Tension Stiffening Of Concrete Research Articles

Simplified Evaluation of Shear Stiffness Degradation of Diagonally Cracked Reinforced Concrete Beams.

Shear cracking in concrete box-girder bridges, which could cause excessive deflection during the serviceability limit state, cannot be effectively avoided by code-guided design. While elastic shear deformation only accounts for a small proportion of total deformation for un-cracked reinforced concrete (RC) beams, the magnitude of after-cracking shear deformation becomes comparable to flexural deformation for RC beams. However, there is still a lack of practical models to predict the after-cracking shear deformation of RC beams. First, six thin-webbed I beams were tested to investigate the shear stiffness degradation mechanism and the decrease ratio. Then, a very simple truss strut angle formula, which is the crucial parameter for shear stiffness, was established. Furthermore, a stiffness degradation rule for partially cracked beams was proposed considering the influence of concrete tension stiffening, which is essential for predicting the development process of after-cracking shear deformation. Finally, directly measured shear strains were used to validate the proposed shear stiffness model. The results showed that the shear stiffness drops to about 30~40% of the original stiffness after the first diagonal crack, and the remaining shear stiffness is only about 10% of the original one when the stirrup yields. Increasing the stirrup ratio is a more effective method to control shear stiffness degradation for diagonally cracked RC beams. Also, the proposed shear stiffness model well captures the main features of the shear stiffness degradation, and it provides a relatively accurate prediction of the equivalent shear stiffness at the post-cracking stage.

Long-term loss of tension stiffening of concrete containing recycled aggregate and steel fibres

This paper presents experimental results on the long-term loss of tension stiffening of concrete containing recycled aggregate and steel fibres. Washed construction and demolition wastes (CDW) size 20 mm were used as a replacement for the natural coarse aggregate, and hooked-end steel fibres (DRAMIX 3D 65/35BG) were added to the mixes. Square section prisms of concrete (120x120x1200 mm) reinforced with a central steel bar were prepared and cast with different replacement percentages of recycled aggregate and volume fractions of steel fibres. A direct tensile load was applied to the steel bar and the measurements of the strain on the concrete surfaces were then recorded for a period of 35 days to assess the long-term loss of tension stiffening. The results indicated that the substitution of NA by RA increased the loss of tension stiffening over time up to 12.9%. However, the addition of steel fibres proved to be highly beneficial; the inclusion of 0.5% and 1.0% steel fibre content to the NC and RAC reduced the loss up to 9.8% and 20.4%, respectively. According to the obtained results, modifications to the Eurocode2 method for predicting the long-term deflection of reinforced concrete beams were proposed to be implicated in the calculation steps for this type of concrete.

Linear Concrete Tension Stiffening Model for Reinforced Concrete Elements

Linear expressions for tension stiffening of concrete are nowadays widely used in software packages of structural analysis. Nevertheless, more elaborated expressions of tension stiffening available in the literature have been used successfully in the past. The use of linear approximations is justified since the influence of the tension stiffening effect in the deformation of the structure is small but not negligible. In this sense, linear approximations are simpler and can be accurate enough. However, this linear approximation, in its present form, does not provide good results in terms of deformations at the element level. This paper proposes a linear expression of the tension stiffening supported by the experimental formulation used to predict the flexural behavior of concrete beams. A detailed example is presented.

Long-term behaviour of recycled aggregate concrete beams prestressed with carbon fibre-reinforced polymer (CFRP) tendons

