Debonding in RC Beams Shear Strengthened with Complete FRP Wraps

Substantial research has been conducted on the shear strengthening of reinforced concrete (RC) beams with bonded fiber reinforced polymer (FRP) strips. The beams may be strengthened in various ways: complete FRP wraps covering the whole cross section (i.e., complete wrapping), FRP U jackets covering the two sides and the tension face (i.e., U jacketing), and FRP strips bonded to the sides only (i.e., side bonding). Shear failure of such strengthened beams is generally in one of two modes: FRP rupture and debonding. The former mode governs in almost all beams with complete FRP wraps and some beams with U jackets, while the latter mode governs in all beams with side strips and U jackets. In RC beams strengthened with complete wraps, referred to as FRP wrapped beams, the shear failure process usually starts with the debonding of FRP from the sides of the beam near the critical shear crack, but ultimate failure is by rupture of the FRP. Most previous research has been concerned with the ultimate failure of FRP wrapped beams when FRP ruptures. However, debonding of FRP from the sides is at least a serviceability limit state and may also be taken as the ultimate limit state. This paper presents an experimental study on this debonding failure state in which a total of 18 beams were tested. The paper focuses on the distribution of strains in the FRP strips intersected by the critical shear crack, and the shear capacity at debonding. A simple model is proposed to predict the contribution of FRP to the shear capacity of the beam at the complete debonding of the critical FRP strip.     

Flexural Response of Steel Beams Strengthened with Partial-Length CFRP Plates

This paper presents the flexural behavior of rolled steel beams that were strengthened with partial-length, adhesive-bonded carbon fiber-reinforced polymer (CFRP) plates. The hybrid beams had two types of failure mode, depending on the length of the plate: (1) plate debonding in beams with short plates;?and (2) plate rupture at midspan in beams with long plates. The flexural behavior that was investigated includes the development of tensile stresses in the plate, the moment-curvature of the strengthened section, and the load-deflection of the strengthened beam. The analytical methods used include shear lag analysis, section analysis, and application of the virtual work principle. Agreement between the experimental results and the analytical predictions is discussed.     

Effect of End Tapering on Crack-Induced FRP Debonding from the Concrete Substrate

The technique of bonding fiber-reinforced plastic (FRP) plates on the tensile side of concrete members has been proved to be an effective method for structural strengthening. For a RC beam strengthened with FRP plates, failure may occur by concrete cover separation near the plate end, or crack-induced debonding initiated by an opening crack away from the plate end. Experimental investigations have shown that tapering of the FRP plate at its ends is effective in reducing the stress concentrations and increasing the loading for plate end failure to occur. However, with reduced averaged thickness of the tapered plate, crack-induced debonding is also easier to occur. To optimize plate tapering in practical designs, an approach to analyze crack-induced debonding of tapered FRP plates is required. In the present investigation, FRP debonding is first studied with the finite-element method. In the analysis, a three-parameter model is employed for the shear slip relation between concrete and the FRP plate. Based on the findings from FEM analysis, simplifying assumptions are derived and an analytical model is developed for calculating the stresses in the FRP plate and along the concrete-to-FRP interface. The analytical stress distributions show good agreement with those from the FEM analysis. Using the analytical model, the effect of FRP tapering is quantitatively assessed. Also, the effects of various parameters on the ultimate failure load are simulated.     

Intermediate Crack Debonding in FRP-Strengthened RC Beams: FE Analysis and Strength Model

Reinforced concrete (RC) beams strengthened in flexure with a bonded fiber-reinforced polymer (FRP) plate may fail by intermediate crack (IC) debonding, in which debonding initiates at a critical section in the high moment region and propagates to a plate end. This paper first presents a finite-element (FE) model based on the smeared crack approach for concrete for the numerical simulation of the IC debonding process. This finite-element model includes two novel features: (1) the interfacial behavior within the major flexural crack zone is differentiated from that outside this zone and (2) the effect of local slip concentrations near a flexural crack is captured using a dual local debonding criterion. The FE model is shown to be accurate through comparisons with the results of 42 beam tests. The paper also presents an accurate and simple strength model based on interfacial shear stress distributions from finite-element analyses. The new strength model is shown to be accurate through comparisons with the test results of 77 beams, including the 42 beams used in verifying the FE model, and is suitable for direct use in design.     

