Fixed-end Rotation Research Articles

Nonlinear Modeling of RC Substandard Beam–Column Joints for Building Response Analysis in Support of Seismic Risk Assessment and Loss Estimation

The paper discusses how joint damage and deterioration affect the seismic response of existing reinforced concrete frames with sub-standard beam–column joints. The available simplified modeling techniques are critically reviewed to propose a robust, yet computationally efficient, technique for simulating the nonlinear behavior of substandard beam–column joints. Improvements over the existing models include the simulation of the cyclic deterioration of joint stiffness and strength, as well as pinching in the hysteretic response, implemented considering a deteriorating hysteretic rule. A fiber-section forced-based inelastic beam–column element is developed, considering improved material models and fixed-end rotation due to bond failure, rebars-slip, and inelastic extension, to simulate the deteriorating cyclic behavior of existing pre-cracked beam–column members. For the assessment of frames with substandard exterior beam–column joints, a nonlinear model for the exterior joint is developed and validated through a full-scale quasi-static cyclic test performed on a substandard T-joint connection. The proposed model allows considering structural performance in risk assessment while accounting for true inelastic mechanisms at the joints. An assessment of a five-story RC frame revealed that the activation of the joint shear mechanism increases the chord rotation demand on the connecting beam members by up to 85%, with increases of up to 62% (mean drift) and 89% (mean + 1.std.) on the lower floors when determining the inter-story drift demand, and the collapse probability of structures subjected to design base ground motions increased from 4.20% to 29.20%.

Probabilistic structural performance of RC frames with corroded smooth bars subjected to near- and far-field ground motions

This paper investigates the seismic vulnerability of existing RC frames exposed to corrosion and subjected to near-field and far-field ground motions. A threefold approach for corrosion is adopted to illustrate the probabilistic framework and define time-dependent performance criteria for an accurate seismic fragility assessment. A bond-slip model is employed to simulate the fixed-end rotation and column-beam joints behaviour to account for the deficit in the bond strength of plain rebars. Such a model is calibrated using experimental studies from the literature and considering the effects of corrosion. An inelastic buckling model of steel bars is also incorporated in the finite element model through a hysteretic material to investigate its impact on the deformation capacity of RC members. The effects of near-field and far-field earthquakes are investigated through incremental dynamic analyses (IDA) and cloud analyses on a typical four-storey RC frame with plain bars. Results from the fragility analysis indicate that corrosion has significant effects on the seismic performance of such RC frames over time and near-field pulse-like motions are more destructive than both near-field no-pulse-like and far-field earthquakes.

Experimental Assessment of Second-Generation Hybrid Sliding-Rocking Bridge Columns under Reversed Lateral Loading for Free and Fixed End Rotation Conditions

Abstract Hybrid sliding-rocking (HSR) bridge columns are among the resilient column designs recently developed to allow accelerated bridge construction for bridge substructures in seismic areas. HS...

Strain penetration effect on cyclic response of corroded RC columns

The anchorage slip of longitudinal reinforcement in the foundation (also called strain penetration effect) may affect the cyclic behavior of RC columns by inducing fixed-end rotations. This strain penetration effect could become more significant under reinforcement corrosion, which frequently occurs in RC structures exposed to the attack of aggressive agents such as chlorides. It is hence important to take corrosion effects into account in the modeling of strain penetration phenomena. This paper presents a modification of an existing stress versus slip hysteretic model for reinforcing steels to incorporate corrosion effects. Results of both pull-out tests of deformed steel bars and quasi-static tests of corroded RC columns are adopted for validation. Moreover, a parametric investigation is carried out to demonstrate the impact of structural parameters and corrosion levels on the cyclic response of corroded RC columns considering the strain penetration effect. The results highlight that the modified hysteretic model can efficiently simulate the anchorage slip. In addition, it is found that the strain penetration effect tends to be more significant for the RC columns with higher corrosion level, smaller aspect ratio, larger longitudinal reinforcement ratio, or lower axial load ratio.

