Modelling experimental bond fatigue failures of concrete beams strengthened with NSM CFRP rods

Near surface mounting (NSM) is a promising strengthening technique provided that the full bond between the strengthening material and the existing structure develops. Wahab et al. (2011) reported fatigue bond failures by de-bonding between the CFRP rod and the epoxy that started at mid span. As the load was cycled, the de-bonding propagated towards the support. The model presented here describes the failure of those beams. The de-bonding was modeled as a crack growing at the interface between the CFRP rod and the epoxy where the driving force was the interfacial shear stresses between the CFRP rod and the epoxy. Once the stresses at the crack tip exceeded the allowable fatigue stresses between the CFRP rod and the epoxy, de-bonding occurred and the crack length increased. Ahead of the crack tip, the CFRP rod was fully bonded to the epoxy and the forces decayed exponentially. Behind the crack tip, the rod was partially de-bonded. The experimental and calculated number of cycles until excessive slipping between the CFRP rod and the epoxy occurred and the forces in the CFRP rod at all locations in the shear span at the onset of failure were in good agreement.     

Numerical optimization of strengthening disturbed regions of dapped-end beams using NSM and EBR CFRP

This paper presents a parametric investigation, based on non-linear finite element modeling, to identify the most effective configuration of carbon fiber-reinforced polymers (CFRP) for strengthening reinforced concrete (RC) dapped-end beams. Following a field application and laboratory tests, it focuses on effects of 24 externally bonded (EBR) and near surface mounted reinforcement (NSMR) configurations on yield strain in steel and the capacity and failure mode of dapped-end beams. The investigated parameters were the mechanical properties of the CFRP, the strengthening procedure and the inclination of the fibers with respect to the longitudinal axis. Two failure scenarios were considered: rupture and debonding of the FRP. The results indicate that high-strength NSM FRPs can considerably increase the capacity of dapped-end beams and the yielding strains in reinforcement can be substantially reduced by using high modulus fibers.     

Mechanical behaviour of corroded RC beams strengthened by NSM CFRP rods

Corrosion of steel in reinforced concrete leads to several major defects. Firstly, a reduction in the cross-sectional area of the reinforcement and in its ductility results in premature bar failure. Secondly, the expansion of the corrosion products causes concrete cracking and steel–concrete bond deterioration and also affects the bending stiffness of the reinforced concrete members, causing a reduction in the overall load-bearing capacity of the reinforced concrete beams. This paper investigates the validity of a repair technique using Near Surface Mounted (NSM) carbon-fibre-reinforced polymer (CFRP) rods to restore the mechanical performance of corrosion-damaged RC beams. In the NSM technique, the CFRP rods are placed inside pre-cut grooves and are bonded to the concrete with epoxy adhesive.Experimental results were obtained on two beams: a corroded beam that had been exposed to natural corrosion for 25 years and a control beam, (both are 3 m long) repaired in bending only. Each beam was repaired with one 6-mm-diameter NSM CFRP rod. The beams were tested in a three-point bending test up to failure. Overall stiffness and crack maps were studied before and after the repair. Ultimate capacity, ductility and failure mode were also reviewed. Finally some comparisons were made between repaired and non-repaired beams in order to assess the effectiveness of the NSM technique. The experimental results showed that the NSM technique improved the overall characteristics (ultimate load capacity and stiffness) of the control and corroded beams and allowed sufficient ductility to be restored to the repaired corroded elements, thus restoring the safety margin, despite the non-classical mode of failure that occurred in the corroded beam, with the separation of the concrete cover due to corrosion products.     

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

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

Analytical approach for the flexural analysis of RC beams strengthened with prestressed CFRP

The objective of this paper is to propose a simplified analytical approach to predict the flexural behavior of simply supported reinforced-concrete (RC) beams flexurally strengthened with prestressed carbon fiber reinforced polymer (CFRP) reinforcements using either externally bonded reinforcing (EBR) or near surface mounted (NSM) techniques. This design methodology also considers the ultimate flexural capacity of NSM CFRP strengthened beams when concrete cover delamination is the governing failure mode. A moment–curvature (M–χ) relationship formed by three linear branches corresponding to the precracking, postcracking, and postyielding stages is established by considering the four critical M–χ points that characterize the flexural behavior of CFRP strengthened beams. Two additional M–χ points, namely, concrete decompression and steel decompression, are also defined to assess the initial effects of the prestress force applied by the FRP reinforcement. The mid-span deflection of the beams is predicted based on the curvature approach, assuming a linear curvature variation between the critical points along the beam length. The good predictive performance of the analytical model is appraised by simulating the force–deflection response registered in experimental programs composed of RC beams strengthened with prestressed NSM CFRP reinforcements.     

