• Journal of the Korea Concrete Institute
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• v.11 no.4
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• pp.83-93
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• 1999

This paper presents tension stiffening effect of Reinforced concrete members obtained from experimental results on direct tension and bending. From the direct tension test program, crack patterns were investigated with tension softening behaviors of concrete. Tension stiffening effects and losses of strain energy were, also, analyzed from the load-deflection curve with the main experimental variables such as concrete strength, yielding stress and reinforcement ratio of rebar. Tension stiffening effect of RC members increase linearly until the first crack initiate, decrease inversely with number of cracks, and then decrease rapidly when splitting cracks are happened. The tension stiffening effect is shown to be more important at the member of lower reinforcement than that of higher. Therefore, it necessitates to consider the tension stiffening effects at a nonlinear analysis. From the above analysis, a tension stiffening model of concrete is proposed and verified by applying it to bending members. From the numerical analysis by finite element approach, it is shown that the proposed model evaluates a little higher in analyzing at nonlinear region of high strength concrete, but, perform satisfactorily in general.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.141-148
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• 1998

An analytical model which can simulate the post-cracking behavior of reinforced concrete structures subjected to in-plane shear and normal stresses is presented. Based on the force equilibriums, compatibility conditions, and bond stress-slip relationship between steel and concrete, a criterion to simulate consider the tension-stiffening effect is proposed. The material behavior of concrete is described by an orthotropic constitutive model, and focused on the tension-compression region with tension-stiffening and compression softening effects defining equivalent uniaxial relations in the axes of orthotropy. Correlation studies between analytical results and available experimental data are conducted with the objective to establish the validity of the proposed model.

• Magazine of the Korean Society of Agricultural Engineers
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• v.40 no.4
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• pp.120-129
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• 1998

The tension stiffening in reinforced concrete member means increase of stiffness caused by the effective tensile stress between cracks and the tension softening behavior of concrete. This paper presents on the tensile behavior and tension stiffening of RC tension members. Direct tension tests were performed with a main experimental variables such as concrete strength, rebar diameter and strength. The tension stiffening was analyzed from the load-displacement relationship and was compared with ACI code, CEB model and the proposed by Collins ＆ Mitchell. The results are as follows : The tension behaviors of RC members were quite different from those of bare bar and were characterized by loading and concrete cracking steps. The effect of tension stiffening decreased rapidly as the rebar diameter and strength increased, and the concrete strength increased. The proposed by Collins ＆ Mitchell described well the experimental results, regardless of rebar types and concrete. But, ACI code and CEB model described a little differently, depending on the types. The effect of tension stiffening in RC member was the biggest near at concrete cracking step and decreased gradually to the bare bar's behavior as loading closed to the breaking point. Thus, tension stiffening in RC members should be taken into account when the load-deflection characteristics of a member are required or a precise analysis near the load of concrete clacking is needed.

• 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.

• 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.

• Computers and Concrete
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• v.3 no.4
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• pp.213-233
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• 2006

Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always 'converges'. Bifurcations are prevented due to the scaling technique.

• Computers and Concrete
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• v.1 no.1
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• pp.77-98
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• 2004

This paper presents a numerical model for simulating the nonlinear response of reinforced concrete (RC) shear walls subject to cyclic loadings. The material behavior of cracked concrete is described by an orthotropic constitutive relation with tension-stiffening and compression softening effects defining equivalent uniaxial stress-strain relation in the axes of orthotropy. Especially in making analytical predictions for inelastic behaviors of RC walls under reversed cyclic loading, some influencing factors inducing the material nonlinearities have been considered. A simple hysteretic stress-strain relation of concrete, which crosses the tension-compression region, is defined. Modification of the hysteretic stress-strain relation of steel is also introduced to reflect a pinching effect depending on the shear span ratio and to represent an average stress distribution in a cracked RC element, respectively. To assess the applicability of the constitutive model for RC element, analytical results are compared with idealized shear panel and shear wall test results under monotonic and cyclic shear loadings.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.799-823
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• 2016

