Tension Stiffening Behavior Research Articles

FEA Implementation of Smeared Cyclic Bond Slip-Based Two-Dimensional Membrane Model

A reinforced concrete (RC) material model that includes frictional bond-slip behavior is proposed for use in a two-dimensional (2D) total strain-based finite element analysis (FEA). The initial motivation for this model is to improve tension stiffening behavior in total strain-based models. The proposed material model is based on a simplified mechanistic concept and is capable of modeling these mechanistic behaviors under cyclic loading in a smeared (average) manner. It is validated with shear wall test results available herein. Another motivation for this model is to understand the significance of crack strains so that the model can be extended in the future to include shear friction behavior for cracked concrete. This paper presents an FEA implementation of the proposed RC material model in the OpenSees framework.

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.

Corrosion effects on tension stiffening behavior of reinforced concrete

The investigation of corrosion effects on the tensile behavior of reinforced concrete (RC) members is very important in region prone to high corrosion conditions. In this article, an experimental study concerning corrosion effects on tensile behavior of RC members is presented. For this purpose, a comprehensive experimental program including 58 cylindrical reinforced concrete specimens under various levels of corrosion is conducted. Some of the specimens (44) are located in large tub containing water and salt (5% salt solution); an electrical supplier has been utilized for the accelerated corrosion program. Afterwards, the tensile behavior of the specimens was studied by means of the direct tension tests. For each specimen, the tension stiffening curve is plotted, and their behavior at various load levels is investigated. Average crack spacing, loss of cross-section area due to corrosion, the concrete contribution to the tensile response for different strain levels, and maximum bond stress developed at each corrosion level are studied, and their appropriate relationships are proposed. The main parameters considered in this investigation are: degree of corrosion (<TEX>$C_w$</TEX>), reinforcement diameter (d), reinforcement ratio (<TEX>${\rho}$</TEX>), clear concrete cover (c), ratio of clear concrete cover to rebar diameter (c/d), and ratio of rebar diameter to reinforcement percentage (<TEX>$d/{\rho}$</TEX>).

ELASTIC-PLASTIC FRACTURE ANALYSIS OF STRUCTURAL COLUMNS

This research is achieved in the general frame‐work of the study of the concrete behaviour. It has for objective the development of a numerical tool able to predict the behaviour of reinforced concrete columns with circular and square cross‐sections under an increasing compressive axial load. The concrete behaviour is assumed as elastic‐plastic model with an associated flow rule in compression region and as elastic with tension stiffening behaviour in the tension region. Two yield surfaces have been taken into account according to the Drucker‐Prager and Rankine failure criterions. However, the reinforcing steel is assumed as an elastic strain hardening model. A finite element method using solid cube elements for concrete, and bar elements for the reinforcement have been used. Correlation study between numerical and experimental results is conducted with the objective to establish the validity of the proposed model and identify the significance of the transverse reinforcement volumetric ratio effect on the response of reinforced concrete members. Good agreement has been observed in comparing these results.

인장증강효과를 고려한 철근콘크리트 보의 유효휨강성 평가

Until recently tensile stresses in concrete have not been considered, since it does not affect the ultimate strength of reinforced concrete flexural members significantly However, to verify the load-deflection relationship, the effect of tensile stresses between reinforcing bars and concrete, so-called tension stiffening effect must be taken into account. Main parameters of the tension stiffening behavior are known as concrete strength, and bond between concrete and reinforcing bars. In this study total twenty specimens subjected to bending were tested with different concrete strength, coverage, and de-bonding length of longitudinal bars. The effects of these parameters on the flexural rigidity, crack initiation and propagation were carefully checked and analyzed.

Modeling of Tension-Stiffening Behavior of Reinforced Concrete Ties Strengthened with Fiber Reinforced Plastic Sheets

A model to analyze the behavior of reinforced concrete tension ties strengthened with fiber reinforced plastic (FRP) laminates is developed that allows introduction of a nonlinear constitutive relationship for materials and bond-slip laws at the steel and FRP interface. Experimental results are introduced and compared with analytical results confirming the model reliability. By using the model, a numerical study is carried out to provide evidence of the influence of the amount of fibers and the tension-stiffening behavior of strengthened elements. Considering elements with the same mechanical percentage of reinforcement but composed of different amounts of steel and fibers, the stiffness is influenced only after steel yielding, even if the crack width is reduced by the external strengthening. Finally, evidence is provided for the reduction of tension stiffening in strengthened elements due to reduction of crack spacing.

