Tension Stiffening Effect Research Articles

Cracking and Tension Stiffening Behavior of High-Strength Concrete Tension Members Subjected to Axial Load

This paper presents the test results of 35 direct tensile specimens to investigate the effect of concrete strength on the tension stiffening effect and cracking response in axially loaded reinforced concrete tensile members. Three concrete strengths 25, 60 and 80 MPa were included as a major experimental parameter together with six concrete cover thickness ratios. The results showed that as higher strength concrete was employed, not only splitting cracks along the reinforcement more extensive, but also the transverse crack spacing became smaller. Thereby, the effective tensile stiffness of the high-strength concrete specimens at the stabilized cracking stage was much smaller than those of normal-strength concrete specimens. This observation is contrary to the current design provisions, and the reduction in the tension stiffening effect by employment of high-strength concrete is much greater than that would be expected. Based on the present results, a modification factor is proposed to account for the effect of the cover thickness and the concrete strength.

Tension Stiffening Model for Numerical Analysis of RC Structures by Using Bond-Slip Relationship

In this paper, a tension stiffening model based on the bond-slip relationship is introduced and adopted in a finite multilayered shell element formulation for surface structure analysis. The tension stiffening effect evaluated at the meso-level is taken into account in the constitutive law of reinforcement at the macro level by defining a crack element at the Gauss point. The crack element is iteratively analyzed by means of a step-by-step integration, which allows application of any complicated bond laws. To define the crack element, a crack spacing model considers the crack formation grade. As a relevant factor in this tension stiffening concept, the reinforcement cracking stress may be evaluated by taking the fractile value of the concrete tensile strength. Through several simulations, the validity of the concept is systematically in-vestigated under monotonic and cyclic loading. The analysis under cyclic loading shows the effect of the re-contact of the crack flanks. The numerical examples demonstrate the applicability of the applied reinforced concrete model with a tension stiffening effect.

Two-dimensional FE model for evaluation of composite beams, I: Formulation and validation

This paper develops a two-dimensional finite element model for composite beams, based on the use of the commercial package ANSYS. Different degrees of continuity can be taken into account, permitting the investigation of systems ranging from simply-supported to fully-continuous. Beams with either full or partial shear connection can be considered, as well as different slab typologies. The model represents the behaviour of all components of the composite arrangement, based on the best available current understanding, including the reinforcing bars (considering the tension-stiffening effect), the load–slip characteristic of the shear connectors, and the key components of the beam to column connection. In addition, material nonlinearity for all components is taken into account. The model has been fully verified by extensive comparisons against experimental and numerical results and it has been demonstrated that it is suitable for comprehensive parametric studies of the behaviour of composite beams. A sensitivity study focusing on both the required and the available rotation capacities and their importance for moment redistribution in semi-continuous composite beams is presented in the companion paper.

Nonlinear analysis of reinforced concrete beam with/without tension stiffening effect

The aim of this paper is to do materially nonlinear failure analysis of RC beam by using finite element method. In the finite element modeling, two different approaches and different tension stress–strain models with/without tension stiffening effect are used by considering two different mesh sizes. In the first approach, the material matrices of concrete and reinforcement are constructed separately, and then superimposed to obtain the element stiffness matrix. In the second approach, the reinforcement is assumed to be uniformly distributed throughout the beam. So, the beam is modeled as a single composite element with increasing the modulus of elasticity of concrete by considering the reinforcement ratio. For these two approaches, elastic-perfectly plastic stress–strain relationship is used for concrete in compression. For the concrete in tension, a stress–strain relationship with/without tension stiffening is used. It is concluded that the approaches and the models considered in this study can be effectively used in the materially nonlinear analysis of RC beams.

Gelžbetoninių Sijų Tempiamosios Zonos Elgsenos Modeliavimas Armatūros Diagram

After cracking, the stiffness of the member along its length varies, which makes the calculation of deformations complicated. In a cracked member, stiffness is largest in the section within the uncracked region while remains smallest in the cracked section. This is because in the cracked section, tensile concrete does not contribute to the load carrying mechanism. However, at intermediate sections between adjacent cracks, concrete around reinforcement retains some tensile force due to the bond-action that effectively stiffens member response and reduces deflections. This effect is known as tension-stiffening. This paper discusses the tension-stiffening effect in reinforced concrete (RC) beams. Numerical modelling uses the approach based on tension-stiffening attributed to tensile reinforcement. A material model of reinforced steel has been developed by inverse analysis using the moment-curvature diagrams of RC beams. Total stresses in tensile reinforcement consist of actual stresses corresponding to the average strain of the steel and additional stresses due to tension-stiffening. The carried out analysis employed experimental data on RC beams tested by the authors. The beams had a constant cross section but a different amount of tensile reinforcement. It has been shown that additional (tension-stiffening) stresses in the steel depend on the area of reinforcement. However, the resulting internal forces are less dependent on the amount of reinforcement.

