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Bonded concrete repairs are widely used in civil engineering applications. During the installation of these repairs, an interface is created between the concrete and the bonding agent. In the case of concrete members strengthened with fiber-reinforced polymers (FRPs), the behavior of the interface and materials surrounding it often governs the structural performance of the concrete elements being repaired. The bond quality and characteristics between concrete and FRP composites have been studied using experimental, analytical, and empirical approaches. The framework of fracture mechanics has been effectively used by different research groups to characterize and predict interfacial behavior under Mode I loading, Mode II loading or mixed-mode. Both linear and nonlinear elastic fracture mechanics approaches have been explored to characterize debonding failures. The purpose of this special publication is to highlight recent developments on the use of the framework of fracture mechanics to evaluate the performance of reinforced concrete (RC) structures strengthened with FRP composites. We hope that the information provided in this publication will be useful to the researcher and practicing engineer by presenting experimental and analytical tools based on a fracture approach that can assess the shear and flexural capacity of strengthened RC members.

The scaling of the ultimate load in fibre-reinforced polymer (FRP)–concrete debonding with the relative width of the FRP is experimentally investigated in this paper. Shear debonding tests are performed to evaluate the cohesive stress transfer between the adherents during the interface crack growth which produces debonding. Concrete specimens with two different widths and different widths of FRP are used in the experimental programme. The nominal stress at debonding increases with the FRP-to-concrete width ratio. For a given width of FRP composite sheet, lower debonding stress is obtained from concrete specimens with a larger width. The strain distribution on the FRP and concrete free surface at different stages of debonding was determined using a full-field optical technique known as digital image correlation. The contribution of the two factors, the boundary effect and the restraint from the surrounding concrete, was studied from the measured strain distribution. The strain distributions across the FRP composite sheet and the concrete within the cohesive stress transfer zone associated with the interface crack are shown to be very inhomogeneous. A region of constant width associated with high shear strains is found at the edge of the FRP sheet during the entire debonding process. The increase in the ultimate nominal stress at debonding is shown to be due to the decrease in the proportion of the total width of the FRP occupied by the edge region. It is shown that the boundary region within the FRP is of a fixed width. The width of concrete close to the edge of the FRP involved in stress transfer, however, increases with the width of FRP. It is established that when the FRP-to-concrete width ratio is smaller than 0.5, the level of restraint from concrete increases with the FRP width.

The topic of this research work is the fatigue behavior of externally strengthened concrete beams with fiber-reinforced polymers. An increase of the fatigue life after strengthening is generally reported in literature and is attributed to the reduced stress level in the steel reinforcement due to the presence of FRP. This paper presents an experimental analysis devoted to investigate the fatigue-induced properties of the FRP-concrete interface. Strain patterns along the bonded length and the surrounding concrete were measured using digital image correlation. A decrease of the effective length during cycling is observed, indicating a different debonding mechanism during fatigue. Post-fatigue response of the FRP-concrete interface appears to be qualitatively similar to the monotonic one.

The increasing use of carbon fiber reinforced polymer (FRP) sheets for strengthening existing reinforced concrete beams has generated considerable research interest in understanding the debonding mechanism of failure in such systems. The influence of the width of the FRP on the load carrying capacity is investigated in this paper. The interfacial crack propagation and strain distribution during shear debonding are studied using a full-field optical technique known as digital image correlation. The results indicate the development of high stress/strain gradients at the interface as a consequence of the relative slip between the FRP and the concrete. The interface stress transfer between the FRP and concrete produces axial strain gradients in the FRP along its length. In the vicinity of the edges along the width of the FRP, edge regions comprising of both FRP and concrete are established. The edge region is characterized by high strain gradients in a direction perpendicular to the length and is of fixed width throughout the debonding process. The size of the edge regions is also found to be quite independent of the width of the FRP. Mode-II fracture condition exists in the interface directly below the FRP away from the edge regions. The interfacial crack is shown to be associated with a cohesive stress transfer zone of fixed length. During debonding, the stress transfer zone is shown to propagate in a self-similar manner at a fixed load. The interface fracture properties obtained from the portion of FRP away from the edge regions are shown to be independent of the FRP width. It is shown that when the width of concrete is larger than that required for establishing the edge regions, the nominal stress at debonding increases with an increase in the width of FRP. The scaling in the load carrying capacity during shear debonding is shown to be the result of the edge regions which do not scale with the width of the FRP.

Carbon fiber reinforced polymer (CFRP) sheets have been extensively used for strengthening deteriorated concrete structures. When applied to the tension side of the beam, the FRP com-posite increases the internal moment of resis-tance of the strengthened section. The effec-tiveness of such strengthening depends upon the load transfer from concrete to the FRP composite. Shear debonding is usually caused by a crack that forms and then propagates at the interface between the adherents. The influence of the geometric parameters of the adherents on the fracture propagation is still a subject of re-search despite the large number of experimental and numerical analyses that have been carried out. This paper presents an experimental inves-tigation performed on direct shear specimens to study the influence of the relative width of FRP and concrete on the load carrying capacity of the bond and the stress transfer between the adherents. The fracture behavior of FRP-concrete interface is considered for different widths of the FRP. The results from the limited data indicate a scaling in the ultimate stress at complete debonding while the stress-transfer between the FRP and the concrete remains un-changed when varying the FRP widths. Rea-sons for the scaling are shown to be a result of the edge strips of FRP that do not scale propor-tionally with the width of FRP.

