Estimation of monotonic behavior of reinforced concrete columns considering shear‐flexure‐axial load interaction

Reinforced concrete columns with insufficient transverse reinforcement and non‐seismic reinforcement details are vulnerable to brittle shear failure and to loss of axial load carrying capacity in the event of a strong earthquake. In this paper, a procedure is presented after examining the application of two macro models for displacement‐based analysis of reinforced concrete columns subjected to lateral loads. In the proposed model, lateral load‐deformation response of the column is simulated by estimating flexural and shear deformation components separately while considering their interaction and then combining these together according to a set of rules depending upon column's yield, flexural and shear strengths. In addition, lateral deformation caused by reinforcement slip in beam–column joint regions and buckling of compression bars are taken into account and considered in the analysis. Implementation of the proposed procedure produces satisfactory lateral load–displacement relationships, which are comparable with experimental data. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Experimental investigation of damage behavior of RC frame members including non-seismically designed columns

Reinforced concrete (RC) frame structures are one of the mostly common used structural systems, and their seismic performance is largely determined by the performance of columns and beams. This paper describes horizontal cyclic loading tests often column and three beam specimens, some of which were designed according to the current seismic design code and others were designed according to the early non-seismic Chinese design code, aiming at reporting the behavior of the damaged or collapsed RC frame strctures observed during the Wenchuan earthquake. The effects of axial load ratio,shear span ratio, and transverse and longitudinal reinforcement ratio on hysteresis behavior, ductility and damage progress were incorporated in the experimental study. Test results indicate that the non-seismically designed columns show premature shear failure, and yield larger maximum residual crack widths and more concrete spalling than the seismically designed columns. In addition, longitudinal steel reinforcement rebars were severely buckled. The axial load ratio and shear span ratio proved to be the most important factors affecting the ductility, crack opening width and closing ability, while the longitudinal reinforcement ratio had only a minor effect on column ductility, but exhibited more influence on beam ductility. Finally, the transverse reinforcement ratio did not influence the maximum residual crack width and closing ability of the seismically designed columns.     

Cyclic behaviour of interior beam–column joints reinforced with plain bars

The seismic damages commonly observed on beam–column joints of old reinforced concrete structures, built with plain bars and without proper detailing, justifies the need to further study the behaviour of this type of structures. The response of these structures when loaded cyclically, as occurs during the earthquakes, is partially controlled by the bond properties between the reinforcing bars and the surrounding concrete. This paper presents the results of an experimental campaign of unidirectional cyclic tests carried out on six full‐scale beam–column joints built with plain bars. These joint specimens are representative of existing reinforced concrete structures, that is, built without adequate reinforcement detailing for seismic demands. For comparison, an additional specimen is built with deformed bars and tested. The seven specimens are designed and detailed to allow the investigation of the influence of bond properties, lapping of the longitudinal bars in columns and beams, bent‐up bars in the beams, slab contribution and concrete strength. The lateral force–drift relationships, global dissipated energy evolution, contribution of the joint, beams and columns to the global dissipated energy, ductility, equivalent damping, final damage observed, homogenized reinforced concrete damage index, displacement components, curvature evolutions and Eurocode requirements are presented and discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

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.     

T形配钢钢骨混凝土柱抗震性能数值分析

为研究非对称配钢钢骨混凝土柱的抗震性能,基于12根T形配钢钢骨混凝土柱的拟静力试验研究进行非线性数值模拟,了解其破坏机制、承载力、延性及耗能能力,探讨轴压比、配钢率、剪跨比对抗震性能的影响。结果表明,低周反复荷载作用下T形配钢钢骨混凝土柱滞回曲线饱满,具有良好的延性和耗能能力。在峰值荷载前,数值模拟结果与试验结果吻合较好。轴压力在一定范围内提高了试件承载力,但降低了延性;增大配钢率能提高试件的承载力、刚度和延性,使得峰值荷载后试件的性能退化趋于平缓;剪跨比对试件破坏形态有显著影响,随剪跨比的增大试件延性性能提高。     

