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.     

A new model for the analysis of composite steel – concrete slab and beam structures with deformable connection

 In this paper a solution to the bending problem of reinforced concrete slabs stiffened by steel beams with deformable connection including creep and shrinkage effect is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface producing lateral deflection and inplane deformation to the plate and lateral deflection and axial deformation to the beams are related with the interface slip through the shear connector stiffness. Any distribution of connectors along the interface and any linear or non-linear load–slip relationship or partial shear connection for the shear connectors can be handled. The creep and shrinkage effect relative with the time of the casting and the time of the loading of the plate is taken into account. The solution of the arising plate and beam problems, which are nonlinearly coupled, is achieved using the analog equation method (AEM). The adopted model compared with those ignoring the inplane forces and deformations, approaches more reliable the actual response of the plate–beams system. Moreover, it permits the evaluation of the shear forces at the interfaces, the knowledge of which is very important in the design of composite steel–concrete structures. Received: 21 June 2002 / Accepted: 5 March 2003     

Performance of steel beams strengthened with CFRP laminate – Part 2: FE analyses

A new method for repairing and strengthening steel is under development and consists of using CFRP (carbon-fibre-reinforced-polymer) laminates bonded to the steel substrate. Research on this method has been conducted by a few research groups in recent years. The idea is to let the CFRP laminate carry a large part of the stresses and thereby reduce the load on the steel, which may have had its capacity lowered due to deterioration or fatigue. The present paper presents the results of FE analyses of steel beams strengthened with bonded CFRP laminates. The interfacial shear and peeling stresses that appear in the bond line between the steel and CFRP laminate are studied in both the elastic and plastic phase of the steel beam. Comparisons with the results obtained from laboratory tests conducted on steel beams strengthened with bonded CFRP laminates show that the behaviour of the strengthened beams can be captured using FE analyses. The distribution of the shear and peeling stresses near the end of the bond line were obtained from the FE analyses, together with the interfacial stresses that develop near beam mid-span due to the yielding of the steel. These stresses may exceed the capacity of the adhesive and cause debonding in this region.     

Surface modification of carbon fiber/epoxy composites with randomly oriented aramid fiber felt for adhesion strength enhancement

To increase the strength of an adhesive joint whose adherend is composed of a carbon fiber/epoxy composite, the surface of the adherend is reinforced with randomly oriented aramid fiber felt before the full cure of the adherend. With this smart cure cycle, the aramid fibers are exposed from the adherend, promoting a bridging effect between the fibers and the adhesive. The cured carbon fiber/epoxy composite material, on which the aramid fiber felt is placed, is co-cure bonded with a smart cure cycle developed in this work. The improvement of the adhesive bonding strength due to the aramid fiber felt is measured with the single-lap shear test of adhesively bonded joints. Additionally, the flexural strength of the carbon fiber/epoxy composite adherend with the co-cure bonded aramid fiber felt is measured.     

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.     

Theoretical and experimental investigation of bending of sandwich beams

We present the results of theoretical and experimental investigation of problems on bending of composite inhomogeneous sandwich beams. The theoretical results obtained by using the basic equations of the stress-strain state deduced within the framework of classical and refined nonclassical theories of bending of composite beams were compared with the experimental data. The nonclassical theory is based on a hypothesis taking into account the effect of deplanation of cross sections of the beam caused by transversal shear deformations. As experimental data, we use the results of experimental investigation of the process of bending of sandwich beams. Translated from Problemy Prochnosti, No. 3, pp. 76–85, May–June, 2000.     

Stress-function variational method for stress analysis of bonded joints under mechanical and thermal loads

High interfacial stresses near the ends of adherends are responsible for debonding failure of bonded joints used extensively in structural engineering and microelectronics packaging. This paper proposes a stress-function variational method for determination of the interfacial stresses in a single-sided strap joint subjected to mechanical and thermal loads. During the process, two interfacial shear and normal (peeling) stress functions are introduced, and the planar stresses of adherends of the joints are expressed in terms of the stress functions according to the static equilibrium equations. Two coupled governing ordinary differential equations (ODEs) of the stress functions are obtained through minimizing the complementary strain energy of the joints and solved explicitly in terms of eigenfunctions. The stress field of the joints based on this method can satisfy all the traction boundary conditions (BCs), especially the shear-free condition near the adherend ends. Compared to results based on finite element method (FEM) and other analytic methods in the literature, the present variational method is capable of predicting highly accurate interfacial stresses. Dependencies of the interfacial stresses upon the adherend geometries, moduli and temperature are examined. Results gained in this study are applicable to scaling analysis of joint strength and examination of solutions given by other methods. The present formalism can be extended conveniently to mechanical and thermomechanical stress analysis of other bonded structures such as adhesively bonded joints, composite joints, and recently developed flexible electronics, among others.     