The utilisation of recycled aggregate concrete (RAC) is commonly recognised as one of the most effective means to achieve cleaner and sustainable development in civil engineering. To promote the application of RAC, prestressing technique can be employed to overcome the inherent disadvantages of RAC beams associated with poor cracking resistance and large deflections. However, the research on the prestressed RAC beam is quite limited, and no research has been performed on their long-term behaviour. This paper presents a finite element (FE) analysis for investigating the long-term behaviour of RAC beams prestressed with carbon fibre-reinforced polymer (CFRP) tendons considering the effects of concrete creep, concrete shrinkage, tendon relaxation as well as the cracking and tension stiffening of concrete. Based on the principle of superposition, the variations of the stress and strain with time are considered in the numerical analysis using step-by-step method. The FE model is calibrated with the experimental results obtained from the literature. Based on the validated model, a comprehensive parametric study is performed to investigate the effects of the replacement ratio of recycled coarse aggregate (RCA), concrete strength, reinforcement ratio, prestress level, and sustained load level on the long-term behaviour of prestressed RAC beams. The obtained results demonstrate that increasing the prestress load is an effective way to reduce the long-term deflection of RAC beams, and the use of RAC with low RCA replacement ratio is suggested. Besides, the main causes of the long-term deflection and axial shorting of the CFRP prestressed RAC beams are also studied. This research provides a pioneering and insightful study of the long-term behaviour of CFRP prestressed RAC beams. The obtained results demonstrate that the time-dependent effects should be well considered in the design before the prestressed RAC beam is used in practice.

General Mathematical Model for Analysing the Bending Behaviour of Rectangular Concrete Beams with Steel, Fibre-Reinforced Polymers (FRP) and Hybrid FRP–Steel Reinforcements

The design guidelines available in building codes for steel and fibre reinforced polymer (FRP) reinforced concrete (RC) beams have been developed on the basis of empirical models. While these models are successfully used for practical purposes, they require continuous improvements with more experimental data. This paper aims to develop a general mathematical model derived from the intrinsic material properties of concrete and certain reinforcements to analyse the bending behaviour of reinforced concrete beams. The proposed model takes into account the effects of non-linearity and ductility on the real behaviour of concrete under compression as well as the concrete tension stiffening. The model focused on analysing the flexural behaviour of rectangular steel, FRP and hybrid FRP–steel RC beams, using the moment–curvature relationship. A general static equilibrium equation was developed and mathematically solved with precise methods to establish a moment–curvature relationship. The effective flexural stiffness (EFS) is therefore calculated by the slope of the moment–curvature diagram, and then the load–deflection response is immediately deduced according to the loading conditions. The present model results were compared with numerous test data reported by various researchers. The comparisons reveal a good accuracy for predicting the EFS and load–deflection response for either steel, FRP, and hybrid reinforced concrete beams, with an error average less than 10%.

Simplified biaxial tension stiffening model for the analysis of shear panels using softened membrane model

Many of the existing tension stress–strain relations for concrete used in smeared shear models consider the contribution of concrete in tension even after steel yielding. Although the contribution of concrete in tension is less significant than its contribution in compression, the use of these existing models often leads to overestimating the shear response of reinforced concrete (RC) panels. An improved concrete tension stiffening model incorporating the effect of biaxial stresses is proposed in this study. The effect of tension stiffening on the behaviour of shear panels under normal and shear stresses is investigated by incorporating tension stiffening in the softened membrane model (SMM). The existing SMM algorithm can be used to estimate the behaviour of RC panels subjected only to pure shear. In the proposed analysis using SMM, a new secant-based algorithm is used to estimate the behaviour of RC panels under combined normal and shear loads. Estimates from the proposed model are compared with estimates from original SMM and experimental results. The comparison shows that the proposed model provides better estimates of shear response for RC panels that undergo high shear strains than the original SMM. Furthermore, the proposed secant-based algorithm estimates panel behaviour under combined loading in reduced computational time.

The effect of tension stiffening in moment-curvature responses of prestressed concrete members

