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Numerical analysis of reinforced concrete beams strengthened in shear by externally bonded (EB) fibre reinforced polymer (FRP) sheets

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Abstract

In this paper, a fibre beam model previously developed by the authors for the nonlinear analysis of strengthened elements, including the effects of shear, is used to predict the response of reinforced concrete (RC) beams strengthened in shear with fibre reinforced polymers (FRP) sheets. This model has been extended not only for wrapped configurations but also for debonding failure in order to allow for its application to beams strengthened with U-shaped and side-bonded configurations. When simulating existing experimental tests, the model reproduces, with reasonable accuracy the behavior of the beams, being then a useful tool for practical engineering.

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... Cohen M., Montepone A., Potapenko S. conducted a numerical experiment with the finite element model calculation of a beam reinforced with automatic gearbox with modeling of reinforcement adhesion to concrete and the cracks appearance [6]. The team under supervision of E. O. Ibar carried out the calculation in the nonlinear stage of the beam reinforced material work by the PCR [7]. ...
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The use of externally bonded fiber-reinforced polymer (EB-FRP) composites for shear strengthening of reinforced concrete (RC) beams presents many challenges given the complex phenomena that come into play. Premature bond failure, the behavior of the interface layer between FRP composites and the concrete substrate, the complex and brittle nature of shear cracks, and the adverse interaction between internal steel stirrups and EB-FRP are some of these phenomena. Compared to experimental investigations, the finite element (FE) technique provides an accurate, cost-effective, and less time-consuming tool, enabling practicing engineers to perform efficient, accurate nonlinear and dynamic analysis as well as parametric studies on RC beams strengthened with EB-FRP. Since 1996, many numerical studies have been carried out on the response of RC beams strengthened using FRP. However, only a few have been related to RC beams strengthened in shear using EB-FRP composites. In addition, the analytical models that have been reported so far have failed to address and encompass all the factors affecting the contribution of EB-FRP to shear resistance because they have mostly been based on experimental studies with limited scopes. The aim of this paper is to build an extensive database of all the studies using finite element analysis (FEA) carried out on RC beams strengthened in shear with EB-FRP composites and to evaluate their strengths and weaknesses through various studied parameters.
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The objective of this paper is to contribute to the understanding of the shear resisting mechanisms in RC beams shear-strengthened by externally bonded fiber-reinforced polymer (FRP) sheets. For this purpose, a fiber beam model of RC frames subjected to combined normal and shear forces, previously developed by the authors, has been extended to include the response of externally bonded FRP shear reinforcement in a wrapped configuration. No FRP delamination phenomena or tensile strength reductions in the corner zones are taken into account in the model. The numerical results have been compared with eight existing experimental results and the influence of the FRP sheets on the shear strength of the beam has been studied. The effects of the contribution of FRP ratio on the concrete, on the transversal steel strains and stresses, on the longitudinal tensile steel stresses, and on the diagonal compression struts have been analyzed. It is concluded that the presence of FRP reinforcement modifies the inclinations of cracks and struts, the concrete confinement stresses, and other parameters related to the shear response, producing an interaction between the concrete, internal steel, and FRP components of the shear strength. (C) 2013 American Society of Civil Engineers.
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In recent years, numerous investigations have addressed the shear strengthening of reinforced concrete (RC) beams with externally bonded fiber-reinforced polymer (FRP) composites. Despite this research effort, the mechanisms of shear resistance that are developed in such a strengthening system have not yet been fully documented and explained. This clearly inhibits the development of rational and reliable code specifications. This paper aims to contribute to the understanding of the shear resistance mechanisms involved in RC beams strengthened in shear with externally bonded FRP. It is based on results obtained from an experimental program, involving 17 tests, performed on full size T beams, and using a comprehensive and carefully optimized measuring device. The resistance mechanisms are studied by observing the evolution of the behavior of the strengthened beams as the applied loads are increased. The local behavior of the FRP and the transverse steel, in particular in the failure zones, are thoroughly examined. The operative resistance mechanisms are also studied through the load sharing among the concrete, the FRP, and the transverse steel, at increasing levels of applied load.
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An attractive technique for the shear strengthening of reinforced concrete beams is to provide additional web reinforcement in the form of externally bonded fiber-reinforced polymer (FRP) sheets. So far, theoretical studies concerning the FRP shear strengthening of reinforced concrete members have been rather limited. Moreover, the numerical analyses presented to date have not effectively simulated the interfacial behavior between the bonded FRP and concrete. The analysis presented here aims to capture the three-dimensional and nonlinear behavior of the concrete, as well as accurately model the bond-slip interfacial behavior. The finite-element model is applied to various strengthening strategies; namely, beams with vertical and inclined side-bonded FRP sheets, U-wrap FRP strengthening configurations, as well as anchored FRP sheets. The proposed numerical analysis is validated against published experimental results. Comparisons between the numerical predictions and test results show excellent agreement. The finite-element model is also shown to be a valuable tool for gaining insight into phenomena (e.g., slip profiles, debonding trends, strain distributions) that are difficult to investigate in laboratory tests.