Adhesive joining of composite journal bearings to back-up metals

Composite journal bearings are becoming popular for marine applications because they eliminate the possibility of seizure to steel journals, which is a drawback of white metal bearings. However, a reliable joining method for composite bearings to steel housings is required. In this work, hybrid composite journal bearings composed of carbon/phenolic and glass/epoxy laminated composites were manufactured with different stacking sequences and adhesively bonded to steel housings. The effect of deformations of the composite bearings due to thermal residual stresses on the adhesive joint performance was estimated with respect to stacking sequence by finite element method, and compared to the experimental results. From the measured and experimental results, it was found that the outward radial deformation of the composite bearings was beneficial to the adhesively bonded joint strength of the hybrid composite journal bearing.     

复合材料补片加固含椭圆孔钢板刚度分析

针对复合材料补片加固损伤钢板的受力特点, 建立三维弹性力学模型, 对复合材料补片双面加固轴向受拉平板进行了应力和变形分析。研究了粘贴界面的剪应力分布规律, 钢板和补片内轴向拉力的分布规律, 分析了加固后平板相对加固前的相对刚度。研究了含椭圆孔钢板经复合材料补片加固后相对加固前以及相对完好钢板的刚度。结果表明, 复合材料胶接修补含孔钢板的刚度随着补片厚度的增加而增加, 且增强的趋势逐渐趋于缓和。当补片层数大于5层后, 单纯依靠增加补片的厚度并不能有效提高修复效果。解析法与有限元法的计算结果及试验结果吻合得比较好。      

New designs of adhesive joints for thick composite laminates

New joint designs are proposed for adhesive bonding of thick multilayered composite adherends. The objective is to reduce or eliminate the failure modes associated with delamination and tensile and/or shear failure of the surface plies that are often observed in lap joints, and provide for a better stress distribution in the adhesive. In contrast to lap-joint designs, which transfer in-plane tensile stresses and other loads from the adherends to doubler plates by out-of-plane shearing of the surface plies, the new joint configurations transfer most of the load by in-plane shear and normal stresses, through bonded inserts or interlocking interfaces which have the same thickness as the laminate adherends. Doublers will transfer a calculated percentage of the load. Finite-element evaluations of the internal stresses in laminates, joined in both the conventional lap method and the new manner, suggest that the proposed load-transfer mechanism may improve joint efficiency by substantially increasing the size of adhesively bonded areas, and by making the stresses in the adherends nearly uniform through the thickness of the laminate. Some of the designs allow for selected ratios of shear to normal stresses in the adhesive layers. The stress concentrations often found in conventional designs, in the adherend surface plies and the adhesive layer at the leading edges of the doublers, are substantially reduced.     

Analysis of laminated composite beams and plates with piezoelectric patches using the element-free Galerkin method

 An efficient meshfree formulation based on the first-order shear deformation theory (FSDT) is presented for the static analysis of laminated composite beams and plates with integrated piezoelectric layers. This meshfree model is constructed based on the element-free Galerkin (EFG) method. The formulation is derived from the variational principle and the piezoelectric stiffness is taken into account in the model. In numerical test problems, bending control of piezoelectric bimorph beams was shown to have the efficiency and accuracy of the present EFG formulation for this class of problems. It is demonstrated that the different boundary conditions and applied actuate voltages affects the shape control of piezolaminated composite beams. The meshfree model is further extended to study the shape control of piezo-laminated composite plates. From the investigation, it is found that actuator patches bonded on high strain regions are significant in deflection control of laminated composite plates. Received: 23 October 2001 / Accepted: 29 July 2002     