Finite-Element Analysis of Reinforced Concrete Flat Plate Structures by Layered Shell Element

A finite-element model for nonlinear analysis of reinforced concrete flat plate structures is presented. A flexible layering scheme incorporating the transverse shear deformation is formulated in shell element environment. Each node of the layered shell element can be specified as either a normal node or a node with shear correction. A three-dimensional hypoelastic material model is implemented to model reinforced concrete. The cracking effects of tension softening, aggregate interlock, tension stiffening, and compression softening in multidirectionally cracked reinforced concrete are incorporated explicitly and efficiently. A flat plate, a flat slab with drop panel, and a large size flat plate with irregular column layout have been analyzed. The influence of the distribution of transverse shear strain on the punching shear failure mode has been identified in the numerical studies. The proposed finite-element model has been proved to be capable of simulating the localized punching shear behavior of slab-column connections and to be suitable for global analysis of structural performance of flat plate structures.

New Approach for Estimating the Deflection of Beams Reinforced with FRP Reinforcement

Due to concerns with corrosion, the use of fiber-reinforced polymer (FRP) as a replacement to conventional steel reinforcement has greatly increased over the last decade. Researchers have identified the distinctive mechanical and bond properties of FRP reinforcement that prevent the use of existing relationships to establish serviceability of concrete structures reinforced with such products. Although studies have modified these empirical relationships to describe the behavior of structures reinforced with FRP reinforcement, this paper will provide a new approach to estimate deflection of concrete beams by considering material properties of the reinforcement and incorporating the effects of tension stiffening. Accuracy and precision of the approach was established by performing a statistical analysis on a database containing 171 FRP-reinforced concrete beams. Results were compared to those from existing proposed relationships and indicate the potential of the method to estimate deflection at various service conditions.

Analysis of composite beams in the hogging moment regions using a mixed finite element formulation

Cracking of the concrete slab in the hogging moment region decreases the global stiffness of composite steel–concrete structures and also reduces the effect of continuity, thus making the structural behaviour highly nonlinear even for low stress levels. In this paper, the behaviour of continuous composite beams with discrete shear connection is investigated using a nonlinear mixed finite element model. The model includes appropriate nonlinear constitutive relationships for the concrete, the steel and tension stiffening effect. Furthermore, the discrete nature of the shear connection is embedded in the model and the tension stiffening effects are introduced in the analysis by using a concrete constitutive model proposed in the CEB-FIB Model Code 1990 which incorporates embedded steel. Special attention is paid to the hogging moment regions, where cracking occurs. Comparisons between the numerical analyses and experimental results in the current literature are undertaken to validate the accuracy of the model. Furthermore, a parametric study is carried out to study the influence of span length and degree of shear connection on the strength and ductility of continuous composite beams.

비선형 부착 특성에 기반한 철근콘크리트 휨부재의 균열폭과 처짐 해석

This paper describes a proposal for average crack width and immediate deflection calculation in structural concrete members. The model is mathematically derived from actual bond stressslip relationships and tension stiffening effect between reinforcement and the surrounding concrete, and the actual strains of steel and concrete are integrated respectively along the embedded length between the adjacent cracks so as to obtain the difference in the axial elongation. With these, a model for average crack width and immediate deflection in reinforced concrete flexural members are proposed utilizing difference in the axial elongation and average steel strain and moment-curvature relationship with taking account of bond characteristics. The model is applied to the test specimens available in literatures, and the crack width and deflections predicted by the proposal equation in this study are closed to the experimentally measured data compared the current code provisions.

