• Proceedings of the Korea Concrete Institute Conference
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• 1999.10a
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• pp.479-482
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• 1999

The tension stiffening effect, which means the maintaining a part of stiffness after cracking of concrete in tensile, exists at a reinforced concrete member because of the concrete softening and bonding stress between cracks. It is required to consider it for precise analysis and evaluation o structural behavior, due to the possibility of discrepancy between the actual behavior and the analysis without considering the tension stiffening effect. Making and adopting a tension stiffening model is the most simple and effective way for considering it at nonlinear analysis which indicated the estimation from models and experimental results were similar each others. The comparisons on RC beam were, also performed in order to analyzed the influence of concrete strength and steel ratio into the structural behavior. They indicated that the results from analysis estimated quite closely to the test results at low steel ratio, however, overestimated at high steel ratio. The overestimation increase linearly as concrete strength or steel ratio increased.

• Nuclear Engineering and Technology
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• v.36 no.6
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• pp.512-527
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• 2004

This paper describes the finite element (FE) analysis results of a 1/4 scale model of a prestressed concrete containment vessel (PCCV) by considering the tension stiffening effect, which is a result of the bond effect between the concrete and the steel. The tension stiffening model is assumed to be an exponential form based on the relationship between the average stress and the average strain of the concrete. The objective of the present FE analysis is to evaluate the ultimate internal pressure capacity of the PCCV, as well as its failure mechanism, when the PCCV model is subjected to a monotonous internal pressure beyond is design pressure capacity. With the commercial code ABAQUS, the FE analysis used two concrete failure criteria: a 2-dimensional axi-symmetric model with modified Drucker-Prager failure criteria and a 3-dimensional model with a damaged plasticity mod디. The results of our FE analysis on the ultimate pressure capacity and failure modes of PCCV have a good agreement with the experimental data.

• Computers and Concrete
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• v.1 no.4
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• pp.417-432
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• 2004

An analytical model which can simulate the post-cracking nonlinear behavior of reinforced concrete (RC) members such as bars and panels subject to uniaxial and biaxial stresses is presented. The proposed model includes the description of biaxial failure criteria and the average stress-strain relation of reinforcing steel. Based on strain distribution functions of steel and concrete after cracking, a criterion to consider the tension-stiffening effect is proposed using the concept of average stresses and strains. The validity of the introduced model is established by comparing the analytical predictions for reinforced concrete uniaxial tension members with results from experimental studies. In advance, correlation studies between analytical results and experimental data are also extended to RC panels subject to biaxial tensile stresses to verify the efficiency of the proposed model and to identify the significance of various effects on the response of biaxially loaded reinforced concrete panels.

• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.997-1016
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• 2015

The contribution of tensioned concrete between cracks (tension-stiffening) cannot be ignored when analysing deformation of reinforced concrete elements. The tension-stiffening effect is crucial when it comes to adequately estimating the load-deformation response of steel reinforced concrete and the more recently appeared fibre reinforced polymer (FRP) reinforced concrete. This paper presents a unified methodology for numerical modelling of the tension-stiffening effect in steel as well as FRP reinforced flexural members using the concept of equivalent deformation modulus and the smeared crack approach to obtain a modified stress-strain relation of the reinforcement. A closed-form solution for the equivalent secant modulus of deformation of the tensioned reinforcement is proposed for rectangular sections taking the Eurocode 2 curvature prediction technique as the reference. Using equations based on general principles of structural mechanics, the main influencing parameters are obtained. It is found that the ratio between the equivalent stiffness and the initial stiffness basically depends on the product of the modular ratio and reinforcement ratio ($n{\rho}$), the effective-to-total depth ratio (d/h), and the level of loading. The proposed methodology is adequate for numerical modelling of tension-stiffening for different FRP and steel reinforcement, under both service and ultimate conditions. Comparison of the predicted and experimental data obtained by the authors indicates that the proposed methodology is capable to adequately model the tension-stiffening effect in beams reinforced with FRP or steel bars within wide range of loading.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.507-521
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• 1997

The ultimate behavior of a reinforced concrete hyperbolic paraboloid saddle shell under uniformly distributed vertical load is investigated using an inelastic, large displacement finite-element program originally developed at North Carolina State University. Unlike with the author's previous study which shows that the saddle shell possesses a tremendous capacity to redistribute the stresses, introducing tension stiffening in the model the cracks developed are no longer through cracks and formed as primarily bending cracks. Even though with small tension stiffening effect, the behavior of the shell is changed markedly from the one without tension stiffening effect. The load-deflection curves are straight and the slope of the curves is quite steep and remains unchanged with varying the tension stiffening parameters. The failure of the shell took place quite suddenly in a cantilever mode initiated by a formation of yield lines in a direction parallel to the support-to-support diagonal. The higher the tension stiffening parameters the higher is the ultimate load. The present study shows that the ultimate behavior of the shell primarily depends on the concrete tensile characteristics, such as tensile strength (before cracking) and the effective tension stiffening (after cracking). As the concrete characteristics would vary over the life of the shell, a degree of uncertainty is involved in deciding a specified ultimate strength of the saddle shell studied. By the present study, however, the overload factors based on ACI 318-95 are larger than unity for all the cases studied except that the tension stiffening parameter is weak by 3 with and without the large displacement effect, which shows that the Lin-Scordelis saddle shell studied here is at least safe.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.267-274
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• 2001

