Hysteretic Model for Flexure-shear Critical Reinforced Concrete Columns

A model for predicting the cyclic lateral load-deformation response of flexure-shear critical reinforced concrete (RC) columns subjected to combined axial load and cyclic shear is proposed. Strength deterioration in the primary curve due to the effect of shear after yielding is considered by a modification coefficient. Rules for unloading and reloading branches of the hysteretic curve are obtained from regression analysis of test results. Unloading stiffness is fitted as a function of displacement ductility and secant stiffness of the point with maximum displacement in the primary curve. Pinching is simulated by changing the slope of reloading branch. Path-based cyclic strength deterioration is incorporated in the proposed model. In the expression of cyclic strength deterioration, the effects of aspect ratio and axial-load ratio are considered. Comparison between the predicted cyclic response and experimental results indicates that the proposed model can predict the observed hysteretic response of flexure-shear critical RC columns well.     

Experimental Study on Damage Behavior of Reinforced Concrete Shear Walls Subjected to Cyclic Loads

Previous experimental research on shear walls has mainly focused on load carrying capacity, deformation, or hysteretic characteristics, with relatively little attention paid to individual damage states and their corresponding responses during the entire loading process until failure. The damage behavior of seven reinforced concrete shear wall specimens subjected to cyclic loading is presented in this study. The effects of the axial load ratio, transverse reinforcement ratio of confining boundary elements, and cross-section shape on damage characteristics, ductility, shear deformation, and crack width of the specimens were analyzed comprehensively.     

REHABILITATION OF REINFORCED CONCRETE COLUMNS USING CORRUGATED STEEL JACKETING

An experimental investigation was conducted to study the failure mode of existing reinforced concrete columns designed during the 1960s. The effectiveness of using corrugated steel jackets for enhancing the seismic flexural strength and ductility of these types of columns was examined. Three large-scale columns were tested under cyclic loading. The three columns represent existing column, current code-detailed column and rehabilitated column. The variables in the test specimens include the amount of column transverse reinforcement and jacketing of the column. The corrugated jacket was found to be effective in the rehabilitation of the selected existing structure, which does not meet the current seismic code requirements. A method is proposed for the design of the corrugated steel jacket to enhance the lap splice capacity and ductility of the column.     

Development and Seismic Behavior of Precast Concrete Beam-to-Column Connections

A new precast concrete beam-to-column connection for moment-resisting frames was developed in this study. Both longitudinal bar anchoring and lap splicing were used to achieve beam reinforcement continuity. Three full-scale beam-to-column connections, including a reference monolithic specimen, were investigated under reversal cyclic loading. The difference between the two precast specimens was the consideration of additional lap-splicing bars in the calculation of moment-resisting strength. Seismic performance was evaluated based on hysteretic behavior, strength, ductility, stiffness, and energy dissipation. The plastic hinge length of the specimens is also discussed. The results show that the proposed precast system performs satisfactorily under reversal cyclic loading compared with the monolithic specimen, and the additional lap-splicing bars can be included in the strength calculation using the plane cross-section assumption. Furthermore, the plastic hinge length of the proposed precast beam-to-column connection can be estimated using the models for monolithic specimens.     

IDENTIFICATION AND VERIFICATION OF SEISMIC DEMAND FROM DIFFERENT HYSTERETIC MODELS

The goal of this paper is to develop a modified Bouc-Wen hysteretic model from cyclic loading test data for reinforced columns, including the behavior of stiffness degradation, strength deterioration, pinching and softening effects of RC members. Seismic demands on this inelastic single degree of freedom system when subjected to both near-fault ground motion and far-field ground motion excitations were examined.

The cyclic loading test of reinforced concrete columns was experimentally observed and a system identification computer program was developed to solve each control parameter of the hysteretic model. A least-squared method for identifying parameters of the model is proposed in this paper. The hysteretic constitutive law produces a smoothly varying hysteresis such as the control-parameters for strength deterioration, stiffness degradation, pinching and softening effects. Two implementations of (1) flexure damage and (2) shear damage were conducted to provide better understanding of hysteretic behavior of RC structural members. A pseudo-dynamic experiment was also developed to verify the model parameters.

Based on the developed hysteretic model, the seismic demand of this inelastic model was investigated by using both near-fault ground motion data and far-field ground motion data as input motion. An R-μT inelastic response spectrum from different hysteretic models was generated.     