Interfacial Stresses in Beams and Slabs Bondedwith Thin Plate

A new popular method for retrofitting reinforced concrete beams and slabs is to bond fiber-reinforced plastic (FRP) plates to the soffit. An important failure mode for such strengthened members is the debonding of the FRP plate from the member due to high interfacial stresses near the plate ends. Accurate predictions of the interfacial stresses are a prerequisite for designing against debonding failures. In this paper, a theoretical interfacial stress analysis is presented for simply supported beams and slabs bonded with a thin FRP composite or steel plate and subjected to a uniformly distributed load in combination with a uniform bending moment. The analysis leads to an exact closed-form solution, in which a plane stress model is used for beams and a plane strain model is used for slabs. The salient features of the new analysis include the consideration of nonuniform stress distributions in and the satisfaction of the stress boundary conditions at the ends of the adhesive layer. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions in beams and slabs.     

Interface Shear Stress: A New Design Criterion for Plate Debonding

This paper critically assesses the applicability and reliability of existing analytical techniques to predict and∕or prevent brittle plate debonding failure that occurs in reinforced concrete (RC) beams strengthened with externally bonded steel or fiber-reinforced-polymer composite plates. The experimental results, available to date in literature, have been very carefully reviewed and analyzed for this purpose. A new approach, very different from existing methods, and based on the interface shear stress obtained form elastic analysis of RC beam cross section and the fundamentals of force transfer mechanism in a bonded joint, is presented to predict the premature plate debonding phenomenon. The paper identifies important structural, material, and force parameters that influence this critical interface shear stress value between the bonded plate and concrete. The relations between these parameters and interface shear stress value are also examined and found to be consistent and logical to predict plate debonding at the plate cutoff end. The validity of this new design-oriented approach and scope for further research are also discussed.     

Study of Intermediate Crack Debonding in Adhesively Plated Beams

The main disadvantage of reinforced concrete beams retrofitted with steel or fiber reinforced polymer (FRP) plates adhesively bonded to the external surfaces is the premature debonding of the plates before reaching the desired strength or ductility. One of the main mechanisms of debonding failure is intermediate crack (IC) debonding, which is initiated by the formation of flexural cracks in the vicinity of the plates causing slip to occur at the plate/concrete interfaces. Much of the existing research focuses on the bond–slip relationship at the plate/concrete interface, with a lack of attention on the IC debonding behavior of flexural members. In this research, a model is described for IC debonding of plated RC beams that is based on partial interaction theory. To allow a better understanding of the IC debonding behavior of plated members, studies are carried out using the proposed model to study the effects of variations in crack spacings and rate of change of moment, and it is shown that both of these factors as well as the number of cracks in the beam can have large effects on the local behavior and the resultant strains in the plated member.     

Analytical Solution for Fracture Analysis of CFRP Sheet–Strengthened Cracked Concrete Beams

Fiber-reinforced polymer (FRP) composite materials have been widely used in the field of retrofitting. Theoretical analysis of FRP plate- or sheet-strengthened cracked concrete beams is necessary for estimating service reliability of the structural members. In previous studies, the effect of a perfectly bonded FRP plate or sheet was equivalent to a cohesive force acting at the bottom of crack to delay the crack propagation in concrete and reduce the crack width. However, delamination between FRP and cracked beam is inevitable due to interfacial shear stress concentration at the bottom of crack. The intention of this paper is to present an analytical solution for fracture analysis of carbon FRP (CFRP) sheet–strengthened cracked concrete beams by considering both vertical crack propagation in concrete and interfacial debonding at CFRP-concrete interface. The interfacial debonding is modeled as the interfacial shear crack propagation in this paper. Four different stages are discussed after initial cracking state of the concrete. At the first stage, only fictitious crack propagation occurs in the concrete. At the second stage, macrocrack propagates in the concrete without interfacial debonding. At the third stage, both vertical macrocrack propagation in the concrete and horizontal shear crack propagation at the CFRP-concrete interface occur in the strengthened beam. The tensile stress in the CFRP sheet and interfacial shear stress along the span are formulated based on the deformation compatibility condition at the CFRP-concrete interface at this stage. Finally, macroshear crack propagates at the interface until the CFRP sheet is completely peeled out from the beam, and then the member is fractured. The applied load is determined as a function of the referred two crack lengths at different stages. At the beginning, the applied load increases to one peak value with the full propagation of fictitious crack at the first stage. At the third stage, the applied load is improved to another peak value due to the relatively high cohesive effect of the CFRP sheet. Then the two peak values are determined by the Lagrange multiplier method. The validity of the proposed analytical solution is verified with the experimental results and numerical simulations. It can be concluded that the proposed analytical solution can predict the load-bearing capacity of CFRP sheet-strengthened cracked concrete beams with reasonable accuracy.     