Rehabilitation of earthquake damaged external RC beam‐column joints by joint enlargement using prestressed steel angles

The effectiveness of a rehabilitation method based on joint enlargement using prestressed steel angles to enhance the seismic behavior of damaged external reinforced concrete beam‐column joints was experimentally investigated. Three half‐scale joints having either non‐seismic or seismic reinforcement details were tested both before and after rehabilitation by applying lateral cyclic loading of increasing amplitudes. Two defects were considered for the two non‐seismic units, being the absence of transverse steel hoops and insufficient bond capacity of beam bottom steel reinforcing bars in the joint panel zone. The damaged specimens were rehabilitated by injecting epoxy grout into existing cracks and installing stiffened steel angles at the re‐entrant corners of the beam‐column joint, both above and below the beam, that were mounted and held in place using prestressed high‐tensile strength bars. The test results indicated that the seismic performance of the rehabilitated specimens in terms of strength, stiffness, and ductility was fully recovered and comparable with the performance of the seismically detailed specimen. Copyright © 2016 John Wiley & Sons, Ltd.     

Cyclic loading test of self-centering precast segmental unbonded posttensioned UHPFRC bridge columns

Three 1/3-scale precast segmental bridge columns, manufactured with ultrahigh-performance fiber-reinforced concrete (UHPFRC) incorporating river sand and coarse aggregate, were tested under cyclic loading. Energy dissipation (ED) bars, embedded in ultrahigh-performance concrete (UHPC) grout, maintained continuous across segment joints and unbonded at the bottom joint. Self-centering prestressing force was provided by unbonded posttensioning (PT) tendons. The research parameters included PT force level and the amount of ED bars. Test results showed that all the specimens exhibited no less than 8% drift capacities, which were remarked with the first fracture of ED bars. No obvious cracking and limited UHPFRC spalling were observed. Both PT force level and the amount of ED bars have notable effects on stiffness, lateral strength, and ductility. Increased PT force may improve ductility with the total axial loading ratio less than 0.08. All PT tendons were elastic and no yield or rupturing was found, but the stress loss was significant. The equivalent unbonded length can be evaluated with 0.007d_bf_y for ED bars embedded in UHPC grout. The rotation of the bottom joint dominated lateral deformation and the contribution of joint sliding can be neglected. The contribution λ_ED of ED bars to lateral strength should be no more than 25% to maintain self-centering capacity.     

Prediction of the force–drift envelope for RC columns in flexure by the CAE method

A non‐parametric empirical approach, called the conditional average estimator (CAE) method, has been applied for the prediction of the normalized lateral force–drift envelope of reinforced concrete (RC) rectangular columns, as well as their characteristic drifts (effective yield drift, capping drift and ultimate drift), and drift‐related parameters (the ratio between the effective yield drift and elastic drift, and two ductility measures). A subset of the PEER RC column database was used. Five input parameters were employed: axial load index, index related to confinement, shear span index, concrete compressive strength, and longitudinal reinforcement index. The results suggest that the relations between the input and output parameters are complex, and that it is difficult to isolate the influence of a single parameter. Nevertheless, some trends were observed. The axial load index is the most influential input parameter. All the results decrease with an increasing axial load index, whereas they increase with an increasing longitudinal reinforcement index. An increase in the index related to confinement results in increases in the ultimate drift and in ductility. The influence of the shear span index is the most complex. The influence of the concrete strength is small with the exception of two output parameters related to elastic drift, which substantially decrease with increasing strength. The dispersion of the results is relatively large. The results of the predictions can be used for mathematical modelling of moment–rotation backbone curves for plastic hinges, and for the estimation of the deformation capacity of columns in seismic performance assessments. Copyright © 2007 John Wiley & Sons, Ltd.     