Laminated glass is used in several engineering and architecture applications to enhance their structural integrity. The mechanical behaviour after glass fracture, whose main aspect is a re-sidual stiffness, determines their utility. A theoretical model to predict the loading ca-pacity of a laminated glass flexural beam is proposed. The beam is subjected to four-point bending. A fracture approach which takes into account imperfections in glass plies and crack growth is employed.

L’efficacia del rinforzo di travi in c.a. con FRP è legata al trasferimento delle tensioni di trazione dal calcestruzzo al rinforzo esterno in FRP. Il fenomeno del “debonding” consiste in una separazione del composito dal calcestruzzo attraverso la propagazione di un crack lungo la regione di interfaccia tra i due materiali. In letteratura non sembra esserci sufficiente attenzione all’influenza dell’effetto scala sulla propagazione in Modo-II del crack nell’interfaccia. Nel presente lavoro viene studiata sperimentalmente la capacità di carico dell’interfaccia composito-calcestruzzo in funzione della larghezza del composito (b1) e del provino di calcestruzzo (b). I risultati ottenuti fino ad ora confermano l’esistenza di un effetto scala in riferimento alla tensione nel composito all’atto della completa delaminazione. Mentre la modalità di trasferimento di tensioni di trazioni dal calcestruzzo al composito sembra essere indipendente dalla rapporto b1/b.

The analysis of buckling of elastic columns is one of the first problem in structural engineering that was historically solved. Critical loads of perfect columns with various end restrains have been derived . Nevertheless, the perfect column is an idealized model. In reality, inevitable imperfections should be considered. Solutions for later disturbing load, crookedness or load eccentricity have been proposed. Another frequent imperfection to be taken into account is the weakness at an interior location due to a partial crack. In this paper the influence of this type of imperfection on the critical load is analyzed. The weakness can be modeled as an internal hinge strengthened by a rotational spring. The spring constant can be determined on the basis of the energy released due to the crack and Catigliano’s theorem. Exact critical loads for various end conditions, crack locations and cross sections are obtained.

The solution of the elastostatic problem of an orthotropic body having a central inclined crack and subjected at infinity to a uniform biaxial load has been employed. It is assumed that the crack line does not coincide with an axis of elastic symmetry of the body. Crack initiation and growth behaviour in anisotropic materials can differ from the isotropic case both qualitatively and quantitatively. Crack initiation behaviour can be readily found by application of the Strain Energy Density Criterion where the failure load and direction of crack initiation can be determined for different properties of orthotropy and directions of biaxial loading. The influence of the non singular terms on the crack initiation angle is also investigated. The Fracture Loci are also represented and compared with the ones obtained from the Maximum Circumferential Stress Criterion.

The solution of the elastostatic problem of an orthotropic body having a central inclined crack and subjected at infinity to a uniform biaxial load has been employed. It is assumed that the crack line does not coincide with an axis of elastic symmetry of the body. The stress filed is reported. The topic of the present paper is the extension of the maximum Circumferential Tensile Stress Criterion to orthotropic materials, in order to obtain the crack initiation angle, pointing out the effects of orthotropy and load biaxiality. The influence of the non singular terms on the crack initiation angle is also investigated.

The research would draw attention to the historical technology, especially to the masonry herring-bone pattern. The first examples could be found into the Roman Architecture. It was used for covering wide rooms using small clay brick elements. The herring-bone pattern and other geometrical and constructive devices had allowed to realise monumental constructions without wood framework. These monumental structures are still in service. The Authors aim is to develop an analytical model in order to investigate the structural behaviour of masonry barrel vaults built with herring-bone pattern. These structural elements are analysed in the field of shell theory and linear elastic behaviour of material; the masonry barrel vaults are modelled as bi-dimensional orthotropic elements. Starting with membrane components, the necessity to evaluate the effect of herring-bone pattern on the stresses configuration requires the introduction of flexural components in the equilibrium conditions. Formulated the static problem, the angle a of masonry configuration in herring-bone pattern is assumed as parametric element for the analysis. The range of the angle a will be the following: “head” and “flat” considering the brick along arch ring. The intermediate brick configurations are defined as herring-bone pattern and a assumes the values between 0 and p/2. The displacement field is evaluated for each configuration of masonry brickwork. Possible stress peaks, identified by the analytical model, are the start point for the definition of collapse mechanism which could modify the static behaviour of these masonry vaults.

The elastostatic problem of an orthotropic body having a central inclined crack and subjected at infinity to a uniform biaxial load is considered. It is assumed that the crack line does not coincide with an axis of elastic symmetry of the body. The problem must be considered as one of general orthotropy, due in particular to the fact that the elastic coefficients of the material change with rotation of the reference system. The stress fields at the crack tip are reported and the presence of the non-singular terms underlined. The Strain Energy Density Theory is extended to orthotropic materials. It is assumed that the Critical Strain Energy Density Factor has a polar variation. The crack initiation is determined via minimization of the ratio of the strain energy density over the material critical strain energy density, pointing out the effects of orthotropy and load biaxiality . The aim of the present paper is to point out the effects of the non-singular terms on crack growth for different orthotropic materials, underling the relation between orthotropy and non-singular terms.