Failure of RC beams strengthened in bending with unconventionally arranged CFRP laminates

This paper describes the experimental tests made on RC beams retrofitted by unconventionally arranged CFRP strips and on a reference, not retrofitted one. Diagonal CFRP strips were applied on the lateral faces of the specimens and connected to the longitudinal ones in order to improve the anchorage length of the latters. The experimental outcomes prove that this CFRP strips distribution can improve the load carrying capacity of the retrofitted beams, provided that the diagonal strips are long enough and that the longitudinal reinforcement is arranged along the whole beam. Comparison with the predictions based on CNR-DT 200 and ACI 440.2R-02 guidelines is finally displayed.     

An engineering formula for the stress concentration factor of orthotropic composite plates

An engineering formula for the theoretical stress concentration factor of orthotropic notched plates under tension is provided, as a function of the material elastic constants and the K_t of the corresponding isotropic case. The accuracy and limits of applicability of the new solution are discussed by comparison to data from the literature and results from FE analyses on notched geometries of practical interests. The proposed solution represents a very useful tool to estimate the stress concentration factor of notched orthotropic plates, composite orthotropic laminae, orthotropic unidirectional laminates and homogenised orthotropic composite laminates.     

Shear coupling effects of the core in curved sandwich beams

We consider a composite package formed by two curved external Euler-Bernoulli beams, which sandwich an elastic core with negligible bending strength but providing the shear coupling of the external layers. This coupling considerably affects the gross response of the composite structure. There is an extensive literature on straight sandwich beams of this type, but very little attention has been paid to the effects of curvature. Here, an analytical linear elastic model is proposed for beams with arbitrary variable curvature. Equilibrium equations and boundary conditions are obtained through a variational approach. Useful simplifications are possible for the case of moderately curved beams and beams with constant curvature.     

Debonding failure modes of flexural FRP-strengthened RC beams

In this paper, different types of debonding failure modes are described. Then, experimental results of four-point bending tests on FRP strengthened RC beams are presented and debonding failure mechanisms of strengthened beams are investigated using analytical and finite element solutions. Reasonable results could be obtained for modelling of debonding failure load of tested beams.

Existing international codes and guidelines from organizations such as ACI, fib, ISIS, JSCE, SIA, TR55, etc. are presented and compared with the results from the experiments and calculations. A discrepancy of up to 250% was seen between different codes and guidelines for predicting the debonding load. Furthermore, a new recommendation for debonding control is given.     

Numerical evaluation of shear strengthening performance of CFRP sheets/strips and sprayed epoxy coating repair systems

A numerical study is conducted to evaluate the shear strengthening performance of two repair systems: CFRP sheets/strips and a sprayed epoxy coating. Micromechanical constitutive models for the CFRP sheets/strips and sprayed FRP coating proposed by Liang et al. [Liang Z, Lee HK, Suaris W. Micromechanics-based constitutive modeling for unidirectional laminated composites. Int J Solids Struct 2006;43:5674–89] and Lee et al. [Lee HK, Avila G, Montanez C. Numerical study on retrofit and strengthening performance of sprayed fiber-reinforced polymer. Eng Struct 2005;27:1476–87] and Lee and Simunovic [Lee HK, Simunovic S. Modeling of progressive damage in aligned and randomly oriented discontinuous fiber polymer matrix composites. Composites: Part B 2000;31:77–86] in conjunction with damage models, are implemented into the finite element code ABAQUS to solve boundary value problems. Using the implemented computational model, numerical simulations of four-point bending tests on concrete beams repaired with the repair systems are conducted to quantify their strengthening abilities. The numerical tests yield load–deflection curves from which the shear strengthening performance of the repair systems is evaluated. Furthermore, the present prediction is compared with available experimental data to assess the accuracy of the proposed computational model.     

Shear design of reinforced concrete beams with FRP longitudinal and transverse reinforcement

The shear resisting mechanisms of reinforced concrete (RC) beams with longitudinal and transverse FRP reinforcement can be affected by the mechanical properties of the FRP rebars. This paper presents a mechanical model for the prediction of the shear strength of FRP RC beams that takes into account its particularities. The model assumes that the shear force is taken by the un-cracked concrete chord, by the residual tensile stresses along the crack length and by the FRP stirrups. Failure is considered to occur when the principal tensile stress at the concrete chord reaches the concrete tensile strength, assuming that the contribution of the FRP stirrups is limited by a possible brittle failure in the bent zone. The accuracy of the proposed method has been verified by comparing the model predictions with the results of 112 tests. The application of the model provides better statistical results (mean value V_test/V_pred equal to 1.08 and COV of 19.5%) than those obtained using the design equations of other current models or guidelines. Due to the simplicity, accuracy and mechanical derivation of the model it results suitable for design and verification in engineering practice.     