Recent progress of seismic research on tall buildings in China Mainland

To study the seismic behavior of high strength concrete fi lled double-tube(CFDT) columns,each consisting of an external square steel tube and an internal circular steel tube,quasi-static tests on eight CFDT column specimens were conducted.The test variables included the width-to-thickness ratio(β1) and the area ratio(β2) of the square steel tube,the wall thickness of the circular steel tube,and the axial force(or the axial force ratio) applied to the CFDT columns.The test results indicate that for CFDT columns with a square steel tube with β1 of 50.1 and 24.5,local buckling of the specimen was found at a drift ratio of 1/150 and 1/50,respectively.The lateral force-displacement hysteretic loops of all specimens were plump and stable.Reducing the width-to-thickness ratio of the square steel tube,increasing its area ratio,or increasing the wall thickness of the internal circular steel tube,led to an increased fl exural strength and deformation capacity of the specimens.Increasing the design value of the axial force ratio from 0.8 to 1.0 may increase the fl exural strength of the specimens,while it may also decrease the ultimate deformation capacity of the specimen with β1 of 50.1.     

Discrete‐like crack simulation by smeared crack‐based FEM for reinforced concrete

A numerical process that simulates crack propagation in reinforced concrete through post‐crack stress redistribution is presented. This process is developed within the context of the smeared crack approach. Continuity and orientation of the reinforcing bar components are automatically recognized in the pre‐processing stage. The process explicitly outputs crack widths by computing the bond slips along reinforcement, without imposing any additional nodes between the reinforcement and concrete. The process is incorporated with a finite element algorithm, and the validation is investigated through sample 3D static analyses of nine concrete specimens subjected to monotonic shear and flexure loads. These specimens contain relatively well‐distributed steel bars and fiber reinforced polymer (FRP) sheets of reinforcement ratio from 0.11 to 0.57%. The analyses predict the crack patterns and crack widths well, although some disagreements are found between the test and the analysis results. The proposed process outputs discrete, continuous in crack directions, and element boundary‐free crack patterns. Copyright © 2007 John Wiley & Sons, Ltd.     

Critical response of structures to multicomponent earthquake excitation

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are defined along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is defined as the largest value of response for all possible incident angles. The ratio r_cr/r_srss between the critical value of response and the SRSS response—corresponding to the principal components of ground acceleration applied along the structure axes—is shown to depend on three dimensionless parameters: the spectrum intensity ratio γ between the two principal components of horizontal ground motion characterized by design spectra A(T_n) and γA(T_n); the correlation coefficient α of responses r_x and r_y due to design spectrum A(T_n) applied in the x‐ and y‐directions, respectively; and β = r_y/r_x. It is demonstrated that the ratio r_cr/r_srss is bounded by 1 and . Thus the largest value of the ratio is , 1.26, 1.13 and 1.08 for γ = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of γ, say 0.75. The correlation coefficient α depends on the structural properties but is always bounded between −1 and 1. For a fixed value of γ, the ratio r_cr/r_srss is largest if β = 1 and α = ±1. The parametric variations presented for one‐storey buildings indicate that this condition can be satisfied by axial forces in columns of symmetric‐plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical‐plan buildings. Copyright © 2000 John Wiley & Sons, Ltd.     

Seismic behavior and strength capacity of steel tube‐reinforced concrete composite columns