In this paper, a analytical model which can simulate the post-cracking behavior and tension stiffening effect in a reinforced concrete(RC) tension member is proposed. Unlike the classical approaches using the bond stress-slip relationship or the assumed bond stress distribution, the tension stiffening effect at post-cracking stage is quantified on the basis of polynomial strain distribution functions of steel and concrete, and its contribution is implemented into the reinforcing steel. The introduced model can be effectively used in constructing the stress-strain curve of concrete at post-cracking stage, and the loads carried by concrete and by reinforcing steel along the member axis can be directly evaluated on the basis of the introduced model. In advance, the prediction of cracking loads and elongations of reinforced steel using the introduced model shows good agreements with results from previous analytical studies and experimental data.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.601-620
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• 2006

The paper presents an effective stiffness model for deformational analysis of reinforced concrete cracked members in bending throughout the short-term loading up to the near failure. The method generally involves the analytical derivation of an effective moment of inertia based on the smeared crack technique. The method, in a simplified way, enables us to take into account the non linear properties of concrete, the effects of cracking and tension stiffening. A statistical analysis has shown that proposed technique is of adequate accuracy of calculated and experimental deflections data provided for beams with small, average and normal reinforcement ratios.

• Journal of the Korea Concrete Institute
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• v.11 no.5
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• pp.131-137
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• 1999

The use of higher strength materials with the strength methed of design has resulted in more slender member and shallower sections. For this reason, it is necessary to satisfy the requirements of serviceability even though the structural safety is the most important limit state. This paper is only concerned with the control of deflections in the serviceability. In this study, an analytical model is presented to predict the deflections of reinforced concrete beams to given loading and environmental conditions. This model is based on the finite element approach in which a finite element is generally divided into a number of stiffening effect due to cracking, creep and shrinkage. Comparisons are made with available measured deflections reported by others to assess the capability of the layered beam model. The calculated values of instantaneous and long-term deflection show good agreement with experimental results in the range of tension stiffening parameter $\beta$ between 2.5 and 3.0.

• Journal of the Korea Concrete Institute
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• v.19 no.6
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• pp.745-754
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• 2007

This paper presents a unified modeling technique for tension stiffening effect in structural concrete members. The model is mathematically derived from the bond stress-slip relationships which account for splitting crack. The relationships in CEB-FIP Model Code 1990 and Eurocode 2 are employed together with the assumptions of a linear slip distribution along the interface and the uniform condition of concrete tensile contribution for the mid section of cracked member at the stabilized cracking stage. With these assumptions, a model of tension stiffening effect is proposed by accounting for the force equilibrium and strain compatibility condition associated to the steel strain and concrete contribution by bond stress. The model is applied to the test results available in literatures, and the predicted values are shown to be in good agreement with the experimentally measured behavior.

• Structural Engineering and Mechanics
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• v.81 no.3
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• pp.349-365
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• 2022

Steel fibre-reinforced concrete (SFRC) is an emerging class of composite for construction. However, a reliable method to assess the flexural behaviour of SFRC structural member is in lack. An analytical technique is proposed for determining the moment-curvature response of concrete beams reinforced with steel fibres and longitudinal bars (R/SFRC members). The behaviour of the tensile zone of such members is highly complex due to the interaction between the residual (tension softening) stresses of SFRC and the tension stiffening stresses. The current study suggests a transparent and mechanically sound method to combine these two stress concepts. Tension stiffening is modelled by the reinforcement-related approach assuming that the corresponding stresses act in the area of tensile reinforcement. The effect is quantified based on the analogy between the R/SFRC member and the equivalent RC member having identical geometry and materials except fibres. It is assumed that the resultant tension stiffening force for the R/SFRC member can be calculated as for the equivalent RC member providing that the reinforcement strain in the cracked section of these members is the same. The resultant tension stiffening force can be defined from the moment-curvature relation of the equivalent RC member using an inverse technique. The residual stress is calculated using an existing model that eliminates the need for dedicated mechanical testing. The proposed analytical technique was validated against test data of R/SFRC beams and slabs.