Insights into the cracking and tension stiffening behaviour of reinforced concrete tension members revealed by computer modelling

Research carried out jointly by the University of Leeds and the University of Durham into the behaviour of axially reinforced prisms subjected to pure tension led to formulae for the prediction of the deformations of such members that depended on the crack spacing under any particular load. This is a subject that does not appear to have been studied significantly in the past, and this paper describes an investigation of the development of crack spacing. This has been done by developing stochastic models of the process of crack formation. These models permitted various possible assumptions to be considered and the most realistic identified. The results of the stochastic modelling have then been used to develop formulae for the prediction of deformations, which have been tested against a large body of experimental data. Agreement between the experimental and calculated results has been shown to be good.

Insights into the cracking and tension stiffening behaviour of reinforced concrete tension members revealed by computer modelling

Insights into the cracking and tension stiffening behaviour of reinforced concrete tension members revealed by computer modelling

Tension Stiffening and Cracking of Steel Fiber-Reinforced Concrete

Fiber-reinforced concrete used in structural applications requires characteristic material properties that can be easily incorporated into existing design procedures. This paper investigates the postcracking response of reinforced concrete tension members made with both plain and steel fiber-reinforced concrete (SFRC). Loading was either monotonic or cyclic, and shrinkage effects are included in analysis of the member response. Tension-stiffening results are used to determine the average tensile response of concrete after cracking, and an expression is developed to predict this smeared behavior as a material property for cracked SFRC, as well as to estimate crack spacings. Specimens with steel fibers exhibited increased tension stiffening and smaller crack spacings, which both contributed to a reduction in crack widths. The postcracking tensile strength of fiber concrete at the cracks is the determining factor affecting behavior and is a fundamental material property used to predict tension stiffening and crack behavior for conventionally reinforced SFRC. The uniaxial strength of SFRC immediately after cracking governs serviceability behavior, while the postcracking strength at larger deformations governs strength design and is responsible for tension stiffening after yielding of the reinforcement. Cyclic loading did not have a significant effect on either tension stiffening or crack width control for the specimens tested.

유연도법 섬유요소모델에 의한 반복하중을 받는 철근콘크리트 교각의 연성능력 평가

유연도법 섬유요소모델을 통하여 반복하중을 받는 철근콘크리트 교각의 비탄성 이력 거동을 추적하고 직접적인 방법에 의해 변위연성도 평가를 수행하였다. 철근 콘크리트 교각의 극한상태까지의 비탄성 거동을 합리적으로 추적하기 위해 인장강성거동, 기둥-기초면의 불연속 변위 등을 고려하여 철근과 콘크리트의 평균응력-평균변형률 관계, 접촉면요소 등을 실험과 잘 일치하는 기존의 해석 모델을 수정, 적용하였다. 또한 수치해석시 간편하게 적용할 수 있는 직접적인 방법에 의하여 교각의 연성능력을 평가하였으며, 항복변위 및 극한변위의 산출에 영향을 미치는 적분점의 위치, 콘크리트 압쇄 후 강루 철근의 low-cycle fatigue에 의한 파단 시점 등에 대하여 유연도법 섬유요소모델에 적용할 수 있는 값들을 제시하였다. 해석에 의한 변위연성도는 10%이내의 오차를 보이므로, 적용한 해석기법 및 모델에 의한 항복변위 및 극한변위의 평가는 타당하다고 할 수 있다. The evaluation of displacement ductility is performed by direct method through tracking the inelastic hysteretic behavior of RC bridge columns subject to cyclic loading using a flexibility-based fiber element mode. To reasonably track the inelastic behavior until the RC bridge column reaches its ultimate state, the average stress-average strain relations and joint elements, which agree well with experiments, are modified and applied considering the tension stiffening behavior and discontinuous displacement between the column and its base. In addition the evaluation of displacement ductility is performed by a direct method easily applicable to numerical analysis. Locations for the integration points, values for the post-crushing concrete strength and low-cycle fatigue failure of longitudinal reinforcement that affect the calculation of yielding and ultimate displacements are proposed for the application to flexibility-based fiber element model. Since less than 10% of error occurs during the displacement ductility analysis, the yielding and ultimate displacements evaluated by the applied analysis method and model appear to be valid.