Cyclic response and modelling of special moment resisting beams exhibiting fixed-end rotation

Rebar slippage in reinforced concrete (RC) elements results in concrete expansion, large cracks, and consequently, early deterioration of strength as well as premature stiffness degradation, particularly in the inelastic energy dissipating zones. Although design standards prescribe different minimum concrete compressive strength, seismic evaluation and retrofit standards, and guidelines permit the use of provisions regarding bond strength and bar slippage issues regardless of the minimum specified concrete strength postulated in design standards. To better understand the seismic behavior of special moment-resisting (SMR) beams exhibiting fixed-end rotation resulting from the rebars inelastic elongation and slip, quasi-static cyclic tests were performed on eight full-scale SMR beams. The chosen beams have longitudinal reinforcement ratios of 0.84% (Type-1) and 1.26% (Type-2) with a shear-span to depth ratio of 6.14 and detailed following the provisions of ACI-318-19. Two specimens were prepared for each reinforcement ratio using concrete with compressive strengths equal to 2000 psi (14 MPa, M14) and 3000 psi (21 MPa, M21). The specimens were tested under cyclic displacement protocols, exhibiting flexure yielding that was followed by diagonal shear cracking and, ultimately, bond failure at the beam–block interface. It is even though the beams fulfill the requirements of ACI 318-19 for steel bars embedment and end hooks for anchorage. Force–displacement hysteretic response curves were obtained revealing pinching behavior in the cyclic response. Both types of beams deformed up to maximum chord rotations of 5.22% and 5.73% in case of beams with M14 and M21 concrete, respectively, and experienced cover concrete crushing at the compressed toe. Representative numerical models were assembled implementing fiber-section force-based inelastic beam elements. Additionally, lumped inelastic rotational springs were added to the model for fixed-end rotation. A tri-linear moment-rotation hysteretic response curve has pinching behavior was used to simulate the reduction in re-loading stiffness. This was verified with the measured response of tested beams; excellently simulates the hysteretic response. Moreover, to examine the seismic response of a total structural system regarding these findings, several response history analyses were performed on capacity-designed five-story frames to demonstrate the importance of modeling beam element fixed-end rotation for predicting the story drift demands subjected to different earthquake ground motions. It was found that despite the bar-slip phenomenon the beams developed their yield capacities; however, the response of the frame was subjective depending on the characteristics of input motions, particularly the valleys and hills of the spectral shape.

Blast and Impact Analyses of RC Beams Considering Bond-Slip Effect and Loading History of Constituent Materials

An improved numerical model that can simulate the nonlinear behavior of reinforced concrete beams subjected to blast and impact loadings is introduced in this paper. The layered section approach is based in the formulation, and the dynamic material behaviors of concrete and steel are defined with the use of the dynamic increase factor. Unlike the classical layered section approach that usually gives conservative structural responses because of no consideration of the bond-slip effect, the introduced numerical model takes into account the bond-slip between reinforcing steel and surrounding concrete by changing the bending stiffness EI of elements placed within the plastic hinge length. Since the bond-slip developed after yielding of reinforcing steel is dominant and accompanies fixed-end rotation, the equivalent bending stiffness to be used in the critical region can be evaluated on the basis of the compatibility condition. In advance, the consideration of the unloading and reloading histories of reinforcing steel and concrete makes it possible to exactly trace the structural behavior even after reaching the maximum structural response. Finally, correlation studies between analytical results and experimental data are conducted to establish the validity of the introduced numerical model, and the obtained results show that it is important to consider the bond-slip effect and the loading history of constituent materials.

Experimental response of an existing RC bridge with smooth bars and preliminary numerical simulations

The paper discusses the experimental seismic performance assessment of a structural prototype simulating typical existing highway bridges which were designed with poor seismic details. The structural system is a reinforced concrete (RC) 1:3 scale single span bridge which has been tested dynamically with shaking tables by considering strong motions of the 1980 Irpinia (Italy) earthquake. Low-strength concrete and smooth bars were used for the RC circular bridge piers of the tested prototype. Comprehensive modal response analysis has been carried out for the single piers and for the bridge sub-assemblage to estimate period elongations and variations of equivalent viscous damping coefficients at increasing levels of strong motions. The effects of cumulative damage induced by earthquake sequences have also been investigated experimentally. The sample bridge pier possesses low aspect ratio; nevertheless the piers exhibited a flexural response. Fixed-end rotations, with significant longitudinal reinforcement slip, were observed at the base of the bridge pier at about 0.40% lateral drift ratio. As a consequence, a rocking mechanism of the bridge pier initiated; such mechanism affected significantly the pier response at large shaking intensities. An in-depth analysis of local and global response quantities has been provided in order to accurately identify the structural behaviour. Finally, available analytical formulations and refined numerical models were considered to simulate the earthquake response of the tested bridge. The pier lateral response has been investigated by means of push-over analysis and nonlinear time histories. The accuracy of the proposed models, the differences and recommendations for numerical modelling of bridge piers with smooth internal reinforcements are also discussed.

