On the reduce of interfacial shear stresses in fiber reinforced polymer plate retrofitted concrete beams

One major problem when using bonded fiber reinforced polymer (FRP) plate is the presence of high interfacial shear stresses near the end of the composite (edge effect) which might govern the failure of the strengthening schedule. It is known that the decrease of plate thickness reduces the magnitude of stress concentration at plate ends. Another way is to use a plate end tapering. In this paper, the analytical solution of interfacial shear stresses obtained has been extended by a numerical procedure using the modal analysis of finite element method (FEM) in a retrofitted concrete (RC) beam with the FRP plate with tapered end, which can significantly reduce the stress concentration. This approach allows taking into consideration the variation of elastic properties of adhesive and plate as well as the complicated geometrical configurations and effects of thermal loads.     

Time-dependent behavior of RC beams strengthened with externally bonded FRP plates: interfacial stresses analysis

External bonding of fibre reinforced polymer (FRP) composites has becomes a popular technique for strengthening concrete structures all over the world. An important failure mode of such strengthened members is the debonding of the FRP plate from the concrete due to high interfacial stresses near the plate ends. For correctly installed FRP plate, failure will occur within the concrete. Accurate predictions of the interfacial stresses are prerequisite for designing against debonding failures. In particular, the interfacial stresses between a beam and soffit plate within the linear elastic range have been addressed by numerous analytical investigations. In this study, the time-dependent behavior of RC beams bonded with thin composite plate was investigated theoretically by including the effect of the adherend shear deformations. The time effects considered here are those that arise from shrinkage and creep deformations of the concrete. This paper presents an analytical model for the interfacial stresses between RC beam and a thin FRP plate bonded to its soffit. The influence of creep and shrinkage effect relative to the time of the casting and the time of the loading of the beams is taken into account. Numerical results from the present analysis are presented to illustrate the significance of time-dependent of adhesive stresses.     

Interface stress redistribution in FRP-strengthened reinforced concrete beams using a three-parameter viscoelastic foundation model

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, a novel analytical solution has been developed to predict the interface stress redistribution of FRP-strengthened reinforced concrete beams induced by the viscoelastic adhesive layer. Both the FRP plate and the RC beam are modeled as Timoshenko’s beams, connected through the adhesive layer. The adhesive layer is modeled as a three-parameter viscoelastic foundation (3PVF) using Standard Linear Solid model. The 3PVF model satisfies the equilibrium equation of the adhesive layer and the zero shear-stress boundary condition at the free edge. Closed-form expressions of the time-dependent interface stresses and deflection of the beam are obtained using Laplace transform. Finite element analysis is also conducted to verify the analytical solution using a subroutine UMAT based on the Standard Linear Solid model. Numerical results suggest that the stress concentrations within the FRP–concrete interface relax with time. The axial force in the FRP plate also reduces with time due to the creep of the adhesive layer. However, this relaxation is limited to a small zone close to the end of the FPR plate.     

FRP debonding from a concrete substrate: Some recent findings against conventional belief

For beams strengthened with FRP plates, many existing theories and concepts related to debonding failure are challenged by recent experimental observations in our laboratory. For debonding initiated by stress concentrations at the plate end, ultimate failure is always preceded by the formation of a major crack in the concrete member, causing interfacial stresses to change significantly from the elastic distribution. Existing elastic models are therefore not applicable to failure prediction. For debonding initiated from a flexural crack near mid-span, fracture mechanics based models indicate that the plate stress at failure is inversely proportional to the square root of the thickness. Test results from beams of various sizes and retrofitted with plates of different thickness show a different trend. To delay debonding failure, bonding of U-shape FRP ‘stirrups’ to the end of the FRP plate has been proposed. Test results indicate that ‘stirrups’ applied away from the plate end can indeed be more effective under some practical situations.     

Modeling of composite/concrete interface of RC beams strengthened with composite laminates

In this paper a finite element model for predicting shear and normal stresses in the adhesive layer of plated reinforced concrete beams has been developed. The numerical results carried out agree with those obtained in previous studies by other authors. It is found that shear stresses and high concentrations of peeling forces are present at the ends of the plates when the composite beam is loaded in flexure. These concentrations can produce premature failure of the strengthened beam because of debonding of the plate or cracking of the concrete cover along the level of internal steel reinforcement. The numerical simulation captures the actual interfacial stresses and, in particular, the maximum values of shear and normal stresses.     