Simplified Flexural Response of Steel Fiber-Reinforced Concrete Beams

In the present paper, an analytical model is proposed that is able to determine the flexural response of supported beams under four-point bending tests. Cases of normal strength reinforced concrete beams with longitudinal bars in the presence of reinforcing hooked steel fibers and transverse stirrups are considered. A simplified analytical model is presented that is able to calculate the load-deflection curves and the maximum and ultimate deflections occurring in the case of shear or flexure failures. In the case of shear failure, the maximum shear strength of the beams is evaluated by using a recent analytical expression proposed by the author able to account for the shear-to-moment interaction, which covers a large range of shear span-to-depth ratios. This expression is based on the evaluation of shear strength contribution due to beam and arch actions including their interaction with the fibers. In the case of flexural failure, the hypothesis of perfect bond of steel bars and concrete and limiting the range of shear-to-depth ratios to between two and four was considered to determine the ultimate moment. No tension stiffening and size effects were considered. A nonlinear finite element analysis program (ATENA) was utilized to verify the simplified model. The program was utilized by assigning the constitutive laws in compression and in tension for fibrous concrete available in the literature. Finally, on the basis of test data obtained by the author and of that available in the literature, a comparison was made to show the ability of the simplified proposed model to also predict the flexural response of beams when shear failure is attained.

철근의 부착상태에 따른 철근콘크리트 연속보에서의 모멘트재분배에 대한 실험적 검증

Samsung Co. Ltd., Sungnam 463-721, KoreaABSTRACT The moment redistribution in continuous reinforced concrete beams is very feasible phenomenon, by which the effi-ciency and the economy in designing reinforced concrete members can be enhanced. However, to understand the structural behaviorby moment redistribution phenomenon, it is desirable to verify its mechanism experimentally considering tension stiffening effect,the relationship of moment redistribution and beam deflection, crack pattern, and effective stiffness. Six reinforced concrete con-tinuous beam specimens were fabricated, and each specimen had a dimension of 250 mm × 350 mm and 7,000 mm long. The loca-tion of de-bonding was taken as the primary test parameter to investigate tension stiffening effect. The moment redistribution ratioof the specimens was different depending on the position of de-bonding, and in particular no moment redistribution was observedwhen de-bonding exist at both ends, the maximum negative moment region and the maximum positive moment region. Keywords : continuous beam, moment redistribution, tension stiffening effect, maximum crack width, crack spacing

Revisiting the Tension Stiffening Effect in Reinforced Concrete Slabs

In the design of reinforced concrete floors slabs, deflection and crack control at service load levels are usually the governing considerations, and accurate modelling of the stiffness after cracking is required. Various approaches for modelling the post-cracking stiffness in lightly- reinforced concrete slabs are evaluated critically and empirical predictions are compared with actual load versus deflection plots for a variety of concrete slabs. Finally, recommendations are included for changes to the Australian Standard AS3600.

Deflection behaviors of polymer mortar sandwich panels reinforced with GFRP

This study prepared sandwich panel specimens composed of methyl methacrylate (MMA)-modified polymer mortar at the core and reinforced with high-tensile GFRP on both faces to propose a method to predict the deflection of polymer mortar sandwich panels under flexural load. Nine experimental specimens of different thickness at the core and face were prepared for the flexural load test to determine the moment-deflection relationship, and the experimental results were compared with existing theoretical models. The comparison study revealed that the deflection behavior of the specimens in response to the variation in the thickness of the specimens at the core and face could be well predicted. Additionally, an analytical model, which revised a bilinear method, to explain the tension stiffening effect of the prepared sandwich panel specimens under the influence of flexural load is proposed. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

비선형 부착 특성에 기반한 철근콘크리트 부재의 인장증강효과 모델

초록·키워드 목차 오류제보하기 등록된 정보가 없습니다. ABSTRACT1. 서론2. 부착에 관한 기반 이론 고찰3. 인장증강효과 해석 모델4. 해석 결과 및 검증5. 결론참고문헌요약

Analytical Modeling of Concrete Beams Reinforced with Carbon FRP Bars

A non-linear finite element model is presented for the analysis of simply supported reinforced concrete beams. Cracked concrete is considered as an orthotropic material and the crack formation is simulated as smeared cracks. A rotating crack method is employed based on the total strain crack model. The analysis was carried out with the help of 2D isoparametric plane stress elements. Compression and tension softening and tension stiffening effects of the cracked concrete were considered. The tension reinforcement consisted of either steel or fiber reinforced polymer (FRP) bars. Excellent convergence and numerical stability of the formulation was found. The model showed good agreement with the recorded data of the tested beams.

