Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate

The paper presents the results of an analytical and numerical solution for interfacial stresses in carbon fiber reinforced plastic (CFRP)–reinforced concrete (RC) hybrid beams studied by the finite element method. The analytical analysis is based on the deformation compatibility approach where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the concrete beam and the bonded plate. In numerical analysis, the mesh sensitivity test shows that the finite element results for interfacial stresses are not sensitive to the finite element mesh. The finite element analysis then is used to calculate the interfacial stress distribution and evaluate the effect of the structural parameters on the interfacial behavior. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. 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. We can conclude that this research is helpful for the understanding the mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

A Theoretical Improved Adhesively Bonded Bi-material Beam Model for FRP–RC Hybrid Beams

In this paper we present an improved bi-material beam theory with adhesive interface, which has been applied to the study of the interfacial behavior in a concrete beam reinforced by an externally bonded fibre reinforced polymer (FRP) plate. The work explicitly considers the interfacial slip effect on the structural performance by including the effect of adherend shear deformations. This new method needs only one differential equation to determine both shear and normal interfacial stress whereas the others solutions in the literature need two differential equations. Compared with previously published analytical results, this one improves the accuracy of predicting the interfacial stresses and the solution is in a closed form. This research is helpful in the understanding of the mechanical behavior of the interface and design of FRP–reinforced concrete (RC) hybrid beams.     

On the Effect of Time-Dependent Deformations on the Interface Behaviour of RC Beams Strengthened by FRP Plates

In this paper, the effect of time-dependent deformations (such as shrinkage and creep) on the interfacial stresses between a concrete beam and a fibre reinforced polymer plate is presented. The analysis given here involves a closed-form solution for such stresses and includes creep and shrinkage effects. The adherend shear deformations have been included in the present theoretical analysis by assuming a parabolic shear stress through the thickness of both concrete beam and fibre reinforced polymer panel. Contrary to some existing studies, the assumption that both the concrete beam and the fibre reinforced polymer panel have the same curvature is not used in this investigation. 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 examples of a typical concrete beam strengthened with an externally bonded fibre reinforced polymer plate are discussed with the emphasis on the shear and normal stresses at the edge of the plate.     

Effect of shear deformation on interfacial stresses in plated beams subjected to arbitrary loading

Bonding a fibre reinforced polymer (FRP) composite or metallic plate to the soffit of a reinforced concrete (RC), timber or metallic beam can significantly increase its strength and other aspects of structural performance. These hybrid beams are often found to fail due to premature debonding of the plate from the original beam in a brittle manner. This has led to the development of many analytical solutions over the last two decades to quantify the interfacial shear and normal stresses between the adherends. The adherends are subjected to axial, bending and shear deformations. However, most analytical solutions have neglected the influence of shear deformation of the adherends. For the few solutions which consider this effect in an approximate manner, their applicability is limited to one or two specific load cases. This paper presents a general analytical solution for the interfacial stresses in plated beams under an arbitrary loading with the shear deformation of the adherends duly considered. The shear stress distribution is assumed to be parabolic through the depth of the adherends in predicting the interfacial shear stress and Timoshenko's beam theory is adopted in predicting interfacial normal stress to account for the shear deformation. The solution is applicable to a beam of arbitrary prismatic cross-section bonded symmetrically or asymmetrically with a thin or thick plate, both having linear elastic material properties. The effect of shear deformation is illustrated through an example beam. The influence of material and geometric parameters of the adherends and adhesive on the interfacial stress concentrations at the plate end is discussed.     

A New Coupled Solution for Interfacial Stresses Analysis in a Repaired Beam with an Adhesively Bonded Prestressed FRP Plate

This paper focuses on a new coupling solution for determining the elastic interfacial shear and normal stresses in an adhesive joint between a strengthening plate and a simply supported beam. The mismatch of the curvatures in the beam and plate is considered by including both the effect of the adherend shear deformations and the prestressed laminates model. This new method leads to the coupling of governing differential equations for the interfacial shear and normal stresses. Most of the other solutions in the literature assume that the beam and plate have an equal curvature to uncouple this effect. In this paper, however, a solution is presented to calculate the interfacial stresses of beams strengthened with a prestressed composite plate having a new rigidity model coupled with the shear lag effect, which are neglected by the previous studies. It is found that the present method can predict accurately stresses in the interior and near the ends of the adhesive layer, where the stress fields can be significantly influenced by the edge effects. A parametric study was carried out to show how the stress concentration and distribution are influenced by the dimensions of the adherends and the material properties of the strengthened beam.     