Design criterion for fatigue strengthening of riveted beams in a 120-year-old railway metallic bridge using pre-stressed CFRP plates

This study presents a design criterion developed for fatigue strengthening of a 120-year-old metallic railway bridge in Switzerland and presents a pre-stressed un-bonded reinforcement (PUR) system developed to apply the strengthening. The PUR system uses carbon fiber reinforced polymer (CFRP) plates; however, unlike conventional pre-stressed CFRP reinforcement methods, preparation of the existing metallic bridge surface is not required. This decreases the time required for on-site strengthening procedures. The principle of the constant life diagram (CLD) and two fatigue failure criteria (Johnson and Goodman) are described. Analytical formulations are developed based on the CLD method to determine the minimum CFRP pre-stress level required to prevent fatigue crack initiation. The PUR system uses an applied pre-stress force to reduce the mean stress level (and stress ratio) to shift an existing fatigue-susceptible metallic detail from the ‘at risk’ finite life regime to the ‘safe’ infinite life regime. The applied CLD method is particularly valuable when the stress history of the detail is not known and it is difficult to assess the remaining fatigue life. Moreover, it is shown that the currently adopted approach in many structural codes which emphasizes stress range as the dominant parameter influencing fatigue life are non-conservative for tension–tension stress patterns (i.e., stress ratios of 0 < R < 1). Analyses show that the modified Johnson formula accurately reflects the combined effect of stress range, mean stress level, and material properties, and offers a relatively easy design procedure. Details of a retrofit field application on members of a riveted wrought iron railway bridge are given. A wireless sensor network (WSN) system is used for long-term monitoring of the on-site CFRP stress levels and temperature of the retrofitted details. WSN measurements indicate that increases in ambient temperature result in increased CFRP pre-stress levels.     

Flexural strengthening of RC beams using Hybrid Composite Plate (HCP): Experimental and analytical study

Hybrid Composite Plate (HCP) is a reliable recently proposed retrofitting solution for concrete structures, which is composed of a strain hardening cementitious composite (SHCC) plate reinforced with Carbon Fibre Reinforced Polymer (CFRP). This system benefits from the synergetic advantages of these two composites, namely the high ductility of SHCC and the high tensile strength of CFRPs. In the material-structural of HCP, the ultra-ductile SHCC plate acts as a suitable medium for stress transfer between CFRP laminates (bonded into the pre-sawn grooves executed on the SHCC plate) and the concrete substrate by means of a connection system made by either chemical anchors, adhesive, or a combination thereof. In comparison with traditional applications of FRP systems, HCP is a retrofitting solution that (i) is less susceptible to the detrimental effect of the lack of strength and soundness of the concrete cover in the strengthening effectiveness; (ii) assures higher durability for the strengthened elements and higher protection to the FRP component in terms of high temperatures and vandalism; and (iii) delays, or even, prevents detachment of concrete substrate. This paper describes the experimental program carried out, and presents and discusses the relevant results obtained on the assessment of the performance of HCP strengthened reinforced concrete (RC) beams subjected to flexural loading. Moreover, an analytical approach to estimate the ultimate flexural capacity of these beams is presented, which was complemented with a numerical strategy for predicting their load-deflection behaviour. By attaching HCP to the beams' soffit, a significant increase in the flexural capacity at service, at yield initiation of the tension steel bars and at failure of the beams can be achieved, while satisfactory deflection ductility is assured and a high tensile capacity of the CFRP laminates is mobilized. Both analytical and numerical approaches have predicted with satisfactory agreement, the load-deflection response of the reference beam and the strengthened ones tested experimentally.     

An approach to the positioning of FRP provisions in vaulted masonry structures

In the paper, one starts from a theoretical formulation aimed at analysing masonry vaults by selecting, in an inverted approach, families of load shapes that may be equilibrated by sets of admissible solutions, in order to develop an operative method for the positioning of FRP reinforcements in masonry vaulted constructions. On the basis of this premise a strategy is outlined for identifying the areas of the vault to be selected for introducing the FRP provisions. As shown in the numerical investigation, higher intensities of the stress state are then allowed by the introduction of the reinforcement and the local relaxation of some of the constraints of the problem is possible.     