Although tensile resistance of concrete is often neglected in calculating the nominal flexural capacity of a concrete member, it needs to be taken into account to accurately trace the deformation response of concrete members as it affects pre- and post-cracking behavior. To adequately address tensile resistance contributed by concrete in moment–curvature analysis, it is necessary to exploit a proper concrete tensile stress–strain model. While constitutive stress–strain models of reinforced concrete in tension have been studied by many researchers and well documented, those of prestressed concrete have gained relatively less attention. There are also conflicting results on how prestressing force affects concrete tension stiffening. This study fills the gap in existing studies and suggests an appropriate and simple model capturing the concrete tensile stress–strain relationship of prestressed concrete in a moment–curvature analysis. Based on an inverse-engineering approach using experimental test data and nonlinear analysis results, the effect of concrete tension stiffening varied by the level of prestressing force is investigated. The results show that concrete tensile properties hardly affect the force–deformation response of beams with high-level prestressing. Additionally, several parameters related to concrete tension stiffening are examined in the parameter study. By comparing predicted moment–curvature responses with test data, ideal values for considered parameters are obtained. Based on the parameter study, simple equations are proposed that are expressed in concrete compressive strength to simulate the concrete tensile stress–strain responses of partially prestressed members. The proposed equations are demonstrated using several prestressed beam tests found in previous studies.

Modelling the bond in GFRP bar reinforced concrete thin structural members

This paper analyses the accuracy of FE (Finite Element) modelling of concrete thin slabs, reinforced with GFRP (Glass Fiber Reinforced Polymer) bars, under bending loading conditions. It considers two strategies of concrete/bar interaction approach – direct and indirect. Indirect bond approach was combined with concrete tension stiffening model, whereas the direct bond one employed plain concrete constitutive model. Apart from selection of material and bond models, FE mesh sensitivity was examined. The efficiency of both bond modelling strategies was proven for the slab of standard thickness (100 mm) failed due to concrete crushing, whereas direct bond method was shown indispensable when simulating very thin slabs (40 mm) failed due to bar debonding.

Micromechanical modeling of tension stiffening in FRP-strengthened concrete elements

This article presents a micromodeling computational framework for simulating the tensile response and tension-stiffening behavior of fiber reinforced polymer–strengthened reinforced concrete elements. The total response of strengthened elements is computed based on the local stress transfer mechanisms at the crack plane including concrete bridging stress, reinforcing bars stress, FRP stress, and the bond stresses at the bars-to-concrete and fiber reinforced polymer-to-concrete interfaces. The developed model provides the possibility of calculating the average response of fiber reinforced polymer, reinforcing bars, and concrete as well as the crack spacing and crack widths. The model, after validation with experimental results, is used for a systematic parameter study and development of micromechanics-based relations for calculating the crack spacing, fiber reinforced polymer critical ratio, debonding strength, and effective bond length. Constitutive models are also proposed for concrete tension stiffening and average response of steel reinforcing bars in fiber reinforced polymer–strengthened members as the main inputs of smeared crack modeling approaches.

Flexural behavior of rectangular FRP-tubes filled with reinforced concrete: Experimental and theoretical studies

This paper presents experimental and theoretical investigations on the flexural behavior of rectangular concrete-filled fiber-reinforced polymer (FRP) tube (CFFT) beams with steel rebar. Seven full-scale CFFT beams, 3200mm long and 305×406mm2 cross section, were tested under a four-point bending load and were compared to two control steel-reinforced concrete (RC) beams. The CFFT beams had the same flexural steel reinforcement, but they had different wall thicknesses of filament-wound FRP tubes. The experimental results indicate an outstanding performance of the CFFT beams in terms of strength and energy absorption compared to the RC beams since their flexural strength and energy attained values 344% and 1052% higher than that of the RC beams, respectively. A strain compatibility/equilibrium model was developed to predict the moment-curvature response of the CFFT section addressing the issue of confinement and tension stiffening of concrete. The analytical results match well the experimental results in terms of moments, curvature, strains, and neutral axis location. Based on the model, the deflection can be predicted by integrating the curvatures along the span of the flexural member.

Non-linear analysis of reinforced concrete walls under three-dimensional loading

Analytical studies are conducted to develop an effective analytical model to simulate the non-linear response of reinforced concrete (RC) walls subjected to three-dimensional (3D) loads. The interaction between the concrete and steel is taken into account with consideration of the smeared behaviour of steel and tension stiffening of concrete. The proposed model is formulated to address the interaction between the axial force, shear, bending and torsion loads. The shear mechanism along the beam is modelled by adopting a Timoshenko beam approach for 3D frame elements with arbitrary cross-section geometry. The non-linear behaviour of the composite element is derived entirely from the constitutive laws of concrete and steel. The concrete constitutive model follows the softened membrane model that predicts the tensile cracking, compression crushing, strain softening, steel yielding and material damage under combined loadings. The validity of the model is established through a correlation study of experimentally tested RC shear walls subjected to monotonic loading conditions.