On the intralaminar and interlaminar stress analysis of adhesive joints in plated beams

An improved bimaterial adhesive joint model is proposed for the intralaminar and interlaminar stress analysis of adhesively-bonded interfaces in plated beams with thin or moderately thick adhesive layer. To overcome the limitations or unreasonable assumptions in the existing theoretical joint models, both the shear and normal stresses along two adherend–adhesive interfaces are assumed to be different in the present model, and the adhesive layer is modeled as a simplified 2-D elastic continuum. Deformable interfaces are assembled to establish the continuity conditions between the adherend–adhesive interfaces, and the local deformations near the end of the adhesive layer are fully captured. The longitudinal and transverse displacements of the adhesive layer are introduced as two new independent parameters, and the missing “degrees of freedom” in the conventional elastic foundation models are retrieved. Differential governing equation of an adhesively-bonded bi-layer beam is established, and explicit closed-form expressions of beam forces and interface stresses are derived. Comparisons of the present solution with the existing elastic foundation models as well as the full 2-D continuum elastic solutions by the finite element analysis are conducted to validate the presented model. Parametric studies are then conducted to reveal the roles of the adhesive thickness and local interface deformations on the stress distributions both along the adherend–adhesive interfaces (interlaminar) and through the adhesive layer thickness (intralaminar), from which a feasible measure to reduce the strain or stress concentrations is obtained. The present improved adhesive joint model in plated beams sheds light on the effect of adhesive layer thickness in bimaterial bonding assembly and provides a better understanding of potential interface debonding initiation and its propagation path.     

Rheological modeling and finite element simulation of epoxy adhesive creep in FRP-strengthened RC beams

We have shown that a significant creep occurs at the concrete–fiber reinforced polymer (FRP) interface based on double shear long-term test. The primary test parameters were the shear stress to ultimate shear strength ratio, the epoxy curing time before loading as well as the epoxy thickness. The test results showed that when the epoxy curing time before loading was earlier than seven days the shear stress level significantly affected the long-term behavior of epoxy at the interfaces, and in particular the combined effect of high shear stress and thick epoxy adhesive can result in interfacial failure if subjected to high-sustained stresses. In this paper, based on the previous experimental observations, an improved rheological model was developed to simulate the long-term behavior of epoxy adhesive at the concrete–FRP interfaces. Furthermore, the newly developed rheological creep model was incorporated in finite element (FE) modeling of a reinforced concrete (RC) beam strengthened with FRP sheets. The use of rheological model in FE setting provides the opportunity to conduct a parametric investigation on the behavior of RC beams strengthened with FRP. It is demonstrated that creep of epoxy at the concrete–FRP interfaces increases the beam deflection. It is also shown that consideration of creep of epoxy is essential if part or the entire load supported by FRP is to be sustained.     

An Investigation of Interfacial Stresses in Reinforced Concrete Beams Using FRP Laminates

Reinforcement of reinforced concrete (RC) beams against bending through utilization of bonded fibre-reinforced plastic (FRP) laminates has been accepted as an effective method of strengthening. In this study, the effects of FRP reinforcement over the parameters of interfacial stresses in reinforced concrete beams were examined both experimentally and numerically. Essentially, the main goal of the study was to investigate quantitatively the behaviour of the RC beams strengthened with adhesively bonded FRP. In order to achieve this goal, an experimental study was initially carried out. Afterwards, the ANSYS® WB finite element program was employed to model and analyze the RC beams externally bonded to FRP. The obtained results are expected to demonstrate the main characteristics of interfacial stress distributions inside beams strengthened with FRP. The evaluation of interfacial stresses provides the basis for understanding the main characteristics in such beams and for developing suitable design rules.     

Thermal Residual Stresses in Adhesively Bonded In-plane Functionally Graded Clamped Plates Subjected to an Edge Heat Flux