Interfacial shear transfer of RC beams strengthened by bonded composite plates

In this paper an analytical method is proposed to predict the distributions of interfacial shear stress in concrete beams strengthened by composite plates. Non-linear behaviour of concrete under compression is considered in the analysis. The solutions show significant shear stress concentration near the cut-off end of plates. A parametrical study is carried out to show the effects of some design variables, e.g., thickness of adhesive layer, material properties and the distance from support to cut-off end of bonded plates.     

Interfacial shear stress concentration in FRP-strengthened beams

This paper reports the results of an experimental programme designed to study the interfacial shear stress concentration at the plate curtailment of reinforced concrete (RC) beams strengthened in flexure with externally bonded carbon fibre-reinforced polymer (CFRP). Specifically, the study looks at the relationship between the CFRP plate thickness and the interfacial shear stress concentration at the plate curtailment, the failure modes of the CFRP-strengthened beams as well as the efficiency of the CFRP external reinforcing system. Comparing the experimental results with existing models' predictions is another objective of this study. The experimental programme included five RC beams 115 mm×150 mm in cross-section and 1500 mm in length. Four of the RC beams were reinforced externally with CFRP plates of different thicknesses. Tests in this study showed that the thickness of CFRP plate affects not only the load-carrying and deflection capacities of the strengthened beam, but also the shear stress concentration at the CFRP/concrete interface and the beam failure mode.     

Cohesive zone model for the prediction of interfacial shear stresses in a composite-plate RC beam with an intermediate flexural crack

In this paper, an analytical method is developed to predict the distribution of interfacial shear stresses in concrete beams strengthened by composite plates. Accurate predictions of such stresses are necessary when designing to prevent debonding induced by a central flexural crack in a FRP-plated reinforced concrete (RC) beam. In the present analysis, a new theoretical model based on the bi-linear cohesive zone model for intermediate crack-induced debonding is established, with the unique feature of unifying debonding initiation and growth. Adherent shear deformations have been included in the present theoretical analyses by assuming a parabolic shear stress through the thickness of the adherents, verifying the cubic variation of the longitudinal displacement function, whereas all existing solutions neglect this effect. The results obtained for interfacial shear stress distribution near the crack are compared to the Jialai Wang analytical model and the numerical solutions are based on finite element analysis. Parametric studies are carried out to demonstrate the effect of the mechanical properties and thickness variations of FRP, concrete and adhesive on interface debonding. Indeed, the softening zone size is considerably larger than that obtained by other models which neglect adherent shear deformations. However, loads at the limit of the softening and debonding stages are larger than those calculated without the thickness effect. Consequently, debonding at the interface becomes less apparent and the lifespan of our structure is greater.     

Viscoelastic analysis of FRP strengthened reinforced concrete beams

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP-concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP-concrete interface can lead to the FRP debonding from the concrete beam. Although the short-term stress distribution along the FRP-concrete interface has been studied extensively, very few studies have been conducted on the long-term stress distribution, which closely simulates the behavior of the structure during the service-life. In this study, we develop a viscoelastic solution for the long-term interface stress distribution in a FRP plate strengthened reinforced concrete beam. In this solution, the RC beam and the FRP plate are modeled as elastic materials; while the adhesive layer is modeled as a viscoelastic material using the Standard Linear Solid model. Closed-form expressions of the interface stresses and deflection of the beam are obtained using Laplace transform and calculated using the Zakian’s numerical method. The validation of this viscoelastic solution is verified by finite element analysis using a subroutine UMAT based on the Standard Linear Solid model.     

Long-term bond stresses and debonding failure of FRP-strengthened RC cracked members

Most of the existing models to prevent debonding failure in beams externally strengthened by fiber reinforced polymer (FRP) laminates were developed focusing on the short term response. This paper studies the effect of concrete creep on the interfacial shear stresses and consequently, on the debonding failure load. A simplified formulation for the instantaneous and time-dependent bond stresses under sustained load is provided. Its reliability is analysed through the results obtained by a non-linear time-dependent analysis model. Previously, this model has been checked to evaluate the long-term response of existing experimental programmes in terms of deflections and strains.     