Fiber beam–column element model considering reinforcement anchorage slip in the footing

A simple and computationally efficient fiber beam–column element model is developed to consider reinforcement anchorage slip in the footing, which may cause the fixed-end rotation and greatly influence the seismic response of a reinforced concrete column. First, on the basis of an effective macro model for calculating anchorage slip and a classical uniaxial stress–strain relationship of rebar, the reinforcement anchorage slip in the footing is formulated. The macro model assumed a stepped bond stress to deal with the bond–slip relationship, and the slip is derived by integrating the strain over the development length. Then, the derived anchorage slip is introduced into the framework of the conventional fiber element model. By considering the rebar fiber strain in the footing fiber element as the sum of the rebar deformation and the anchorage slip, the stress–strain skeleton curve and the hysteretic law of rebar are modified. After that, the developed fiber model is validated by simulating two quasi-static tests of reinforced concrete columns. The developed model shows good accuracy in simulating the moment capacity and column stiffness, whereas the conventional fiber model may significantly overestimate the column initial and unloading stiffness. Finally, the shake-table test of a full-scale flexure-dominated bridge column is simulated to further validate the developed model. Comparisons indicate the considerably improved accuracy of the developed model in simulating the column displacement time-histories, base moment–column displacement responses, and base moment–base curvature responses. In addition, the rebar anchorage slip and the lateral displacement ratio owing to this slip effect are well predicted by the developed model. Therefore, the model is validated at structural, sectional, and micro levels.

Modified Plastic-Hinge Method for Circular RC Bridge Columns

AbstractThis paper discusses a research program aimed at defining accurate limit-state displacements that relate to specific levels of damage in reinforced concrete bridge columns subjected to seismic hazards. In design, concrete compressive and steel tensile strain limits are related to column deformations through the use of an equivalent curvature distribution. An experimental study was carried out to assess the performance of 30 circular well-confined bridge columns. Material strains, cross-section curvatures, and fixed-end rotations attributed to strain penetration of reinforcement into the adjoining member were quantified by using a three-dimesional (3D) position monitoring system. An equivalent curvature distribution was created that reflects the measured spread of plasticity and components of deformation. When compared with the current approach, the proposed modified plastic-hinge method improved the accuracy of both tensile and compressive strain-displacement predictions, while maintaining similar...

Collapse analysis of reinforced concrete frames including bar fracture

A nonlinear one-dimensional compound frame element is formulated and applied to collapse analysis of reinforced concrete frames including fracture of longitudinal reinforcing bars. The proposed formulation can take account of geometrical and material nonlinearities including cracking and crushing of the concrete, yielding of steel bars, post-yield tension stiffening and fracture of reinforcing steel bars and fixed-end rotation. The material nonlinearities are formulated within the framework of a distributed nonlinearity model, and the rupture of reinforcing bars is captured by nodal springs with damage multipliers. The developed analytical tool is verified against available experimental data in the literature. It is shown that the developed compound element and proposed modelling strategies can capture the full load–deflection response and the ultimate loading capacity of reinforced concrete beam assemblages/frames subjected to large displacements.

Fiber-Element Modeling for Seismic Performance of Square RC Bridge Columns Retrofitted with NSM BFRP Bars and/or BFRP Sheet Confinement

This paper presents an analysis of the seismic performance of square RC bridge columns retrofitted with near-surface-mounted (NSM) basalt fiber-reinforced polymer (BFRP) bars and/or BFRP sheet confinement based on fiber element modeling. An axial stress versus loaded-end displacement model of NSM FRP bars, including both elastic elongation and bond-slip effects, is proposed to account for the significant slippage of FRP bars in the plastic hinge region of strengthened columns. The simplified FRP bar model is then converted into the equivalent stress-strain relationship for easy implementation in fiber-based analysis. Moment-curvature analysis is performed based on the proposed FRP bar model, and the analytical moment versus fixed-end rotation relationship of a strengthened column is calculated and assigned to the rotational spring in the fiber element model. The proposed method avoids the nested iterations in sectional analysis that require force equilibrium and deformation compatibility. Comparisons between the numerical simulations and experimental results indicate that the proposed method is appropriate for predicting pushover curves and the hysteretic response of strengthened columns. Furthermore, the mechanism of the hybrid effect of combining NSM FRP bars with externally bonded FRP sheets can be interpreted after the analytical study; that is, confining the column with FRP sheets improves the bond conditions for NSM FRP bars, while the bond-slip effect mitigates the premature fracturing of the FRP bars, leading to more effective utilization of the NSM reinforcement and a more ductile column behavior.

