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.     

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 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.     

Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations

A recently popular method for retrofitting reinforced concrete (RC) beams is to bond fibre reinforced polymer (FRP) plates to their tensile faces. An important failure mode of such plated beams is the debonding of the FRP plates from the concrete due to high level of stress concentration in the adhesive at the ends of the FRP plate. This paper presents an improved solution for interfacial stresses in a concrete beam bonded with the FRP plate by including the effect of the adherend shear deformations. The 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. In the present theoretical analysis, 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. 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.     

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.     

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.     

Thermal peel,warpage and interfacial shear stresses in adhesive joints

Thermal stresses are determined in a single lap joint with identical adherends, which are due solely to temperature changes. The simple bending model used here includes bending and extension of the adherends and extensional and shear strains in the adhesive. The analytical solution shows 'sinusoidal' deformation consistent with warpage (bending) of the adherends due to thermal mismatch. While a modified shear lag model (MSLM) with no adherend bending leads to peak bondline shear stresses which occur only at the ends of the overlap, the bending model shows that such stresses occur not only near the ends, but also at interior points of the overlap region. Results for aluminum adherends and an epoxy adhesive show how the peel, warpage and interfacial shear stresses are distributed over the overlap region.     

夹层复合材料的弯曲理论分析与计算方法研究

对夹层梁弯曲理论进行了深入研究,并用解析的方法计算了夹层梁的弯曲应力和挠度。在高阶夹层梁理论假设的基础上,假设夹芯只存在剪切变形,根据经典的梁弯曲理论,通过对夹层梁微元的受力分析,确定各层、层间的内力分布和各层间的变形协调关系,从而求出夹层梁各层的正应力、层间剪应力和弯曲挠度的解析表达式。最后,用三维有限元计算结果验证了解析算法结果的准确性。研究结果表明,此方法计算公式简单且精度较高。     

The use of flexible interface theory for fully coupled nonlinear analysis of balanced adhesive single-lap joint

A theoretical model is presented for determining the edge moment factors, the transverse deflections and the interfacial stresses of the balanced adhesive single-lap joint (SLJ). Based on the flexible interface theory, the improved one-dimensional beam model incorporates simultaneously the effects of interfacial compliances, the overlap geometric nonlinearity and the transverse shear deformations for the adherends. On the basis of normal and tangential displacement compatibility condition for the flexible interface, two sets of fully coupled governing equations concerning rotation of transverse normal and longitudinal displacement of adherends are constructed, from which the improved solutions for the edge moment factors, the transverse deflections, and the interfacial stresses can be obtained. The applicability and accuracy of the improved one-dimensional beam model are validated by comparing the present solutions with the results of the classical model, non-linear finite element analysis, and experimental results. Finally, the effects of the interface compliances on the adhesive stresses distributions of the balanced SLJ are studied.     

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.     

A Comparison of Numerous Lap Joint Theories for Adhesively Bonded Joints

Numerous authors have investigated the state of stress in the adhesive of adhesively bonded joints. They have made various assumptions concerning the behavior of the adhesive and adherends to yield tractable differential equations which remove the stress singularities which occur at the edges of the bi-material interfaces. By examining several test problems, this paper investigates the effect of these assumptions on predicted adhesive stress. It was found that predicted maximum adhesive shear stress is insensitive to underlying assumptions and that maximum adhesive peel stress is relatively unaffected by most assumptions except that neglecting shear deformation of the adherends can affect results by as much as 30%. Peel stresses from the well known theory of Goland and Reissner which neglects shear deformation of the adherends and makes several inconsistent assumptions vary as much as 30% from stresses from a consistent lap joint theory which considers shear deformation of the adherends. However, in most cases the effects of the inconsistencies cancel the effects of neglecting the shear deformation of the adherends and the variation is less than 15%. This paper points out that finite element analyses of bonded joints where one layer of 4 node isoparametric elements are used to model the adhesive give results very close to those from consistent lap joint theories.     

碳纤维加固梁中碳纤维受力计算与相关系数的分析

根据弹性理论和部分组合截面假定,分析碳纤维加固混凝土梁体系,建立微元体粘结界面剪力表达式和碳纤维轴向拉力微分方程,从而推导出碳纤维拉力和粘结界面剪应力解析解的一般形式,提出并探讨碳纤维加固作用系数Kf和端部应力集中系数k,说明碳纤维加固机理及端部应力集中现象与影响因素.结合算例指出,碳纤维轴向拉力和粘结界面剪应力分布不均匀,在端部区段应力集中,应采取措施加强锚固.     

Repair technique of pre-cracked reinforced concrete (RC) beams with transverse openings strengthened with steel plate under sustained load

This paper presents a repairing technique of the steel plate that effectively strengthen RC members, control both the failure modes and the stress distribution around the beam chords and enhance the serviceability of pre-cracked RC beams with openings. Furthermore, to evaluate the usage of a temporary pre-stressed force that was applied on the RC beam so as to close all of the presence shear cracks before the steel plate application. Two un-strengthened control beams, five beams that were pre-cracked before the application of the steel plate, and one beam that was strengthened without pre-cracking were tested. Cracking was first induced, followed by repair using various strengthening technique, and then the beams were tested to failure. The advantages of the shear strengthening of RC beams that were obtained using this technique are based on the closing of all the existing cracks around the openings via epoxy injection. The results show that both the pre-existing damage level and the steel plate strengthening have a significant effect on strengthening effectiveness and failure mode at the ultimate strength. An analytical equation for predicting the shear strength of pre-damaged RC beams with circular openings was then proposed, and the obtained results later compared with those from the tests, results were in accordance.     