In this study we have carried out the thermal residual stress analyses of adhesively bonded functionally graded clamped plates for different edge heat fluxes. The material properties of the functionally graded plates were assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations describing the two-dimensional thermo-elastic problem were discretized using the finite-difference method, and the set of linear equations was solved using the pseudo singular value method. The plate material properties near the interfaces played an important role in the interfacial adhesive stresses. The compositional gradient affected considerably both in-plane temperature distributions and heat transfer periods. The type of in-plane heat flux had only a minor effect on the temperature profiles but affected both the temperature levels and heat transfer period. Both plates undergo considerable compressive normal strains and stresses, but shear strains were more effective. Peak equivalent strains were observed for a constant heat flux and plates with a metal-rich composition. The compositional gradient and direction played important role in the profiles and levels of normal, shear and equivalent stresses as well as strains. The equivalent stress and strains concentrated along the free edges of the adhesive layer. The adhesive layer experienced a considerable distortional deformation rather than volumetric deformation. The equivalent stress exhibited small changes through the adhesive thickness and along the overlap length. The equivalent stress remained uniform in a large region of the overlap length and increased to a peak level around the free edges of the first plate–adhesive interface, whereas it increased to a peak level in a large region of the overlap length from a minimum level around the free edges of the second plate–adhesive interface. The strains and equivalent strains were higher for a metal-rich material composition. The direction of the material composition of the plates affected both stress and strain levels; thus, the CM–CM and CM–MC plates exhibited lower strain and stress levels than those in the MC–CM and MC–MC plates. However, only the adhesively bonded CM–MC plate configuration could achieve the lowest deformations and stresses in both plates and adhesive layer.     

Bond characterization of adhesively bonded joints made with the resin infusion (RI) process

In this research, the bond characteristics between concrete and FRP plates processed with resin infusion technique are studied. The bondline thickness is varied and a new modified single lap shear (MSLS) test set-up is implemented to monitor the interface during the experiments. Based on MSLS test set-up, the relative displacement between FRP adherend and substrate can be monitored with higher precision. Nonlinear analysis of the MSLS test results indicates that the maximum applied load increases for thicker bondline until a certain amount of thickness, optimum bondline thickness, beyond which no increase in load is achieved. Therefore, a relationship is proposed to estimate the maximum applied load based on bondline thickness. In addition, the interfacial performance of RI processed plates is also compared with the pultruded laminates bonded to the concrete. Results show that the samples processed by RI technique follow the same debonding mechanism as the pultruded specimens.     

Shear and peel stress analysis of an adhesively bonded scarf joint

The shear and peel stress distributions in a scarf joint made of two isotropic adherends with blunt adherend tips are analysed using a linear elastic analysis. The limits of the analysis with respect to adherend tip thickness have been investigated. A finite difference method is used to solve the differential equations for the shear and peel stress distributions over the joint. The boundary conditions used limit the analysis to the two adherends having the same thicknesses, lengths, and material properties. The adherends are modelled as plates with extensional and bending stiffnesses bonded together with an elastic interlayer. The stresses across the adhesive layer are assumed to be constant. The current analysis applied to cases known from the literature shows good agreement with the shear stresses but the peel stresses are overestimated.     

FRP板加固钢筋砼梁正截面强度分析

根据平面假设对外贴纤维增强复合材料加固钢筋混凝土梁进行了弹塑性变形全过程分析,分析了不同配筋率情况下,加固率与极限弯矩、极限曲率的关系.结果表明:外贴FRP材料可以提高钢筋混凝土梁的极限承载力,但开裂前对钢筋混凝土梁的受力性能影响很小.对于较小的配筋率的钢筋混凝土梁,根据加固率的不同,可能发生FRP板拉断的破坏模式,也可能发生压区混凝土压碎的破坏模式.但对于较大配筋率的钢筋混凝土梁,不管加固率的大小,均不可能发生FRP板拉断的破坏模式.加固效果对相对小配筋率的梁更显著,随着配筋率及加固率的增加,加固钢筋混凝土梁的极限抗弯能力的增加率逐渐减小.     

Interfacial Stresses in Plated Beams with Exponentially-Varying Properties

This paper presents a method for determining the elastic shear and peel stresses in an adhesive joint between a strengthening plate and a functionally graded beam (FGB). The beam is assumed to be isotropic with a constant Poisson's ratio and exponentially-varying elastic modulus through the beam thickness. Stress distributions, depending on an inhomogeneity constant, were calculated and presented in the form of graphs. It is shown that the inhomogeneities play an important role in the distribution of interfacial stresses. This research is helpful in understanding the mechanical behaviour of the interface and design of hybrid structures. The results presented in the paper can serve as a benchmark for future analyses of functionally graded beams strengthened by fibre reinforced polymer plates.     