Energy-Based Modeling Approach for Debonding of FRP Plate from Concrete Substrate

For concrete beams and slabs strengthened with bonded fiber reinforced plastic (FRP) plates, plate debonding from the concrete substrate is a common failure mode. In this paper, the debonding process is modeled as the propagation of a crack along the concrete/adhesive interface, with frictional shear stress acting behind the crack tip. Crack propagation is taken to occur when the net energy release of the system equals the interfacial fracture energy. The analysis is first performed for the special case with constant shear stress along the debonded interface, and then for the general case with slip softening in the debonded zone. From the results, a direct correspondence between energy-based and strength-based analyses can be established for arbitrary softening behavior along the interface. Specifically, through the proper definition of an effective interfacial shear strength, the conventional strength-based approach can be employed to give the same results as the much more complicated energy-based analysis. Also, based on the relation between the effective shear strength and other material parameters, it is possible to explain the very high interfacial shear stresses observed in experimental measurements. As an application example, distribution of plate stress and interfacial shear stress for the linear softening case is derived. The model results are found to be in good agreement with experimental measurements, showing that the simple linear softening model can describe the debonding process in real material systems.     

Debonding Failures of RC Beams Strengthened with Near Surface Mounted CFRP Strips

This paper presents the results of a series of tests conducted on reinforced concrete (RC) beams strengthened in flexure with near surface mounted (NSM) carbon fiber-reinforced polymer (CFRP) strips. As the main focus of the research is on debonding failure mechanisms, the only test variable investigated was the embedment length of the NSM strip and the NSM strip was extensively strain-gauged to monitor its bond behavior. Load-deflection curves, failure modes, strain distributions in the CFRP strip, and local bond stresses at the CFRP–epoxy interface from the tests are all examined in detail and compared with the predictions of a simple analytical model where appropriate. Of the four embedment lengths investigated, all but the shortest one led to a notable increase in the load-carrying capacity and, to a lesser extent, in the postcracking stiffness of the beam. Debonding was found to be the primary failure mode in all cases except for the beam with the longest embedment length. Also reported in this paper are results from preliminary bond tests used to characterize the local bond-slip behavior of the NSM system. Apart from gaining a better understanding of debonding failures in RC beams with NSM FRP strips, the test results reported in the paper should be useful for future verification of numerical and analytical models.     

Flexural Behavior of Reinforced Concrete Beams Strengthened with CFRP Sheets and Epoxy Mortar

Experiments were conducted to study the effect of using epoxy mortar patch end anchorages on the flexural behavior of reinforced concrete beams strengthened with carbon fiber-reinforced polymer (CFRP) sheets. More specifically, the effect of the end anchorage on strength, deflection, flexural strain, and interfacial shear stress was examined. The test results show that premature debonding failure of reinforced concrete beams strengthened with CFRP sheet can be delayed or prevented by using epoxy mortar patch end anchorages. A modified analytical procedure for evaluating the flexural capacity of reinforced concrete beams strengthened with CFRP sheets and epoxy mortar end anchorage is developed and provides a good prediction of test results.     

Fatigue Performance of Concrete Beams Strengthened with CFRP Plates

Recent increases in bridge design loading requirements have highlighted the need for fast, efficient, and durable strengthening methods. External steel plate bonding provides a satisfactory solution, but carbon fiber reinforced plastic (CFRP) offers the added advantages of resistance to corrosion, low weight, and high mechanical strength. This paper examines the fatigue performance of CFRP-strengthened concrete beams as part of a project investigating the use of CFRP as an alternative to steel. Five reinforced concrete beams were tested in fatigue; two control beams and three strengthened with externally bonded CFRP plates. Three loading options were used: (1) apply the same loads to both plated and unplated beams, (2) apply loads to give the same stress range in the rebar in both beams, and (3) apply the same percentage of the ultimate load capacity to each beam. Fatigue fracture of the internal reinforcement steel would appear to be the dominant factor governing failure, and it would appear reasonable to expect the same fatigue life for plated and unplated beams with comparable values of stress range in the steel bar.     