Analytical solutions for nonlinear analysis of composite single-lap adhesive joints

This paper presents analytical nonlinear solutions for composite single-lap adhesive joints. The ply layups of each composite adherend can be arbitrary, but in the overlap region the ply layups of the upper and lower adherends are assumed to be symmetrical about the adhesive layer. In the present formulation, equilibrium equations of the overlap are derived on the basis of geometrical nonlinear analysis. The governing equations are presented in terms of adherend displacements by taking into account large deflections of the overlap adherends and adhesive shear and peel stresses simultaneously. Closed-form nonlinear solutions for adherend displacements, an edge moment factor and adhesive stresses are formulated and then simplified for practical applications. To verify the present analytical solutions for nonlinear analysis of composite single-lap joints, the geometrically nonlinear 2D finite element analysis is conducted using commercial package MSC/NASTRAN. The numerical results of the edge moment factor, deflections and adhesive stresses predicted by the present solutions correlate well with those of the geometrically nonlinear finite element analysis. This indicates that the present analytical solutions capture key features of geometrical nonlinearity of composite single-lap adhesive joints.     

On the thermomechanical behavior of two-dimensional foam/metal joints with shear-deformable adherends: Model validation with FE analysis

The stress distributions in metal/adhesive/foam planar joints subjected to biaxial tensile load and thermal load was investigated through a semi-analytical model. The shear deformation of adherends was accounted for according to a linear law in order to obtain closed-form solutions. For the model validation, a comparative study with a finite element (FE) simulation was carried out. A 2D behavior of stress fields is observed due especially to the Poisson's ratio effects and the biaxial nature of loads. The through thickness shear stresses are comparable to normal stresses; therefore, the adherend shear deformation must be accounted for correct failure prediction. According to the comparison with FE results, the normal stress distributions at any location in the foam and the shear stresses in the foam regions close to the adhesive surface can be well predicted by the proposed model. The through thickness shear stresses, however, showed to vary according to a cubic law rather than a linear law.     

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.     

THE BEHAVIOUR OF ADHESIVELY BONDED BEAMS VERSUS THEIR WELDED EQUIVALENT

The study aims to produce a design guide for the calculations of stresses and deflections of adhesively bonded beams fabricated from steel adherends using a structural epoxy adhesive. Such design calculations already exist for welded but not for bonded beams. Small models based on beams with a T-section profile, at various beam lengths, are formulated. A key to these calculations is the determination of the adhesive/adherend interface factors/coefficients, to correct the estimated values of stress and deflection from three-point bending conditions. This article presents the methodology for evaluating bonded beams in relation to equivalent welded (solid) beams. This includes mechanical testing, an analytical method based on beam and sandwich theory, and finite element techniques. Results from these techniques are presented and compared and values of the coefficients for T-section beams are determined.     

The behaviour of adhesively bonded beams versus their welded equivalent

The study aims to produce a design guide for the calculations of stresses and deflections of adhesively bonded beams fabricated from steel adherends using a structural epoxy adhesive. Such design calculations already exist for welded but not for bonded beams. Small models based on beams with a T-section profile, at various beam lengths, are formulated. A key to these calculations is the determination of the adhesive/adherend interface factors/coefficients, to correct the estimated values of stress and deflection from three-point bending conditions. This article presents the methodology for evaluating bonded beams in relation to equivalent welded (solid) beams. This includes mechanical testing, an analytical method based on beam and sandwich theory, and finite element techniques. Results from these techniques are presented and compared and values of the coefficients for T-section beams are determined.     

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.     

Closed-form solutions for elastic stress-strain analysis in unbalanced adhesive single-lap joints considering adherend deformations and bond thickness

A theoretical model is developed for the stress analysis in adhesive-bonded single-lap joints under tension, for which the two adherends could have different thicknesses and consist of different materials. A two-dimensional (2D) elasticity theory is adopted in the analysis, which simultaneously incorporates the complete strain-displacement and the complete stress-strain relationships for the adherends and adhesive. The approach provides a unified treatment for any possible adhesive layer flexibility and capable of satisfying the stress-free condition at the ends of the bondline. An explicit closed-form analytical solution is formulated for upper and lower adherends/adhesive stresses (strains) and tensile, shear and bending loads acting on the adherends along the overlap and then simplified for practical applications, and simple design formulae for adhesive stresses are produced. The results predicted by the present full and simplified solutions were compared with the previously theoretical solution by Bigwood and Crocombe (1989) [35], and the 2D geometrically nonlinear finite element model using MSC/NASTRAN. The agreement validates the present formulation and solutions for unbalanced bonded joints. The effects of the stiffness unbalanced parameters on the adhesive stress distributions were also discussed.