Bending and time-dependent responses of RC beams strengthened with bonded carbon fiber composite laminates

Externally bonded carbon fiber reinforced polymer (CFRP) sheet has shown excellent performance to repair, restore and increase the load-carrying capacity of RC structures. In this paper results of an experimental test are presented in which fourteen RC beams strengthened with CFRP epoxy bonded sheets in flexure and time-dependent tests are subjected to four-point bending and sustained load respectively. The test variables included different degrees of strengthening scheme and two types of sustained load for both un-cracked and cracked beams. For flexural strengthening, the increase of ultimate strength provided by CFRP was assessed by varying the layers of laminates and incorporating end anchorage. In time-dependent test, deflection reduction coefficient in concrete tension stiffening model is proposed to evaluate the stiffness of the section after cracking for RC beams. It is found that the analytical values based on effective modulus method (EMM) are in general gives conservative estimates of the experimental results.

Modeling of Tension Stiffening Behavior in FRP‐Strengthened RC Members Based on Rigid Body Spring Networks

Abstract: Allowing for the tension stiffening effects resulting from the bond between steel reinforcement and surrounding concrete leads to effective deformation analysis of reinforced concrete (RC) members when using a nonlinear finite element analysis modeled on the smeared crack concept. Nowadays, externally bonded fiber reinforced polymer (FRP) composites are widely used for strengthening existing RC structures. However, it remains unclear to what extent the tension stiffening of postcracking concrete is quantitatively influenced by the addition of FRP composites, as a result of the bond between the FRP and the concrete substrate. This article presents a discrete model, which is based on rigid body spring networks (RBSN), for investigating the tension stiffening behavior of concrete in FRP‐strengthened RC tensile members. A two‐parameter fracture energy‐based model was deployed to represent the bond‐slip behavior of the FRP‐to‐concrete interface. The reliability of the RBSN model was verified through comparisons with previous test results. Further parametric analysis indicates that the tension stiffening of concrete is hardly influenced by the addition of FRP composites before the yield of steel reinforcement has occurred although concrete crack patterns and crack widths may be influenced by the bond‐slip behavior of the FRP‐to‐concrete interface.

A homogenization approach for uncertainty quantification of deflection in reinforced concrete beams considering microstructural variability

Uncertainty in concrete properties, including concrete modulus of elasticity and modulus of rupture, are predicted by developing a microstructural homogenization model. The homogenization model is developed by analyzing a concrete representative volume element (RVE) using the finite element (FE) method. The concrete RVE considers concrete as a three phase composite material including: cement paste, aggregate and interfacial transition zone (ITZ). The homogenization model allows for considering two sources of variability in concrete, randomly dispersed aggregates in the concrete matrix and uncertain mechanical properties of composite phases of concrete. Using the proposed homogenization technique, the uncertainty in concrete modulus of elasticity and modulus of rupture (described by numerical cumulative probability density function) are determined. Deflection uncertainty of reinforced concrete (RC) beams, propagated from uncertainties in concrete properties, is quantified using Monte Carlo (MC) simulation. Cracked plane frame analysis is used to account for tension stiffening in concrete. Concrete homogenization enables a unique opportunity to bridge the gap between concrete materials and structural modeling, which is necessary for realistic serviceability prediction.

