under particular loading conditions of the walls, that is, high axial loads, low axial loads, and nearly constant bending moment. To make it more widely applicable, a shear model based on the modified compression field theory was added to this fiber element. Consequently, this paper shows the formulation of the proposed element and its validation with different experimental results of cyclic tests reported in the literature. It was found that in order to get objective responses in the element, the regularization techniques based on fracture energy had to be modified, and nonlinearities because of buckling and fracture of steel bars, concrete crushing, and strain penetration effects were needed to replicate the experimental cyclic behavior. Thus, even under the assumption of plane sections, which makes the element simple and computationally efficient, the proposed element was able to reproduce the experimental data, and therefore, it can be used to estimate the seismic performance of walls in reinforced concrete buildings. Copyright © 2016 John Wiley & Sons, Ltd.     

Earthquake response of concrete arch dams: a plastic–damage approach

There are several alternatives to evaluate seismic damage‐cracking behavior of concrete arch dams, among which damage theory is the most popular. A more recent option introduced for this purpose is plastic–damage (PD) approach. In this study, a special finite element program coded in 3‐D space is developed on the basis of a well‐established PD model successfully applied to gravity dams in 2‐D plane stress state. The model originally proposed by Lee and Fenves in 1998 relies on isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to capture inelastic behaviors of concrete in cyclic or dynamic loadings. The present implementation is based on the rate‐dependent version of the model, including large crack opening/closing possibilities. Moreover, with utilizing the Hilber–Hughes–Taylor time integration scheme, an incremental–iterative solution strategy is detailed for the coupled dam–reservoir equations while the damage–dependent damping stress is included. The program is initially validated, and then, it is employed for the main analyses of the Koyna gravity dam in a 3‐D modeling as well as a typical concrete arch dam. The former is a major verification for the further examination on the arch dam. The application of the PD model to an arch dam is more challenging because the governing stress condition is multiaxial, causing shear damage to become more important than uniaxial states dominated in gravity dams. In fact, the softening and strength loss in compression for the damaged regions under multiaxial cyclic loadings affect its seismic safety. Copyright © 2013 John Wiley & Sons, Ltd.