Effect of fatigue loading on the bond behaviour between UHM CFRP plates and steel plates

Extensive research has been conducted on static bond behaviour between CFRP and steel. However, very limited research is available on the effect of fatigue loading on the bond behaviour between CFRP and steel. This paper attempts to fill the knowledge gap in this area. A series of static and fatigue tests on UHM (ultra high modulus) CFRP plate and steel plate double strap joints were conducted. Five specimens were tensioned to failure under static loading as control specimens. The other 12 specimens were tested under fatigue loading with load ratios ranging from 0.2 to 0.6 (defined as the ratio of the maximum fatigue load to the average static bond strength of control specimens). After going through pre-set number of fatigue cycles, the specimens were tensioned to failure under static loading. The failure modes, residual bond strength and residual bond stiffness of such specimens were compared with those of control specimens, to facilitate the investigation of the effect of fatigue loading on the bond behaviour. Microscopic investigation was also performed to reveal the underlying failure mechanism.     

Ultimate behaviour of FRP wrapped sections under axial force and bending: Influence of stress–strain confinement model

In the present work, the influence of the adopted confined concrete constitutive law, among those available in the technical literature, on the flexural strength and curvature ductility of reinforced concrete sections strengthened by FRP (fibre reinforced polymer) wrapping is investigated. An important issue to be underlined is that the stress–strain relationship of confined concrete depends not only on the number of layers and on the type of FRP used for wrapping, but also on the size and the shape of the section. By using the main constitutive laws proposed in the technical literature to model the confined concrete behaviour, the moment–curvature diagrams have been evaluated for a significant number of study cases by means of a specifically developed computer program based on a refined fibre model. The results show that even if the different constitutive laws exhibit large differences in the resulting stress–strain behaviour, they lead to negligible differences in terms of flexural resistance, but to very significant differences in terms of curvature ductility. Therefore, the accurate evaluation of the ultimate strain seems of paramount importance compared to the whole stress–strain curve. In addition, the influence of pre-existing loads acting on the structure at the time of the strengthening intervention has been investigated showing that it affects the knee region of the moment–curvature relationship, while the ultimate flexural resistance remains almost unaffected.     

Three-layered plate: Elasticity solution

The subject of this paper is the plate composed of two identical isotropic outer layers and a more compliant inner interlayer, perfectly connected to one another at the interface (three-layered plate). This paper presents a model that describes the behavior of this plate by a system of exact analytical (explicit) equations.An analytical model is preferred over finite element models and simplified formulas if it is fast and easy-to-use. Thus, modeling has been developed within the framework of two-dimensional elasticity, instead of three. In so doing, the model also represents a means for attaining full comprehension of the involved phenomena, something that neither three-dimensional elasticity nor finite element models and simplified formulas can attain. The two-dimensional behavior is governed here by using assumptions that do not impose constraints on the behavior. Starting from these assumptions, the paper illustrates the relationships between displacements and interface stresses. The subsequent sections of the paper describe the model and present some real case applications.The contribution of this paper is to consider both the shear modulus and the elastic modulus of the interlayer. Thus, this model applies to three-layered plates with any interlayer, whether utterly compliant or relatively stiff. Conversely, the previous exact analytical models assumed zero elastic modulus, and hence they applied to utterly compliant interlayers only. Hence, not only does the new model predict the exact behavior of plates that the former analytical models described only approximately, but this model may also be used as a benchmark for finite element models, which cannot assign zero value to the elasticity modulus of the interlayer together with the actual shear modulus.     

Closed form solutions for buckling and postbuckling analysis of imperfect laminated composite plates with piezoelectric actuators

Buckling and postbuckling behavior of symmetric laminated composite plates with surface mounted and embedded piezoelectric actuators subjected to mechanical, thermal, electrical, and combined loads is studied. Formulation is based on the classical laminated plate theory with von-Karman non-linear kinematic relations. Initial geometrical imperfections are also accounted, and finally applying Galerkin procedure, the resulting equations are solved to obtain closed form expressions for non-linear equilibrium paths. Temperature dependency of thermo-mechanical properties is considered. Three cases of simply supported boundary conditions are investigated. Effects of in-plane compressive loading, temperature dependency and independency of properties, electrical loading, lay-up configuration, and geometric imperfection are discussed. Results for various states are verified with the known data in the literature.     

Flexural stiffness modelling of RC slab strengthened by externally bonded FRP

This paper describes the behaviour of strengthened and unstrengthened reinforced concrete slabs, subjected to a single, specific, local, load at their centres. In the experimental stage, the influence of the reinforcement on the various slabs tested was analysed by studying their behaviour at failure and by making a bending stiffness analysis. In order to predict the mechanical behaviour of the slab, a model was developed to predict the value of the bending stiffness, the mid-span displacements and the strain on each material making up the slabs. The experimental results were compared to those of the model and there was good agreement.