A layered finite element for reinforced concrete beams with bond–slip effects

Abstract The behaviour of reinforced concrete members is affected by the slipping of steel bars inserted in the concrete matrix. A tension-stiffening effect and crack evolution occur from the beginning of slipping; thus, the assessment of those phenomena requires the introduction of a bond–slip interaction model. This work presents a beam-layered model, including the constitutive relationships of materials and their interaction, according to the CEB-FIP Model Code 1990. To eliminate the finite element sub-division procedure, a continuous slip function is imposed into the element domain. The results are continuous descriptions of bond stress in the steel–concrete interface, as well as concrete and steel stresses along the element.

Complete nonlinear response of reinforced concrete beams under cyclic loading

AbstractComplete nonlinear analysis is carried out for cyclically loaded reinforced concrete (RC) beams made of normal‐ and high‐strength concrete. The loading stage covers not only the pre‐peak stage but also the post‐peak stage in particular. The analysis is based on a numerical method that employs the actual stress–strain curves and takes into account the stress‐path dependence of concrete and steel reinforcement. The complete nonlinear behavior of RC beams under both non‐reversed and reversed cyclic loading is studied based on the moment–curvature relationship obtained. Generally, the response under cyclic loading is found to be dependent on the loading path in bending. The variation of neutral axis depth is different for under‐ and over‐reinforced sections during cyclic loading. The Bauschinger effect of steel reinforcement is insignificant for non‐reversed cyclic loading but notable for reversed cyclic loading, especially when the loading extends into the post‐peak stage. The beneficial effects of concrete tension stiffening are only observed at the service stage and are more significant for under‐reinforced RC beams than over‐reinforced ones. Copyright © 2007 John Wiley & Sons, Ltd.

Short- and Long-Term Deflections in Reinforced, Prestressed, and Composite Concrete Beams

A model that calculates both short- and long-term deflections (i.e., transverse deflections and section rotations) in reinforced, prestressed (or posttensioned) and composite concrete beams with generalized end conditions subjected to bending about any transverse axis proposed. The effects of creep, shrinkage, and tension stiffening in the concrete and flexural rotational restraints at the beam extremes are included in the proposed model. The model is limited to beams in which torsional moments or deformations along the member are not induced by the externally applied loads or by the prestressing or posttensioning. The moment–curvature (M–ϕ) diagrams are first determined at each section in order to calculate both the transverse deflections and section rotations. The concrete stress–strain curve is modeled by: (1) a hyperbola for high-strength concrete (HSC) for the zone under compression and (2) a straight line combined with a hyperbola for the zone under tension. The stress–strain curves of the reinforcements are modeled using a modified Ramberg-Osgood function for the prestressed steel (bonded or unbonded) and a multilinear function for regular rebars and composites (like fiber-reinforced polymers (FRP) and carbon fiber-reinforced polymers (CFRP)). Five examples are included that show the effectiveness of the proposed method to predict the load–deflection behavior of reinforced, prestressed (or posttensioned), composite HSC beams, and steel-concrete composite beams.

Modeling Debonding Failure in FRP Flexurally Strengthened RC Members Using a Local Deformation Model

Reinforced concrete (RC) beams and slabs can be strengthened by bonding fiber-reinforced polymer (FRP) composites to their tension face. The performance of such flexurally strengthened members can be compromised by debonding of the FRP, with debonding initiating near an intermediate crack (IC) in the member away from the end of the FRP. Despite considerable research over the last decade, reliable IC debonding strength models still do not exist. The current paper attempts to correct this situation by presenting a local deformation model that can simulate IC debonding. The progressive formation of flexural cracks, and the associated crack spacings and crack widths are modelled from initial cracking to the onset of debonding. The bond characteristics between the longitudinal steel reinforcement and concrete, and the FRP and concrete, as well as the tension stiffening effect of the reinforcement and FRP to the concrete, are considered. The FRP-to-concrete bond-slip relation is used to determine the onset of debonding. The analytical predictions compare well with experimental results of FRP-strengthened RC cantilever slabs.

Analysis of continuous reinforced concrete beams in serviceability limit state

The paper investigates to what extent the effect of actions and deformations of statically indeterminate reinforced concrete beams are modified if, instead of the elastic, uncracked model (which is simple but approximate), an elastic, cracked model is applied (which is more accurate) in the computation of the effect of actions at serviceability check. (Continuous beams were modelled with beams fixed at both ends.) The effects of different load levels and moment-redistribution at design were also analysed. It is assumed that the variable load reached its characteristic value prior to the time considered, thus, the location of cracked zones and the tension stiffening effect is determined for that load level. Instead of the interpolation between the two values of deformation, the tension stiffening effect was taken into account by an effective moment of inertia (I_eff), which is equivalent to the other method.