The steel tube‐reinforced concrete (ST‐RC) composite column is a novel type of composite column, which consists of a steel tube embedded in RC. In this paper, the seismic behavior of ST‐RC columns is examined through a series of experiments in which 10 one‐third scale column specimens were subjected to axial forces and lateral cyclic loading. The test variables include the axial force ratio applied to the columns and the amount of transverse reinforcement. All specimens failed in a flexural mode, showing stable hysteresis loops. Thanks to the steel tube and the high‐strength concrete it is filled with, the ST‐RC column specimens had approximately 30% lower axial force ratios and 22% higher maximum bending moments relative to the comparable RC columns when subjected to identical axial compressive loads. The amount of transverse reinforcement made only a small difference to the lateral load‐carrying capacity but significantly affected the deformation and energy dissipation capacity of the ST‐RC columns. The specimens that satisfied the requirements for transverse reinforcement adopted for medium ductile RC columns as specified by the Chinese Code for Seismic Design of Buildings (GB 50011‐2010) and EuroCode 8 achieved an ultimate drift ratio of around 0.03 and a displacement ductility ratio of approximately 5. The design formulas used to evaluate the strength capacity of the ST‐RC columns were developed on the basis of the superposition method. The predictions from the formulas showed good agreement with the test results, with errors no greater than 10%. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of boundary element details on the seismic deformation capacity of structural walls

The objective of this study is to investigate the effect of boundary element details of structural walls on their deformation capacities. Structural walls considered in this study have different sectional shapes and/or transverse reinforcement content at the boundaries of the walls (called boundary element details hereafter). Four full‐scale wall specimens (3000mm (h_w)×1500mm (l_w)×200mm (T)) were fabricated and tested. Three specimens are rectangular in section and the other specimen has a barbell‐shaped cross‐section (a wall with boundary columns). The rectangular wall specimens are reinforced according to the common practice used for reinforced concrete residence buildings in Korea and Chile. In this study, the primary variable for these rectangular specimens is the content of transverse reinforcement to confine the boundary elements of a wall. The barbell‐shaped specimen was designed in compliance with ACI 318‐95. The response of the barbell‐shaped specimen is compared with those of other rectangular specimens. The effective aspect ratio of the specimens is set to two in this study. Based on the experimental results, it is found that the deformation capacities of walls, which are represented by displacement ductility, drift ratio and energy dissipation capacities, are affected by the boundary element details. Copyright © 2002 John Wiley & Sons, Ltd.     

Seismic vulnerability evaluation of axially loaded steel built-up laced members Ⅱ： evaluations

The test results described in Part 1 of this paper （Lee and Bruneau, 2008） on twelve steel built-up laced members （BLMs） subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller kl/r were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger kl/r could meet the ductility demand in most cases. The normalized energy dissipation ratio, EC/ET and the normalized compressive strength degradation, Cr″/Cr of BLMs typically decrease as normalized displacements δ/δb,exp increase, and the ratios for specimens with larger kl/r dropped more rapidly than for specimens with smaller kl/r; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, kl/r, and width-to-thickness ratio, b/t, experienced a larger number of inelastic cycles than those with larger ratios.     

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.     

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.     

Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

Estimation of seismic demands on isolators in asymmetric buildings using non‐linear analysis

A procedure based on rigorous non‐linear analysis is presented that estimates the peak deformation among all isolators in an asymmetric building due to strong ground motion. The governing equations are reduced to a form such that the median normalized deformation due to an ensemble of ground motions with given corner period T_d depends primarily on four global parameters of the isolation system: the isolation period T_b, the normalized strength η, the torsional‐to‐lateral frequency ratio Ω_θ, and the normalized stiffness eccentricity e_b/r. The median ratio of the deformations of the asymmetric and corresponding symmetric systems is shown to depend only weakly on T_b, η, and Ω_θ, but increases with e_b/r. The equation developed to estimate the largest ratio among all isolators depends only on the stiffness eccentricity and the distance from the center of mass to the outlying isolator. This equation, multiplied by an earlier equation for the deformation of the corresponding symmetric system, provides a design equation to estimate the deformations of asymmetric systems. This design equation conservatively estimates the peak deformation among all isolators, but is generally within 10% of the ‘exact’ value. Relative to the non‐linear procedure presented, the peak isolator deformation is shown to be significantly underestimated by the U.S. building code procedures. Copyright © 2003 John Wiley & Sons, Ltd.