Deformation of composite beams under transverse impact loading

Results of experiments on determining the contact force with transverse impact on carbon-filled plastic beams are presented. The problem of transverse impact on beams is stated and solved based on the finite-element method using the Timoshenko shear theory. The Runge-Kutta-Felberg method is used for integrating the main equation of the finite-element method. Analysis of the results of experiments and calculations shows that the form, magnitude, and duration of the contact force of impact depend on elastic and strength characteristics of the contact surface and are determined by the spectrum of natural frequencies of vibrations. Maximum nonsteady deformations in bending and shear are realized for beams, the first natural frequencies of which are comparable with the impact pulse duration. The existence of time-intermediate peaks of nonsteady bending and shear deformations in various sections of the beam, as well as span-intermediate maxima of bending and shear deformations, makes it possible to state and solve the problem of optimizing the structure and form of composite beams in relation to the external nonsteady action.Translated from Problemy Prochnosti, No. 2, pp. 114–119, February, 1990.     

新型U形外包钢-钢筋砼T形截面组合梁的试验

对新型U形外包钢-钢筋混凝土组合简支梁在施工状态下及在正常使用(组合)状态下的性能进行了试验。试验观察到的结构工作性能与试验前对其工作性能的预测基本一致。该组合梁在施工状态下,外部U形钢板独自承担着来自预应力砼预制板构件的偏心荷载,在该偏心荷载作用下,构件产生很小的变形。对于跨度为6m的边梁,在施工过程中需要在梁的跨中截面处设置一个临时支撑,用来阻止U形外包钢的侧边钢板的扭转屈曲变形。在正常使用(组合)状态下,该组合梁的抗剪承载力试验值大大超过有限元软件的理论计算值。试件的荷载-位移曲线表明,该组合梁结构具有很好的延性。在试件破坏前,组合梁中的混凝土和U形外包钢截面之间具有较好的粘结性能。     

Investigation of composite ☐ beam dynamics using a higher-order theory

A higher-order composite ☐ beam theory is developed to model beams with arbitrary wall thicknesses. The theory, which is based on a refined displacement field, approximates the three-dimensional elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the tranverse shear stresses through the thickness of each wall while satisfying stress-free boundary conditions on the inner and outer surfaces of the beam. Numerical results are presented for beams with varying wall thicknesses and aspect ratios. The static results are correlated with available experimental data and show excellent agreement. Dynamic results presented show the importance of including inplane and out-of-plane warping deformations in the formulation.     

Structural behavior and inter-layer displacements in CFRP plated steel beams – Optical measurements,analysis, and comparative verification

The linear elastic structural behavior of steel beams strengthened with externally bonded composite materials is experimentally and analytically investigated. The paper focuses on the full-field inter-layer relative displacements between the beam and the FRP layer. Such displacements result from the interaction between the adhesively bonded components and it is the integrated outcome of the interfacial conditions and the deformability of the adhesive. As such, it is commonly adopted as the state variable in simplified bond shear stress–slip representations. This aspect, as well as other aspects of the global and localized structural response, is analytically and experimentally quantified. The experiment includes a simply supported steel beam strengthened with a CFRP plate. A 3D image correlation technique with sequential measurements is used for the assessment of the full-field inter-layer displacements along the beam. The analysis adopts a high order modeling approach that accounts for the 2D stress and displacement fields through the depth of the adhesive and a 1D shear stress–slip approach using only a linear increasing branch. The comparison between the results provides validation of the analytical and experimental capabilities with emphasis on the inter-layer effects. One of the interesting findings which is discussed and explained in this paper is the fact that the slip values calculated with the shear stress–slip approach are notably different from the ones that can be measured experimentally and determined by the high order model.     

Post-cracking strength and ductility of glass–GFRP composite beams

This paper presents results of experimental and numerical investigations on the structural behaviour of composite beams made of annealed glass panes and glass fibre reinforced polymer (GFRP) pultruded profiles. The main goal of the transparent structural solutions presented here is to increase the post-cracking residual strength and ductility of glass by using GFRP strengthening laminates. The experimental programme included (i) tensile tests on double lap joints between glass and GFRP pultruded laminates, bonded with different types of structural adhesives, and (ii) full-scale flexural tests on glass beams and glass–GFRP composite beams, with different strengthening geometries and structural adhesives. Results obtained in this study show that, unlike glass beams, in glass–GFRP composite beams it is possible to obtain relatively ductile failure modes, with a significant increase of both strength and deformation capacity after the initial cracking of glass. The stiffness of the structural adhesive used, together with the geometry of the GFRP strengthening element, have a major influence on the structural response of the composite beams. Finite element models were developed for all tested beams, allowing to simulate their serviceability behaviour (prior to glass cracking) with fairly good accuracy, namely in what concerns the degree of shear interaction at the bonded interfaces.     