Experimental Investigation of Circular Reinforced Concrete Columns under Different Loading Histories

Three reinforced concrete (RC) circular column specimens without an effective concrete cover were tested under constant axial compressive as well as cyclic lateral loading. The seismic behavior of the specimens under different loading paths was examined with the objective of understanding the influence of displacement history sequence on the seismic behavior of the columns in near-fault earthquakes. The influence of displacement history sequence upon the hysteretic characteristics, stiffness degradation, lateral capacity, as well as energy dissipation analysis was conducted. The hoop strains of lateral reinforcement at varied column heights under cyclic loading were attained by means of 8–16 strain gauges attached along the hoops. Additionally, the characteristics of strain distribution were investigated in the transverse reinforcement. The results of strain distribution were evaluated with Mander’s confinement stress model and the distribution around the cross section. The length of the plastic hinge at the end of the specimen was evaluated by measurement as well as the inverse analysis. Finally, the deformation of the specimen, which includes the components of shear deformation, bending deformation and bonding-slip deformation, was evaluated and successfully separated.     

SEISMIC REHABILITATION OF SHORT RECTANGULAR RC COLUMNS

Non-ductile response of structural elements, particularly columns, has been the cause of numerous documented failures during earthquakes. The objective of this experimental study was to evaluate the non-linear behaviour of non-ductile reinforced concrete short columns under lateral cyclic deformations and to evaluate rehabilitation schemes. Three reinforced concrete short columns were tested under cyclic lateral loads and constant axial load. The behaviour and effectiveness of different rehabilitation systems using carbon fibre reinforced polymers (CFRP) were investigated. Two different techniques to improve concrete confinement were used in the two rehabilitated specimens. It was found that it is possible to eliminate the non-ductile modes of failure of short column using anchored CFRP wraps. In addition, an analytical model to predict the confining effect and the total shear resistance of rectangular reinforced concrete columns with anchored fibre wraps was introduced. The confinement model is an extension to an available model for concrete confined by steel reinforcement. The model was used to predict the shear capacity of the tested specimens and has shown good results.     

A FIBRE FINITE BEAM ELEMENT WITH SECTION SHEAR MODELLING FOR SEISMIC ANALYSIS OF RC STRUCTURES

The paper describes the formulation of a non-linear, two-dimensional beam finite element with bending, shear and axial force interaction for the static and dynamic analysis of reinforced concrete structures. The hysteretic behaviour of “squat” reinforced concrete members, in which the interaction between shear and flexural deformation and capacity is relevant for the overall structural performance, is emphasised. The element is of the distributed inelasticity type; section axial-flexural and shear behaviours are integrated numerically along the element length using a new equilibrium-based approach. At section level a “hybrid” formulation is proposed: the axial-flexural behaviour is obtained using the classic fibre discretisation and the plane sections remaining plane hypothesis, the shear response instead is identified with a non-linear truss model and described with a hysteretic stress-strain relationship. The latter contains a damage parameter, dependent on flexural ductility, that provides interaction between the two deformation mechanisms. The element has been implemented into a general-purpose finite element code, and is particularly suitable for seismic time history analyses of frame structures. Analytical results obtained with the model are compared with recent experimental data.     

Quasi-Static Testing of RC Infilled Frames and Confined Stone-Concrete Bearing Walls

This article presents an experimental investigation of the seismic performance of gravity load-designed RC infilled frames and confined bearing walls of limestone masonry backed with plain concrete. Five infilled frames and two bearing walls were constructed at one-third scale and tested using reversed cyclic lateral loading and constant axial loads. Effects of openings, axial loading, and infill interface conditions were examined using quasi-static experimentation. The two structural systems exhibited similar lateral resistance and energy dissipation capacities with higher global displacement ductility for the infilled frames. Hysteretic behavior of the infilled frame models exhibited pinching of the hysteretic loops accompanied by extensive degradation of stiffness whereas loops of the bearing walls were free of pinching. Test results confirmed the beneficial effect of axial loading on lateral resistance, energy dissipation, and ductility of the bearing walls. Higher axial loading resulted in a substantial decrease in ductility with no significant effect on lateral resistance of the infilled frames. Openings within the infill panel reduced significantly the lateral resistance of infilled frames. Using dowels at the infill panel interfaces with the base block and bounding columns enhanced the maximum load-carrying capacity of infilled frames without impairing their ductility.     

Beam-Column Joint Model for Nonlinear Analysis of Non-Seismically Detailed Reinforced Concrete Frame

An efficient and simplified plane beam-column joint model that can describe the strength deterioration, stiffness degradation, and pinching effect was developed for the nonlinear analysis of non-seismically detailed reinforced concrete frames. The proposed beam-column joint model is a super-element consisting of eight spring components and one panel zone component, representing the bond-slip mechanism of the longitudinal reinforcement and the shear deformation mechanism of the joint concrete core region, respectively. In order to represent the dynamic response at the system level, the elastic constitutive law is applied to the eight connector springs, while the Bouc-Wen-Baber-Noori (BWBN) model is adopted to describe the hysteretic behavior of the panel zone component. For the implementation of the finite element analysis, the algorithmically consistent tangent of the BWBN model is derived as a uni-axial constitutive model, while the initial stiffness of the panel zone component is determined by the concrete compression strut assumption. The accuracy and efficiency of the proposed beam-column joint model were calibrated at both the component and structural levels by comparing the simulated results with the experimental data for non-seismically detailed joint sub-assemblages and a reinforced concrete plane frame.     