Influence of Matrix Ductility on Tension-Stiffening Behavior of Steel Reinforced Engineered Cementitious Composites (ECC)

In this paper, the interaction of structural steel reinforcement and high-performance fiber-reinforced cement composites (HPFRCC) in uniaxial tension is examined. The effects of cementitious composite ductility on the steel reinforced composite deformation behavior are experimentally studied and contrasted to normal reinforced concrete (RC). The substitution of brittle concrete with an engineered cementitious composite (ECC), a particular type of HPFRCC with strain hardening and multiple cracking properties, has shown to provide improved load-deformation characteristics in terms of RC tensile strength, deformation mode, and energy absorption. Analysis of the deformation mechanisms suggests that combining steel reinforcement and ECC results in composite action, where unlike in RC or regular FRC, both constituent materials deform compatibly in the postcracking and postyielding deformation process. This deformation compatibility results in a more uniform strain distribution in reinforcement and composite matrix, reduced interfacial bond stress, and controlled damage at relatively large inelastic composite deformations. Research described here focuses on the influence of composite ductility on the deformation behavior of the RC and its effects on the strain distribution in the reinforcement, composite matrix, and interfacial bond.

Effects of shrinkage on tension stiffening and cracking in reinforced concrete

Basic concepts of tension stiffening behaviour of reinforced concrete members under tension are reviewed, and different approaches to account for this behaviour are linked together. This includes a "load sharing" approach, where the average load carried by the cracked concrete is used to determine the post-cracking stress–strain response of concrete in tension, and a "tension stiffening strain" approach, which evaluates changes in member stiffness to obtain a reduction in member deformation by including the stiffening effect of the tension carried by concrete between cracks. Shrinkage strains are then included in an analysis of tension stiffening and the results of this analysis are validated with experimental data. The experimental study was carried out for symmetrically reinforced axial tension members having reinforcing percentages between 1% and 2% and shrinkage strain values up to 230 µε. Failure to account for initial member shortening caused by shrinkage leads to an apparent reduction in tension stiffening, which becomes more predominant as the percentage of reinforcement increases. Corrected results indicate that tension stiffening is independent of the reinforcing steel ratio, ρ (within the studied field for 1% &lt; ρ &lt; 2%) and continues to decrease during loading after cracking has stabilized. Test results are also compared with a number of proposals made by other researchers in the past. Prediction of crack widths based on results from axial tension member tests is not significantly affected by shrinkage.Key words: bond, cracking, crack widths, reinforced concrete, shrinkage, stress-strain response, tension, tension stiffening.

Analysis of reinforced concrete beams strengthened in flexure with composite laminates

The structural behaviour of reinforced concrete beams strengthened in flexure by means of externally bonded fibre reinforced composite laminates is simulated numerically using a nonlinear finite element layered model. The full-bond assumption between the composite laminate, steel reinforcement, and the concrete is assumed, and shear deformations are neglected. Interlayer compatibility is achieved by imposing the same displacements at the interfaces of adjacent layers. The concrete is assumed to be nonlinear in compression and to exhibit a post-cracking tension-stiffening behaviour in tension. The behaviour of the steel reinforcement is modelled as elastic-plastic, while that for the composite laminate is linear elastic using an equivalent elastic modulus obtained from the so-called "classical lamination theory" of composite structures. An incremental, iterative displacement-control numerical analysis is developed. The finite element code is validated using published test results for conventional reinforced concrete beams, as well as for beams strengthened with composite laminates. A comparison of the numerical and experimental curves shows very good agreement. The effects of various parameters on the behaviour of composite-strengthened concrete beams are examined.Key words: reinforced concrete beams, fibre reinforced composite strengthening, nonlinear finite element analysis.

Tension Stiffening Behavior of Reinforced Masonry

The tensile behavior of reinforced concrete and clay unit masonry was studied by conducting a series of 33 direct tension tests on instrumented specimens. The effect of the steel reinforcement ratio was the principal variable considered. Reinforcing steel bars varied from no. 4 to no. 11 bars, while masonry unit widths varied from 90 to 290 mm. The measured tensile stress-strain curve permitted determination of the decrease in the tension stiffening behavior as a function of the cracking strain. All specimens were strained to levels far in excess of those permitted by design codes without suffering tensile bar failure. Initial behavior was governed by elastic properties. After cracking, a rapid decrease in effective stiffness was observed with the stiffness reducing to that of the reinforcing steel at a strain of approximately four times the cracking strain. This observation is significantly different from that reported for reinforced concrete. Examination of the stress-strain curve after yield showed a very strong influence of the reinforcing ratio on the shape of the stress-strain curve with lower steel ratios resulting in decreased ductility.