Numerical Simulation of FRP-Jacketed RC Columns Subjected to Cyclic and Seismic Loading

This paper presents a numerical model for the cyclic/seismic behavior of reinforced concrete (RC) columns retrofitted with fiber-reinforced polymer (FRP) confining jackets. Such a column model has previously been unavailable despite the popularity of FRP jacketing as a seismic retrofit method for RC columns. The proposed numerical column model is based on a recent stress-strain model for FRP-confined concrete subjected to cyclic axial compression and a hysteretic moment-rotation model to account for the effect of strain penetration of the longitudinal steel bars in the column footing (i.e., effect of fixed-end rotations). This column model was implemented into OpenSees (Open System for Earthquake Engineering Simulation) using its fiber-section force-based nonlinear beam-column element. Predictions of the numerical column model for three FRP-jacketed RC columns subjected to either double-curvature bending or single-curvature bending are shown to be in close agreement with the test results.

Frame Element with Mixed Formulations for Composite and RC Members with Bond Slip. I: Theory and Fixed-End Rotation

AbstractThis paper proposes a composite frame element for the simulation of the inelastic response of structural members made up of two or more components with different materials, such as reinforced concrete (RC), steel-concrete composite members, prestressed members, and members with fiber-reinforced polymer (FRP) reinforcement. The element accounts for the relative slip at the interface between the components. Nonlinear geometry effects are accounted for through the corotational formulation, which permits the response simulation of composite frame elements under large displacements. The element formulation enhances the standard Hu-Washizu variational principle with fields describing the bond-slip behavior between components. Three alternatives for the mixed formulation of the element are derived in this paper, which focuses on theory and implementation: mixed-displacement, mixed-force, and mixed-mixed. The paper presents the benefits and shortcomings of the formulation alternatives for modeling the pul...

Numerical analysis with joint model on RC assemblages subjected to progressive collapse

The behaviour of structures subjected to progressive collapse is typically investigated by introducing column-removing scenarios. Previous experimental results show that large-deformation performances of reinforced concrete (RC) assemblages under a middle column removal scenario (MCRS) involve discontinuity due to bar slip and fracture near the joint interfaces. To consider the effects of the discontinuity on structural behaviour, a component-based joint model is introduced into macromodel-based finite-element analysis (macro-FEA), in which beams are modelled as fibre elements. The joint model consists of a series of non-linear springs, each of which represents a load transfer path from adjoining members to a joint. The calibration procedures of spring properties are illustrated systematically. In particular, a macro-bar stress–slip model is developed to consider the effects of large post-yield tensile strains and finite embedment lengths on the bar stress–slip relationship. Comparisons of simulated and observed responses for a series of RC assemblages indicate that macro-FEA incorporating the joint model is a practical approach to simulate the essential structural behaviour of RC assemblages under a MCRS, including catenary action. Finally, the macro numerical model is used to investigate the effects of boundary conditions, bar curtailment and beam depth on the structural behaviour of RC assemblages. The results suggest that beam depth affects the fixed-end rotation contributed by bar slip, and further significantly influences the development of catenary action.

Evaluation of Mixed Formulation for Modelling RC Columns with Bond Slip

Modelling composite members is a challenge for the computer simulation of structural response under extreme loads, because of the energy dissipation due to relative slip between constituent components. Among several finite element formulations proposed in the last years, the recent mixed formulation proposed by the authors could accommodate the slip discontinuity across the element nodes. In this paper this approach is evaluated with the study of the monotonic and cyclic response of a cantilever reinforced concrete column. The first load case showcases the unique capability of the mixed formulation to estimate the fixed-end rotation at the base of the cantilever column. The second load case demonstrates the accuracy of the mixed formulation in the representation of experimental measurements. The examples reveal that the mixed formulation has great potential in simulating composite structures under extreme loadings demonstrating excellent accuracy for the representation of the global as well as the local response.

Effect of Load History on Performance Limit States of Circular Bridge Columns

In this paper, the importance of displacement history and its effects on performance limit states, the relationship between strain and displacement, and the spread of plasticity in RC structures is explored. An experimental study is underway to assess the performance of 30 circular, well-confined, bridge columns with varying lateral displacement history, transverse reinforcement detailing, axial load, aspect ratio, and longitudinal steel content. Eight of these columns, with similar geometry and detailing, were subjected to various unidirectional displacement histories including standardized laboratory reversed cyclic loading and re-creations of the displacement responses obtained from a nonlinear time-history analysis of multiple earthquakes with distinct characteristics. Longitudinal reinforcing bars were instrumented to obtain strain hysteresis, vertical strain profiles, cross section curvatures, curvature distributions, and fixed-end rotations attributable to strain penetration. Results have shown that the limit state of reinforcement bar buckling was influenced by load history, but the relationship between strain and displacement along the envelope curve was not. The main impact of load history on bar buckling is its influence on accumulated strains within the longitudinal reinforcement and transverse steel.