Geometrically Non-Linear Analysis of Adhesively Bonded Double Containment Corner Joints

In cases where adhesively bonded joints may experience large displacements and rotations whilst the strains remain small, although all joint members behave elastically the small strain-small displacement (SSSD) theory cannot correctly predict the stresses and deformations in the adhesive joint members. Previous studies have shown that the small strain-large displacement theory considering the non-linear effects of the large displacements in the stresses and deformations has to be used in the analysis of adhesively bonded joints. In this study, the geometrical non-linear analysis of an adhesively bonded double containment corner joint was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The objective of the study was to determine the effects of the large displacements on the adhesive and adherend stresses of the corner joint. Therefore, the corner joint was analysed for two different loading conditions; a compressive applied load, P_x, at the free end of the horizontal plate and one normal to the plane of the horizontal plate, P_y. The plates, support and adhesive layer were assumed to have elastic properties. In practice, the adhesive accumulations, called spew fillets, arising around the adhesive free ends were taken into account in the analysis since their presence results in a considerable decrease in the peak stresses around the free ends of the adhesive. The SSLD and SSSD analyses showed that the stress concentrations occurred around the free end of the adhesive, thus at the adherend (slot) corners inside the right vertical and the lower horizontal adhesive fillets, and inside the left vertical and the upper horizontal adhesive fillets for the loading conditions P_x and P_y, respectively. In addition, the plate regions around the adherend (slot) free ends along the outer fibres of the vertical and horizontal plates undergo very high stress concentrations. The SSLD analysis predicted a non-linear effect in the displacement and stress variations at the critical adhesive and plate locations, whereas the SSSD analysis showed their variations were lower and proportional to the applied incremental load. This non-linear effect became more evident for the loading condition P_x, whereas both analyses predicted very close displacement and stress variations in the adhesive fillets and in the horizontal plate for the loading condition P_y. As a result, the geometrical non-linear behaviour of the corner joint is strictly dependent on the loading condition and the large displacements affect the stress and deformation states in the joint members, and result in higher stresses than those predicted by the SSSD theory.     

The transfer of stress through a steel to concrete adhesive bond

This paper describes part of a programme of research aimed at investigating the potential for strengthening reinforced concrete beams in shear by means of externally bonded steel plates. This may be a useful strengthening technique following the assessment of older bridge and building structures designed to outdated codes of practice. In order to produce a design guide for such shear plate bonding, a method for determining the anchorage length needs to be devised. By measuring the strain distribution in a steel plate adhesively bonded to a concrete block, the shear stress distribution within the adhesive and the effective anchorage length can be determined. A series of 15 experimental tests have been conducted to investigate the transfer of stress through a steel-concrete adhesive bond. The experimental programme was supported by theoretical and finite element analysis. The shear stress in a steel-concrete adhesive bond was found to be distributed exponentially, peaking at the loaded end of the specimen. For the specimens used, the stress distribution was distributed over a length of up to 155 mm for serviceability loads.     

芳纶纤维加固钢筋混凝土梁锚固长度的简化计算方法

根据芳纶纤维(Aramid Fiber Reinforced Plastic,简称 AFRP)补强加固钢筋混凝土梁的粘结破坏的试验结果,分析AFRP加固钢筋混凝土抗弯构件粘结界面的剪应力的分布规律,即在纤维截断点处存在较高的应力集中,随着离截断点距离的增大剪应力分布逐渐趋于均匀.粘结锚固长度不足和过高的应力集中是造成AFRP加固钢筋混凝土构件早期破坏的主要原因.采用"齿"状块体力学计算模型和混凝土裂缝理论推导了AFRP加固钢筋混凝土梁所需要的有效锚固长度,并通过修正得出了AFRP加固钢筋混凝土受弯构件最小锚固长度的简化计算公式,提出了AFRP的容许应变值和避免AFRP早期破坏应采用的措施,可供AFRP加固工程设计和施工参考.     

Geometrically non-linear analysis of adhesively bonded corner joints

When adhesively bonded joints are subjected to large displacements, the small strain-small displacement (linear elasticity) theory may not predict the adhesive or adherend stresses and deformations accurately. In this study, a geometricaly non-linear analysis of three adhesively bonded corner joints was carried out using the incremental finite element method based on the small strain-large displacement (SSLD) theory. The first one, a corner joint with a single support, consisted of a vertical plate and a horizontal plate whose left end was bent at right angles and bonded to the vertical plate. The second corner joint, with a double support, had two plates whose ends were bent at right angles and bonded to each other. The final corner joint, with a single support plus angled reinforcement, was a modification of the first corner joint. The analysis method assumes that the joint members, such as the support, plates, and adhesive layers, have linear elastic properties. Since the adhesive accumulations (spew fillets) around the adhesive free ends have a considerable effect on the peak adhesive stresses, they were taken into account. The joints were analyzed for two different loading conditions: one loading normal to the horizontal plate plane P_y and the other horizontal loading at the horizontal plate free edge P_x. In addition, three corner joints were analyzed using the finite clement method based on the small strain-small displacement (SSSD) theory. In predicting the effect of the large displacements on the stress and deformation states of the joint members, the capabilities of both analyses were compared. Both analyses showed that the adhesive free ends and the outer fibres of the horizontal and vertical plates were subjected to stress concentrations. The peak stresses appeared at the slot corners inside the adhesive fillets and at the horizontal and vertical plate outer fibres corresponding to the locations where the horizontal and vertical adhesive fillets finished. The SSLD analysis predicted that the displacement components and the peak adhesive and plate stress components would show a non-linear variation for the loading condition P_x, whereas the SSSD analysis showed smaller stress variations proportional to the applied load. However, both the SSLD and the SSSD analyses predicted similar displacement and stress variations for the loading condition P_y. Therefore, the stress and deformation states of the joint members are dependent on the loading conditions, and in the case of large displacements, the SSSD analysis can be misleading in predicting the stresses and deformations. The SSLD analysis also showed that the vertical and horizontal support lengths and the angled reinforcement length played an important role in reducing the peak adhesive and plate stresses.     