Fiber-Based Modeling of Circular Reinforced Concrete Bridge Columns

This article presents the application of fiber-based analysis to predict the nonlinear response of reinforced concrete bridge columns. Specifically considered are predictions of overall force-deformation hysteretic response and strain gradients in plastic hinge regions. This article discusses the relative merits of force-based and displacement-based fiber elements, and proposes a technique for prediction of nonlinear strain distribution based on the modified compression field theory. The models are compared with static and dynamic test data and recommendations are made for fiber-based modeling of RC bridge columns.     

Seismic Behavior of L-Shaped RC Squat Walls under Various Lateral Loading Directions

Considerable progress has been made on the research of non-rectangular reinforced concrete (RC) squat walls over the past decades. However, the experimental data of L-shaped RC squat walls remain limited, especially for their seismic behaviors under non-principal bending actions. This paper presents an experimental and numerical investigation on L-shaped RC squat structural walls with an emphasis on how varying the directions of lateral cyclic loading influences the seismic responses of these walls. Four L-shaped specimens are tested under lateral cyclic displacements and low levels of axial compression The variables are axial loads and lateral loading directions. The performance of specimens is discussed in terms of cracking patterns, failure mechanisms, hysteretic responses, deformation components and strain profiles. Furthermore, three-dimensional finite element models are developed to supplement the experimental results. The direction of lateral loading is found to have a significant effect on the peak shear strength of L-shaped RC squat walls.     

Influence of Masonry Strength and Openings on Infilled R/C Frames Under Cycling Loading

The influence of masonry infills with openings on the seismic performance of reinforced concrete (R/C) frames that were designed in accordance with modern codes provisions is investigated. Two types of masonry infills were considered that had different compressive strength but almost identical shear strength. Infills were designed so that the lateral cracking load of the solid infill is less than the available column shear resistance. Seven 1/3 – scale, single–story, single–bay frame specimens were tested under cyclic horizontal loading up to a drift level of 40%. The parameters investigated are the opening shape and the infill compressive strength. The assessment of the behavior of the frames is presented in terms of failure modes, strength, stiffness, ductility, energy dissipation capacity, and degradation from cycling. The experimental results indicate that infills with openings can significantly improve the performance of RC frames. Further, as expected, specimens with strong infills exhibited better performance than those with weak infills. For the prediction of the lateral resistance of the studied single-bay, single-story infilled frames with openings, a special plastic analysis method has been employed.     

Estimating the Seismic Performance of CFRP-Retrofitted RC Beam-Column Connections Using Fiber-Section Analysis

Over the past two decades, many experimental techniques have been developed to improve the efficiency of the externally-bonded fiber-reinforced polymers (FRPs) in order to improve the structural performance of reinforced concrete (RC) beam-column connections. Numerical analysis is also being used as a cost-effective tool to predict the experimental results and to further investigate the parameters that are beyond the scope and capacity of experimental tests. In this study, at first, a fiber-section modeling approach is developed for estimating the seismic behavior of RC beam-column connections before and after application of FRP retrofits. The accuracy of the analysis results were validated against a series of the available experimental data under both monotonic and cyclic loadings. It was pointed out that the proposed model can predict the strength and displacement of un-retrofitted and FRP-retrofitted RC beam-column connections up to the failure points. The verified model was then used to perform a parametric study pertaining to the effect of longitudinal reinforcement ratio on the efficiency of the adopted FRP retrofitting technique to improve the structural behavior of RC beam-column connections.     

NONLINEAR ANALYSIS OF REINFORCED CONCRETE SHEAR WALL UNDER EARTHQUAKE LOADING

A constitutive model for predicting the cyclic response of reinforced concrete structures is proposed. The model adopts the concept of a smeared crack approach with orthogonal fixed cracks and assumes a plane stress condition. Predictions of the model are compared firstly with existing experimental data on shear walls which were tested under monotonic and cyclic loading. The same model is then used in the finite element analysis of a complete shear wall structure which was tested under a large number of cyclic load reversals due to earthquake loading at NUPEC's Tadotsu Engineering Laboratory. Two different finite element approaches were used, namely a two-dimensional and a three-dimensional representation of the test specimen. The ability of the concrete model to -reproduce the most important characteristics of the dynamic behaviour of this type of structural element was evaluated by comparison with available experimental data. The numerical results showed good correlation between the predicted and the actual response, global as well as local response being reasonable close to the experimental one.     