Three-Parameter Model for Debonding of FRP Plate from Concrete Substrate

Concrete beams retrofitted with bonded fiber reinforced plastic (FRP) plates often fail by debonding of the plate from the concrete surface. To predict the failure load in design, a proper debonding model is required. As debonding is a nonlinear process involving material softening, it can be analyzed once the interfacial shear (τ) versus sliding (s) relationship is known. Recent experimental results indicate that the simplest τ-s relationship should involve three parameters: the maximum shear stress for debonding to initiate, the initial residual stress right after debonding occurs, and a parameter governing the reduction of shear stress with sliding. In this paper, a FRP debonding model based on these three parameters is developed. The applicability of the model is verified through comparison with experimental results. Through a systematic parametric study, the effect of various material and geometric properties on the debonding process is investigated. Implications to the design of FRP strengthened members are highlighted.     

Delamination Failure of RC Beams Strengthened with FRP Strips—A Closed-Form High-Order and Fracture Mechanics Approach

An analytical model for the prediction of the interfacial delamination failure of reinforced concrete (RC) beams strengthened with externally bonded fiber-reinforced plastic strips (FRPs) is presented. The analysis is conducted through a comprehensive stress analysis of the strengthened member and a failure criterion based on fracture mechanics concepts. The stress analysis follows the closed-form high-order approach for the analysis of deformations, stresses, and stress resultants in the multilayered structure. The model is based on equilibrium and compatibility requirements in and between all constituents of the strengthened beam, i.e., the concrete beam, the FRP strip, and the adhesive layer. The governing equations of the bonded and the delaminated regions are derived, and along with a unique set of boundary and continuity conditions that model the cracking of the RC beam, they are solved in a closed form. The results provide the basis for the fracture analysis stage in which a criterion for the initiation and stable or unstable growth of the interfacial delaminations is derived. This criterion is based on the fracture mechanics concept of the elastic energy release rate and replaces the classical stress-based criteria. The energy release rate is evaluated through the path independent J-integral over the stress, deformation, and energy fields determined by the stress analysis. Three numerical examples concerning interfacial delamination triggered by cracking of the concrete and by the stress concentration at the edge of the FRP strip are presented. The emphasis is put on the development of the internal stress resultants in the RC beam and the FRP strip, the stresses at the adhesive layer, and the energy release rate with the growth of the delamination. The paper is concluded with a summary and some recommendations for the design of such strengthened beams.     

Influence of Changes in Cross Section on the Effectiveness of Externally Bonded FRP Strengthening

There are many situations where strengthening might be required for a nonprismatic reinforced concrete section (i.e., a beam or slab where the depth of the section varies along its length). For example, many bridges in the United Kingdom have inadequate capacity to carry accidental vehicle loads on verges. These shallow depth verges are often cantilevered from the much deeper main bridge deck. The cantilever might be strengthened by applying fiber-reinforced polymer (FRP) composites to the top surface of the cantilever, extending transversely onto the bridge deck. However, a problem may exist with such a situation due to the potential for a dramatic reduction in the degree of strengthening which is achievable. This is due to the effects of cracking, and longitudinal shear stresses. Tests presented in this paper demonstrate that in regions where little or no cracking occurs, local or global debonding of the external FRP may result. Therefore, the strength of some nonprismatic beams, as predicted by current design guidelines, is often shown to be overly conservative and, in one case significantly unconservative. However, more importantly, the predicted failure modes and FRP strains often do not correspond to those observed. Advice on the best approach for analyzing these beams is given.     

Determination of Nonlinear Softening Behavior at FRP Composite/Concrete Interface

For concrete beams and slabs, the bonding of fiber reinforced plastic (FRP) plates to the bottom surface is an effective and efficient technique for flexural strengthening. Failure of strengthened members often occurs due to stress concentrations at the FRP/concrete interface. For debonding failure initiated at the bottom of shear or shear/flexural cracks in the concrete, experimental results clearly indicate a progressive failure process accompanied by gradual reduction in shear transfer capability at the interface. Several existing models for FRP debonding have taken interfacial shear softening into account. However, the assumed shear stress versus slip relations employed in the models have never been properly measured. In this investigation, a combined experimental/theoretical approach for the extraction of interfacial stress versus slip relation is developed. With loading applied to a bonded FRP plate, strain is measured at various points along its length. Based on the strain measurements, the interfacial softening curve is derived from a finite element analysis. The present paper will present the proposed approach in detail, demonstrate its application to typical experimental data, and discuss the implications of the results.     