A parametric study on the failure of bonded single-lap joints of carbon composite and aluminum

A parametric study on adhesively bonded carbon composite-to-aluminum single-lap joints was experimentally conducted. FM73m, a high strength adhesive produced by Cytec, was used for bonding. The primary objective of this study is to investigate the effects of various parameters, such as bonding pressure, overlap length, adherend thickness, and material type, on the failure load and failure mode of joints with dissimilar materials. While metal bonded joints generally fail at the adhesive, the final failure mode of all the tested bonded joints with dissimilar materials was delamination of the composite adherend. Bonding strengths of the tested joints were lower than the metal-to-metal bonded joint strength. The specimens bonded under pressure of 4 and 6 atm yielded higher failure loads than under pressure of 3 atm, which is within the range of the manufacturer-recommended bonding pressure. Failure loads of the joint increased slightly at an overlap length larger than 30 mm. Increasing adherend thickness resulted in an increase of the failure load, but was not linearly proportional to the failure load.     

Effect of manufacturing methods on the shear strength of composite single-lap bonded joints

The present paper experimentally addresses the effect of manufacturing methods on the strength of composite bonded joints. A total of 391 specimens, manufactured by four different fabrication methods, were tested. For each method, various overlap lengths, adherend thicknesses and lay-up patterns were examined. The failure strength was higher in thicker adherend joints and lower in specimens with larger overlap length. Results showed that the secondary bonded joints had higher strength than the co-bonded and adhesively cocured joints and yielded similar strength compared with the non-adhesive cocured case. Changes in the stacking sequence also affected the interlaminar stresses and failure loads.     

Formulation of reference surface element and its applications in dynamic analysis of delaminated composite beams

This paper presents a new finite element formulation, referred to as reference surface element (RSE) model, for numerical prediction of dynamic behaviour of delaminated composite beams and plates using the finite element method. The RSE formulation can be readily incorporated into all elements based on the Timoshenko beam theory and the Reissner–Mindlin plate theory taking into account the transverse shear deformations. The ‘free model' and ‘constrained model' for dynamic analysis of delaminated composite beams and/or plates have been unified in this RSE formulation. The RSE formulation has been applied to an existing 2-node Timoshenko beam element taking into account the transverse shear deformations and the bending–extension coupling. Frequencies and vibration mode shapes are determined through solving an eigenvalue problem. Numerical results show that the present RSE model is reliable and practical when used to predict frequencies and mode shapes of delaminated composite beams. The RSE formulation has also been used to investigate the effects of the number, size and interfacial loci of delaminations on frequencies and mode shapes of composite beams.     

Interfacial mechanical properties of TiN coating on steels by indentation

The elastic theory of indentation on nitride films/steel systems showed distribution of stresses (shear stress, radial stress and circumferential stress) near the interface and in the film. The difference in values for each stress along the distance to the load center increased with increasing Poisson’s ratios of steels. The shear stresses (σ_rz) had the maximum value at a distance to the load center and the difference became more significant with increasing Poisson’s ratios of steel substrates (from 0.2–0.3 of Poisson’s ratio for high-speed steels to 0.3–0.35 for stainless steels), which accounted for the large amount of cracks inside the indent cavity of nitride films/stainless steel in spite of the smoothness outside the cavity. The calculation of σ_r and σ_z showed that the differences in nitride films/steel stress increased with increasing Poisson’s ratios of steels, which also facilitated the formation of ring cracks in the film of nitride films/stainless steel composite. Indentation examination revealed the large amount of cracks inside the indent cavity of nitride film/stainless steel but smooth surface outside the cavity. These were formed under the high sinusoidal shear stress and circumferential radial stress due to the higher Poisson’s ratio of stainless steel and the plastic deformation due to the lower yield stress of stainless steel (SS), which induced more local residual stresses, whereas some cracks or spalling observed around the cavity and no cracks inside the cavity were attributed to the edge effect when the conical indenter strained the surface downward for nitride film/high-speed steel (HSS) system.