A CAPACITY PREDICTION PROCEDURE FOR CONCRETE-FILLED STEEL COLUMNS

A seismic design procedure for partially concrete-filled box-shaped steel columns is presented in this paper. To determine the ultimate state of such columns, concrete and steel segments are modelled using beam-column elements and a pushover analysis procedure is adopted. This is done by means of a new failure criterion based on the average strain of concrete and steel at critical regions. The proposed procedure is applicable to columns having thin- and thick-walled sections, which are longitudinally stiffened or not. An uniaxial constitutive relation recently developed is employed for concrete filled in the thick-walled unstiffened section columns. Modifications are introduced to this model for other types of columns. Subsequently, the strength and ductility predictions obtained using the present and previous procedures are compared with the corresponding experimental results. Comparisons show that the present procedure yields better predictions. It is revealed that the inclusion of the confinement effects and softening behaviour of concrete is important in the present kind of prediction procedures. Furthermore, an extensive parametric study is carried out to examine the effects of procedures and geometrical and material properties on capacity predictions.     

Towards Damage-Based Design Approach for RC Bridge Columns Under Combined Loadings Using Damage Index Models

This article investigates a damage-based design approach for circular reinforced concrete (RC) columns under combined bending, shear, and torsion using decoupled damage index models. The combination of bending moment, shear, axial, and torsional loading affects the structural performance of bridge columns with respect to strength, deformation capacity and progression of damage. The damage index model proposed here permits decoupling these combined actions according to various damage limit states. This work evaluates the interaction between bending and torsional damage indices in terms of progression of damage. It also investigates the effects of the transverse reinforcement ratios and shear span. Based on experimental and analytical results increase of torsion amplified the progression of damage. The increase in transverse reinforcement ratio was found to have delayed the progression of damage and to have changed the torsional dominated behavior to flexural dominated behavior under combined bending and torsion.     

Modeling the Cyclic Flexural and Shear Response of the R. C. Hollow Box Columns of an Existing Viaduct

The cyclic response of R.C. hollow box columns, constructed as part of a typical single-column bent viaduct, built in the 1970’s in Central Europe, was studied both experimentally and analytically. Moderate displacement ductility capacity (between 3 and 4) was observed regardless of the column construction details, which are nowadays considered inappropriate for seismic regions. Standard analytical flexural models correlated with the experimental results quite well. Shear strength was estimated using the two methods included in the EC8 standards, as well as the method developed at the University of California, San Diego. Quite different results were obtained. The most accurate was the third method.     

ANALYTICAL MODELS FOR BRICK MASONRY INFILLED R/C FRAMES UNDER LATERAL LOADING

Proposed in this paper are two analytical models for predicting the inelastic response of unreinforced brick masonry infills in reinforced concrete frames subjected to mono-tonic and reversed cyclic loading. The first model is based on the traditional diagonal strut concept, while the second one is a simple isoparametric element with shear deformation only. All the essential characteristics of the hysteretic behaviour of the panel, including strength and stiffness degradation, pinching and slippage, are explicitly taken into account. The models are implemented in a general-purpose program for the inelastic time-history analysis of structures, and are used for studying the seismic behaviour of typical multistorey frames with various arrangements of infill panels, including structures with an open ground storey. The results of the analysis are in agreement with both experimentally observed behaviour and with experience regarding seismically damaged buildings.     

Experimental Evaluation of Seismically and Non-Seismically Detailed External RC Beam-Column Joints

An experimental investigation was undertaken to study the seismic performance of external reinforced concrete (RC) beam-column joints having representative details for mid-rise RC frame buildings in developing countries such as Iran that were designed and constructed prior to the 1970s. Three half-scale external RC beam-column joints were tested by applying lateral cyclic loading of increasing amplitudes. Tested specimens were comprised of one unit having seismic reinforcement detailing in accordance with the seismic requirements of ACI 318-11, and two units having non-seismic reinforcement detailing in accordance with the 1970s construction practice in many developing countries, such as Iran. Two typical defects were considered for the non-seismic units, being the absence of transverse steel hoops and insufficient bond capacity of beam bottom reinforcing bars in the joint region. Test results indicated that the non-seismically detailed specimens had a high rate of strength and stiffness degradation when compared to the seismically detailed specimen, which was attributed primarily to the joint shear failure or bond failure of the beam bottom bars. The non-seismically detailed specimens also showed a 30% reduction in both average strength and ductility and a 60% loss of energy dissipation capacity in comparison to the seismically detailed specimen.