Cohesive shear stress and strength prediction of composite patch bonded to metal reinforcement

External bonding of fiber reinforced polymer (FRP) composites has become a popular technique for strengthening metal structures. A new concept of edge-elastic region was proposed to deal with the bonded reinforcement at present work. The expressions for interfacial shear stress distribution and failure load are derived under different load stages, accounting for inelastic behavior (plastic and softening) of the adhesive. The closed-form solution which can be regarded as an extension of trapezoidal cohesive zone model (CZM) is capable of satisfying the free shear boundary condition. Validation of the present method was performed by comparison of the interfacial elastic and plastic stress with the results of FEM and the failure load with experimental testing data. Good correlation shows that the present method can provide improved accuracy of the stress analysis, especially the peak shear stress and its location, which will further facilitate the design and optimization of the bonded reinforcement.     

Thermal residual stresses in adhesively bonded in-plane functionally graded clamped circular hollow plates

This study investigates the effects of in-plane compositional gradient exponent and direction on the thermal residual stress and deformations in adhesively bonded functionally graded clamped circular plates. The material composition was assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations in polar coordinates describing the two-dimensional thermo-elastic problem were discretized using finite-difference method, and the set of linear equations were solved using the pseudo-singular-value method. The material composition direction is designed as Ceramic-Metal (CM)–CM, CM–Metal-Ceramic (MC), MC–CM, and MC–MC for the inner and outer plates. The temperature decreased radially along the plates, but exhibited a sharp decrease across the adhesive layer. The compositional gradient exponent and direction affected evidently temperature levels and heat transfer period. The compressive radial and shear strains are more effective on the deformation in the adhesive layer and the plate regions near the plate–adhesive interfaces. The adhesive layer is subjected to considerable shear deformations. The equivalent strain and stresses are very low in a large region of the plates but exhibit sharp peaks on the plate regions near the plate–adhesive interfaces, and decrease towards the adhesive interfaces. These stress and strain peaks in the plates and adhesive layer are affected by the compositional gradient and direction. For an outer edge flux, the largest equivalent strain and stresses are observed in the CM–MC joint but the lowest levels occur in the MC–CM or secondly CM–CM joint. In addition, an inner edge flux results in the lowest and highest peak strains and stresses in the MC–CM and CM–MC joints, respectively. The MC–MC and CM–CM joints result in lower temperature, stress and strain levels around the adhesive layer and along the adhesive interfaces for outer and inner edge fluxes, respectively.     

An improved four-parameter model on stress analysis of adhesive layer in plated beam

The prediction of stresses in an adhesive layer is helpful in revealing the mechanism of debonding failure in plated beams. This study proposes an improved analytical model for the stress analysis of an adhesive layer in a plated beam. The beam and the soffit plate are individually modelled as a single Timoshenko sub-beam with separate rotations, while the adhesive layer is modelled as a two-dimensional elastic continuum in plane stress, which considers different adherend-adhesive interface stresses. The internal forces of the adhesive layer are assumed to satisfy the Timoshenko beam theory, and the shear deformation and bending moment of the adhesive layer can be considered. The internal forces and displacements of the adhesive layer are fully considered in the displacement compatibility equations, and deformable interfaces are assembled so that the effect of interface stresses on local deformation is captured. Based on equilibrium equations and displacement continuity, the governing differential equations of beam forces are derived, and then the analytical solutions of interface stresses and stresses along the thickness of the adhesive layer are obtained. Comparisons of the results of the finite-element analysis and the existing four-parameter model solutions show that the present model is reasonable. The influence of adhesive thickness on stress distributions in adhesive layers is also investigated.