Ductile Design of Reinforced Concrete Beams Retrofitted with Fiber Reinforced Polymer Plates

For reinforced concrete beams retrofitted with fiber-reinforced polymer (FRP) plates, an analytical method is derived for determining the allowable plate area to achieve a targeted value of ductility. Nonlinear models for concrete and reinforcement are applied, and the effects of concrete confinement and spalling and of FRP plate rupture are considered. The derivation of equilibrium and compatibility equations for a rectangular cross section is presented, and the solution to the nonlinear equation for determining the allowable plate area is demonstrated with examples. Analytical results are compared with numerical and experimental data reported in the literature. Subsequently a simplified version of the method is derived, based on regression analysis, to relate the curvature ductility to the FRP plate ratio. It is noted that additional conditions need to be checked to ensure ductile performance, such as local failure of the concrete layer between tension reinforcement and FRP plate or debonding of the plate itself.     

Design Proposal to Avoid Peeling Failure in FRP-Strengthened Reinforced Concrete Beams

According to the available experimental work, the most common failure in existing structures strengthened by plate bonding is the laminate peeling off. In the last few years, an important effort in the development of mathematical models to avoid premature peeling failures has been made. However, a suitable and reliable design method to predict debonding due to the shear flow between crack discontinuities or at the laminate end is still not available. This paper describes a new design procedure for structures strengthened by plate bonding to avoid peeling failure at any location. After calculating the laminate area required for flexural strengthening, a two-step procedure to prevent peeling failure is proposed. The first step, to avoid peeling failure along the span, is based on a shear-bending interaction diagram associated with the theoretical maximum transferred force between laminate and support along the crack spacing before laminate debonding. This interaction diagram can be obtained through the application of nonlinear fracture mechanics. The second step consists of checking for peeling failure at the laminate end. The bonded length between the laminate end and the nearest crack should be enough to transfer the laminate tensile force acting on this crack. The proposed method has been verified with available experimental results assembled in a database. A good agreement between the experimental and predicted failure load has been obtained. Finally, an application example is presented to show the applicability of the method.     

Analytical Solution of Two-Layer Beam Taking into Account Nonlinear Interlayer Slip

This paper presents a fully developed nonlinear analytical (exact) model for analyzing composite beams under transverse bending load. The model reproduces the elements responsible for the relative slip between the layers (shear connectors and interface) with an elastoplastic strain-softening interlayer. Further than the slip, the model predicts stresses due to a given load and ultimate load for debonding of bilayered composite beams. All the details on the mathematical development are presented. This paper advances the state of the art, since the last development available in literature is an analytical (nonexact) linear model. A number of parametric studies are conducted to evaluate the influence of various geometrical and material parameters, the main results of which are presented together with the interpretation, e.g., the dependence of load-carrying capacity, stresses, and deflection on the local nonlinear load-slip relationship. The research proves as well that the shear connection lower and upper bounds (respectively, totally flexible and infinite rigid shear connectors) do not imply any lower and upper bound for the response.     

Failure Mode Analyses of Reinforced Concrete Beams Strengthened in Flexure with Externally Bonded Fiber-Reinforced Polymers

As existing structures age or are required to meet the changing demands on our civil infrastructure, poststrengthening and retrofitting are inevitable. A relatively recent technique to strengthen reinforced concrete (RC) beams in flexure uses fiber-reinforced polymer (FRP) strips or sheets glued to the tension side of the beam. A number of researchers have reported that the failure mode of an FRP-strengthened RC beam can change from the desired ductile mode of an underreinforced beam to a brittle one. This paper analyzes the effects of this strengthening technique on the response and failure modes of a reference RC beam. A nonlinear RC beam element model with bond-slip between the concrete and the FRP plate is used to study how the failure mechanism of simply supported strengthened RC beams is affected by the following parameters: plate length, plate width, plate stiffness, and loading type. The beam geometry is kept constant. The parametric studies confirm the experimentally observed results according to which the most commonly observed failure modes due to loss of composite actions are affected by the plate geometric and material properties. In addition, distributed loads (difficult to apply in an experimental test) may not be as sensitive to plate debonding in the region of maximum bending moment as are beams subjected to point loads.