Stiffness and cyclic deformation capacity of circular RC columns with or without lap-splices and FRP wrapping

Mechanics-based models are developed for the moment, the curvature and the chord rotation at yielding of circular concrete columns or piers, their secant stiffness to the yield point and the ultimate curvature and flexure-controlled ultimate chord rotation in cyclic loading. The strain criteria for yielding or ultimate are calibrated on the basis of over four hundred test results. Besides the model for the secant-to-yield-point stiffness which is in terms of the yield moment and chord rotation, an empirical one, independent of the vertical reinforcement, is fitted to the data. The ultimate chord rotation is obtained from a plastic hinge model employing a plastic hinge length, the yield and the ultimate curvatures of the end section and the fixed-end rotation due to slippage of bars from their anchorage zone beyond the column length. All models are extended to columns the vertical bars of which are lap-spliced within the plastic hinge and to columns with FRP wrapping and continuous or lap-spliced vertical bars. The comprehensive portfolio of expressions proposed for the deformation properties of circular columns is fully consistent across the various situations of continuous or lap-spliced bars, with or without FRP wrapping, and with models developed by the authors from much larger databases of rectangular columns in similar situations; the aspects specific to circular sections are limited to the mechanics-based section analysis for moment and curvature, a purely empirical coefficient for the secant-to-yield-point stiffness and the empirical plastic hinge length.

Analytical Model on the Bond Stress-Slip Relationship between Steel Reinforcement and Concrete for RC Beam-Column Joints

There are no conventionally accepted failure criteria for progressive collapse, and often times, deflection of affected beams over the “missing column” are often used as performance criteria. However, when simulating the deformation behaviour and the strength of reinforced concrete (RC) framed structures for progressive collapse analysis, besides the flexural deformations, the so-called “fixed end” rotation induced by the longitudinal bar slip at the beam-column ends connected to the joints can be significant and result in additional lateral deformations not accounted for in the initial analysis. Hence, it is important to quantify the deformations arising from fixed end rotations. Several bond stress-slip relationships between steel reinforcement and concrete were previously proposed in the literature. In the present work, their merits and demerits are discussed in terms of application limitation. To address the limitations of previous bond-slip models, a new analytical model based on the bond stress integration along the bar stress propagation length is proposed to predict the bar-slip behaviour in the RC beam-column joints. The proposed analytical model on the bond stress-slip relationship is validated against experimental studies from the literature and is shown to be simple and reliable.

The non-linear model of embedded steel–concrete composite column bases

This paper analyses the base connection of partially encased composite columns while considering the solution of embedding the column in a concrete foundation block. The base connection is formed by a socket-type joint that is used for RC pre-cast columns, avoiding the brittle failure that usually occurs in traditional base joints made of plates and bolts due to crashing of the welds and degradation of the bonding. The experimental results from previous tests showed that the innovative joint is more ductile than the traditional joint, but the detailed analysis developed in this paper demonstrates that the fixed end rotation contributes to the global ductility of the joint. A non-linear 3D FE model is constructed and calibrated from the experimental results and is then used for parametric analyses. The influence of the embedded height is examined by determining its value that exploits the entire resistance of the column before the base concrete fails. Another parametric study using the 3D FE model is performed to define the elastic rigidity of the connection. Finally, a simple mono-dimensional model is assessed with a non-linear spring at the base that takes into account the elastic rigidity and the plastic behaviour of the base joint.

ASCE/SEI 41 Provisions on Deformation Capacity of Older-Type Reinforced Concrete Columns with Plain Bars

This study contributes to the improvement of capacity models for older-type reinforced concrete (RC) members to be used in the seismic assessment of existing RC structures. A database of experimental tests on RC columns with plain bars is presented. Due to the low bond strength, the deformation capacity of these members is particularly influenced by fixed-end rotation mechanism compared with members with deformed bars. ASCE/SEI 41 provisions on the deformation capacity of older-type RC columns, including later proposed modifications, are reviewed. Provisions for the evaluation of effective stiffness are reviewed, too, and special attention is paid to failure mode classification. The effectiveness of such provisions for columns with plain bars is evaluated through their application to the presented database. Results obtained from the application of the effective stiffness model are illustrated, and possible improvements are discussed. A significant conservatism in the plastic deformation capacity model is observed. Deformation limits could be relaxed while still meeting code safety requirements. The amount of this adjustment for ASCE/SEI 41 provisions on the deformation capacity of older-type RC columns is evaluated.