Mechanics of bonds in an FRP bonded concrete beam

Fibre-reinforced plastic (FRP) materials have been recognised as new innovative materials for concrete rehabilitation and retrofit. Since concrete is poor in tension, a beam without any form of reinforcement will fail when subjected to a relatively small tensile load. Therefore, the use of the FRP to strengthen the concrete is an effective solution to increase the overall strength of the structure. The attractive benefits of using FRP in real-life civil concrete applications include its high strength to weight ratio, its resistance to corrosion, and its ease of moulding into complex shapes without increasing manufacturing costs. The speed of application minimises the time of closure of a structure compared to other strengthening methods. In this paper, a simple theoretical model to estimate shear and peel-off stresses is proposed. Axial stresses in an FRP-strengthened concrete beam are considered, including the variation in FRP plate fibre orientation. The theoretical predictions are compared with solutions from an experimentally validated finite element model. The results from the theory show that maximum shear and peel-off stresses are located in the end region of the FRP plate. The magnitude of the maximum shear stress increases with increases in the amount of fibres aligned in the beam's longitudinal axis, the modulus of an adhesive material and the number of laminate layers. However, the maximum peel-off stress decreases with increasing thickness of the adhesive layer.     

Interfacial stresses in plated beams with cracks

In this paper, an analytical interfacial stress analysis is presented for cracked reinforced concrete beams bonded with thin plates and subjected to symmetrical tensile forces and/or end bending moments. A representative element between two contiguous cracks is considered under the assumption of plane stress. By means of the principle of minimum complementary energy, the analysis provides a closed-form solution that can be used easily to predict the stress distributions near the cracks in the beams. Numerical results from the present analysis are presented to study the effects of both material and geometric properties of the beams on the distributions of the interfacial stresses.     

Plate end debonding in the constant bending moment zone of plated beams

Reinforced concrete (RC) beams strengthened in flexure by externally bonding fibre reinforced polymer (FRP) or steel plate on their tension face are susceptible to premature plate end debonding failures. Safe design of such a strengthened RC beam demands a reliable and predictive debonding strength model. There are two special cases of plate end debonding failures: flexural debonding for cases when the plate terminates within a constant bending moment region (CMR), and shear debonding for the case when the plate terminates where the shear force is large but the bending moment is minimal. A general plate end debonding case is usually considered as an interaction between these two special cases. This paper is concerned with flexural debonding. A brief review of existing models is presented before the plate end interfacial stresses are examined. Three new models with different levels of accuracy are then developed: a closed-form theoretical model based on a simplified interfacial fracture mechanics analysis; a semi-empirical model; and a wholly empirical model. These three models together with two existing models are assessed against a carefully constructed test database containing 67 test data from an extensive literature survey.     

A systematic analysis and design approach for single-span FRP deck/stringer bridges

There is a concern with worldwide deterioration of highway bridges, particularly reinforced concrete. The advantages of fiber reinforced plastic (FRP) composites over conventional materials motivate their use in highway bridges for rehabilitation and replacement of structures. In this paper, a systematic approach for analysis and design of all FRP deck/stringer bridges is presented. The analyses of structural components cover: (1) constituent materials and ply properties, (2) laminated panel engineering properties, (3) stringer stiffness properties, and (4) apparent stiffnesses for composite cellular decks and their equivalent orthotropic material properties. To verify the accuracy of orthotropic material properties, an actual deck is experimentally tested and analyzed by a finite element model. For design analysis of FRP deck/stringer bridge systems, an approximate series solution for orthotropic plates, including first-order shear deformation, is applied to develop simplified design equations, which account for load distribution factors under various loading cases. An FRP deck fabricated by bonding side-by-side box beams is transversely attached to FRP wide-flange beams and tested as a deck/stringer bridge system. The bridge systems are tested under static loads for various load conditions, and the experimental results are correlated with those by an approximate series solution and a finite element model. The present simplified design analysis procedures can be used to develop new efficient FRP sections and to design FRP highway bridge decks and deck/stringer systems, as shown by an illustrative design example.     

Plate end debonding in the constant bending moment zone of plated beams

Reinforced concrete (RC) beams strengthened in flexure by externally bonding fibre reinforced polymer (FRP) or steel plate on their tension face are susceptible to premature plate end debonding failures. Safe design of such a strengthened RC beam demands a reliable and predictive debonding strength model. There are two special cases of plate end debonding failures: flexural debonding for cases when the plate terminates within a constant bending moment region (CMR), and shear debonding for the case when the plate terminates where the shear force is large but the bending moment is minimal. A general plate end debonding case is usually considered as an interaction between these two special cases. This paper is concerned with flexural debonding. A brief review of existing models is presented before the plate end interfacial stresses are examined. Three new models with different levels of accuracy are then developed: a closed-form theoretical model based on a simplified interfacial fracture mechanics analysis; a semi-empirical model; and a wholly empirical model. These three models together with two existing models are assessed against a carefully constructed test database containing 67 test data from an extensive literature survey.     