A finite element model for the non-linear dynamic analysis of a reinforced concrete (RC) containment shell of a nuclear power plant subjected to extreme loads such as impact and earthquake is presented in this work. The impact is modeled by using an uncoupled approach in which a load function is applied at the impact zone. The earthquake load is modeled by prescribing ground accelerations at the base of the structure. The nuclear containment is discretized spatially by using 20-node brick finite elements. The concrete in compression is modeled by using a modified $Dr{\ddot{u}}cker$-Prager elasto-plastic constitutive law where strain rate effects are considered. Cracking of concrete is modeled by using a smeared cracking approach where the tension-stiffening effect is included via a strain-softening rule. A model based on fracture mechanics, using the concept of constant fracture energy release, is used to relate the strain softening effect to the element size in order to guaranty mesh independency in the numerical prediction. The reinforcing bars are represented by incorporated membrane elements with a von Mises elasto-plastic law. Two benchmarks are used to verify the numerical implementation of the present model. Results are presented graphically in terms of displacement histories and cracking patterns. Finally, the influence of the shear transfer model used for cracked concrete as well as the effect due to a base slab incorporation in the numerical modeling are analyzed.

• Computers and Concrete
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• v.11 no.2
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• pp.123-148
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• 2013

The nonlinear finite element method with eight noded isoparametric quadrilateral element for concrete and two noded element for reinforcement is used for the prediction of the behavior of reinforcement concrete structures. The disturbed state concept (DSC) including the hierarchical single surface (HISS) plasticity model with associated flow rule with modifications is used to characterize the constitutive behavior of concrete both in compression and in tension which is named DSC/HISS-CT. The HISS model is applied to shows the plastic behavior of concrete, and DSC for microcracking, fracture and softening simulations of concrete. It should be noted that the DSC expresses the behavior of a material element as a mixture of two interacting components and can include both softening and stiffening, while the classical damage approach assumes that cracks (damage) induced in a material treated acts as a void, with no strength. The DSC/HISS-CT is a unified model with different mechanism, which expresses the observed behavior in terms of interacting behavior of components; thus the mechanism in the DSC is much different than that of the damage model, which is based on physical cracks which has no strength and interaction with the undamaged part. This is the first time the DSC/HISS-CT model, with the capacity to account for both compression and tension yields, is applied for concrete materials. The DSC model allows also for the characterization of non-associative behavior through the use of disturbance. Elastic perfectly plastic behavior is assumed for modeling of steel reinforcement. The DSC model is validated at two levels: (1) specimen and (2) practical boundary value problem. For the specimen level, the predictions are obtained by the integration of the incremental constitutive relations. The FE procedure with DSC/HISS-CT model is used to obtain predictions for practical boundary value problems. Based on the comparisons between DSC/HISS-CT predictions, test data and ANSYS software predictions, it is found that the model provides highly satisfactory predictions. The model allows computation of microcracking during deformation leading to the fracture and failure; in the model, the critical disturbance, Dc, identifies fracture and failure.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.311-330
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• 2006

Standard compression tests of steel fiber reinforced concrete (SFRC) cylinders are conducted to formulate compressive stress versus compressive strain relationship of SFRC. Axial pullout tests of SFRC specimens are also conducted to explore its tensile stress strain relationship. Cover concrete spalling and reinforcement buckling models developed originally for normal reinforced concrete are modified to extend their application to SFRC. Thus obtained monotonic material models of concrete and reinforcing bars in SFRC members are combined with unloading/reloading loops used in the cyclic models of concrete and reinforcing bars in normal reinforced concrete. The resulting path-dependent cyclic material models are then incorporated in a finite-element based fiber analysis program. The applicability of these models at member level is verified by simulating cyclic lateral loading tests of SFRC columns under constant axial compression. The analysis using the proposed SFRC models yield results that are much closer to the experimental results than the analytical results obtained using the normal reinforced concrete models are.