Effect of steel corrosion pattern on RC beam performance

Chloride-induced corrosion in reinforced concrete leads to a reduction of the steel cross-section and deterioration of the steel–concrete bond. In this paper, experimental results are presented in order to clarify the respective influence of these degradations on beam serviceability (deflection). Pitting corrosion simulations were performed and two naturally corroded beams (14 and 23 years old) were analysed. Corrosion simulations have shown that the reduction in steel cross-section due to local pitting corrosion does not affect serviceability. Increased deflection is due to deterioration of the steel-concrete bond (reduction of concrete tension stiffening). Experimental results obtained on two corroded beams broken and analysed after 14 years and 23 years of chloride exposure showed that, during the natural chloride-induced corrosion process, the corrosion pattern evolves in relation to the corrosion cracking. Localised pitting corrosion is responsible for the initiation of corrosion cracking. Then, as the width of the cracks develops, general corrosion becomes gradually the main corrosion pattern. According to these experimental results, a mechanical model is proposed for serviceability assessment, which takes into account the evolution of the corrosion pattern from local pitting corrosion to general reinforcement corrosion.

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.

Discussion of “Explaining the Riddle of Tension Stiffening Models for Shear Panel Experiments” by Evan C. Bentz

Estimating tension stiffening with an average stress-strain response for cracked concrete is one convenient way to account for tension carried by the concrete between cracks, and this is what the author calls the “concrete tension stiffening curve.” The author models the tension stiffening relationship with a unique approach that uses the concept of bond demand to help explain observed differences between the many tension stiffening curves proposed in the past. While the paper examines tension stiffening in shear panel elements, for simplicity, this discussion focuses on the behavior of axial tension members. An important parameter often ignored is concrete shrinkage and the effect this has on the amount of tension stiffening measured in experiments. Considere 1899, 1902 was probably the first to realize the importance of this effect a few years after his initial work on tension stiffening more than 100 years ago. Aside from Abrishami and Mitchell 1996 and Bischoff 2001 , few have since taken this effect into account. Restraint to shrinkage from the reinforcement puts the reinforcing bar s into compression and places the concrete in tension at the same time. This obviously reduces the cracking load of the member, but, more importantly, restraint to shrinkage causes an offset in the bare bar response, as shown in Fig. 1 here. Because tension stiffening is measured by subtracting the bare bar response from the measured member response, ignoring this offset typically leads to an underestimation of tension stiffening that depends on both the amount of shrinkage and reinforcing ratio since the reinforcing ratio determines the amount of restraint . As

Nonlinear Dynamic Analysis of Reinforced Concrete Slabs

In this study the nonlinear transient dynamic analysis of reinforced concrete slabs using the finite element method is presented. Eight-node Serendipity degenerated elements have been employed. This element is based on isoparametric principles with modifications, which relax excessive constraints. The modifications include reduced order integration to overcome the shear locking. A layered approach is adopted to discretize the concrete through the thickness. Both an elastic-perfectly plastic and strain hardening plasticity approaches have been employed to model the compressive behavior of the concrete. A tensile strength criterion is used to initiation of crack and a smeared fixed crack approach is used to model the behavior of the cracked concrete. Tension stiffening in concrete is assumed such that the concrete can take some tension after cracking. Implicit Newmark with corrector-predictor algorithm is employed for time integration of the equation of motion. Several examples are analyzed using the proposed model. The numerical results showed good agreement with other sources.

Effective Tension Active Cross-Section of Reinforced Concrete Beams After Cracking

In the design of concrete structures, estimation of the deflection of the structural members under the service loads is often a critical factor. Strains and displacements are linked to the tension stiffening effect, which is not quantified in the standards. The CEB-FIP model code proposes an interesting simplified method for evaluating the concrete tension stiffening effect on reinforced concrete behavior. One of the parameters which enables the mechanical contribution of the concrete to be quantified is the effective tensile active section of the reinforced concrete beams. In this paper, a new method for calculating the effective tensile active section Act.ef is proposed. The calculation is based on an analytical model of stress distribution in the full depth of the concrete section. An experimental study on several reinforced concrete beams is reported. The results show that the new proposed model enhances the accuracy of the beam deflection predictions significantly.

콘크리트의 인장강성을 고려한 RC보의 공칭비틀림강도

콘크리트의 인장강성을 고려한 RC보의 공칭비틀림강도