Analytical study of beams strengthened by adhesively bonded reinforcement with variable properties using state space method

This paper uses the state space method to present an analytical solution for beams that are strengthened by externally bonded reinforcement with variable cross-sectional properties. The external reinforcement can be any elastic material, such as fiber-reinforced polymer (FRP) or steel (before yielding), and the variation of the cross-sectional properties of the externally bonded material can be stepped or continuous. Specific interest is directed to the interfacial shear stress and tensile stress of the externally bonded reinforcement, which are important to debonding analyses and the evaluation of strengthening effectiveness but were previously investigated only for externally bonded materials with uniform properties along the span. Solutions for beams under both concentrated and distributed loads are obtained, considering multiple spring supports. Numerical results are presented to evaluate the method and to investigate the interfacial stresses of beams externally bonded by FRP with different types of cross-sections. These results confirm the experimental observations that a tapered section can significantly reduce interfacial shear stress.     

变截面梁的应力计算及其分布规律研究

为了合理计算预应力混凝土变截面箱形梁的剪应力,客观反映其应力分布状况,首先推导了任意变截面梁剪应力计算的一般公式,在此基础上,考虑箱形梁的梁高、底板厚度、腹板厚度沿跨度的变化,导出了变截面箱形梁的剪应力实用计算公式。应用导出的公式,结合矩形及箱形变截面悬臂梁算例,分析了变截面梁的应力分布状况。研究结果表明,变截面梁横截面上的最大剪应力并不发生在截面重心轴处,而是在重心轴以下区域或梁底缘处;变截面箱形梁的底板受有很大剪应力作用,为了合理设计变截面箱形梁,不应采用薄底板,而且应加强其配筋及构造处理。     

Modeling of single-flexural crack induced debonding of FRP plate strengthened concrete beams based on an assumption of heterogeneity

External bonding of fiber reinforced polymer (FRP) plate has become a popular method for strengthening concrete structures in recent years. This paper presents a numerical study of single-flexural crack induced debonding based on a progressive damage model. The ongoing debonding process is simulated. Interfacial stress distributions for different load levels are analyzed. A parametric study, including influence of heterogeneity of the adhesive layer, size of the flexural crack, thickness of the adhesive layer and the FRP plate and elastic modulus of the adhesive layer on the critical load is carried out. The numerical results indicate that the interface shear stress decreases gradually from the pre-existing crack or the debonding tip to the FRP plate ends along the FRP-concrete interface. Although local debondings nucleate at random locations, the dominated debonding initially starts from the pre-existing crack and propagates to the FRP plate ends as the load increasing.     

Analytical and numerical investigation of interfacial stresses of FRP–concrete hybrid structure

This paper presents a study on interfacial stresses of a concrete column confined by fiber-reinforced plastic (FRP) plate, which has been widely applied in the civil engineering for rehabilitation and retrofitting of conventional structures. It is assumed that both the FRP plate and concrete structures are elastic and the interface between them is perfectly bonded. An analytical model for analysis of the interfacial stresses is developed and the finite element modeling is carried out for an axisymmetric FRP–concrete hybrid column. Components of the FRP plate with different geometric and material properties are considered to study their effects on the interfacial stresses. The study shows that the interfacial stresses are influenced by several factors, such as modulus ratio of FRP and concrete and thickness of FRP. This work provides a comprehensive investigation on the mechanical behavior of the interface in hybrid structures.     

Effect of variations in the plate modulus of elasticity on the failure modes of FRP plated R.C. beams

In the absence of FRP plate/glue/concrete interface bond failure (i.e. interfacial debonding), eight possible flexural modes of failure are identified for reinforced concrete beams experiencing lateral loading, and strengthened in flexure with external FRP or steel plates glued to their soffits. All possible changes in such modes of failure, as a result of variations in the modulus of elasticity of the FRP material (assuming an associated constant value of ultimate tensile strength for the FRP plate in a given beam design), have been addressed in some detail, with a quantitative treatment of the critical values of the FRP modulus of elasticity associated with various failure mode transitions (i.e. changes).