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This paper presents a simplified shear design method for reinforced concrete beams strengthened externally with fiber reinforced polymer (FRP) sheets. This design method combines both the strip method and the shear friction approach. The background of the strip method is presented in detail, including the interface shear strength curve, which is compared with some available bond test data found in the literature. A parametric study is performed to propose two simplified equations, which describe the FRP sheet contribution. This contribution is added to the discrete shear friction formulation and, by derivation, a continuous and simplified design equation is proposed. This method well describes the interaction between the concrete, the stirrups, and the FRP sheets. A variable concrete crack angle is used, which enhances the accuracy of the model. No iteration is required. The proposed design formulation gives conservative predictions with 35 experimental test results found in the literature.
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The need for structural rehabilitation of concrete structures all over the world is well known, and a great amount of research is going on in this field. The use of carbon fiber-reinforced polymer (CFRP) plate bonding has been shown to be a competitive method with regard to both structural performance and economic factors. This method consists of bonding it thin carbon-fiber laminate or sheet to the surface of the structure to act as an outer reinforcement layer. However, most research in this area has been undertaken to study flexural behavior. This paper deals with shear strengthening of reinforced concrete members by use of CFRP. Tests on rectangular beams 3.5 to 4.5 m long have been undertaken to study different parameters. such as fatigue. anchorage, and others. The strain field in shear spans of beams simultaneously subjected to shear and bending is also studied. The tests presented also contribute to the existing literature on tests of concrete members strengthened for increased shear capacity.
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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.
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Prefabricated carbon fibre reinforced plastic (CFRP) L-shaped plates can be used to shear strengthen reinforced concrete (RC) T-beams. Previous investigations by EMPA have shown the suitability of the CFRP L-shaped plates for static shear strengthening.In this paper, a large-scale fatigue test is presented which demonstrated the suitability of the CFRP L-shaped plates for shear strengthening of RC T-beams for fatigue reasons. The test beam was subjected to 5 million load cycles at a high load level and a subsequent failure test. Its behaviour is compared with that of a similar, statically tested beam. A fatigue design proposal is presented for users of the CFRP L-shaped plates.
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A procedure is described by which nonlinear finite-element algorithms can be modified to enable the analysis of repaired or rehabilitated concrete structures, taking into account the chronology of the loading, damage, and repair. The method defines and employs plastic strain offsets in the context of a smeared rotating crack model. The ability to engage and disengage elements at various stages of loading, as well as the ability to carry forward strain measures representing previous loading and damage conditions, are key aspects in the analysis method. Analysis of beams and slabs repaired with fiber-reinforced plastics demonstrates the accuracy of the procedure in accounting for changes in strength, stiffness, ductility, and failure mode as a result of strengthening measures. Flexure-dominated and shear-dominated responses are equally well represented. The analysis of a repaired shear wall, subjected to reversed cyclic lends, illustrates the ability to model severely damaged structures where some portions must be removed and reconstructed. In all cases, the analysis procedure was numerically stable and efficient at all stages of loading.
Article
Reinforced concrete structures often exhibit structural and nonstructural cracking due to a variety of reasons. Major cracks are signs of distress and require immediate attention. Results from a study on strengthening of reinforced concrete beams having deficient shear strength and showing major diagonal tension cracks are presented in this paper. The beams with deficient shear strength were damaged to a predetermined level (the appearance of the first shear crack) and then repaired by fiberglass plate bonding (FGPB) techniques. Different shear repair schemes using FGPB to upgrade beams' shear capacity were used: FGPB repair by shear strips, by shear wings, and by U-jackets in the shear span of the beams. Experimental data on strength, stiffness, steel strain, deflection, and mode of failure of the repaired beams were obtained, and comparisons between the different shear repair schemes and the unrepaired control beams were made. Shear repair by FGPB is shown to increase shear capacity and restore the degraded stiffness of the beams. The study results also show that the increase in shear capacity by FGPB was almost identical for both strip and wing shear repairs. However, this increase was not adequate to cause beams repaired by these two schemes to fail in flexure. On the other hand, the enhanced shear capacity by U-jacket was sufficient that flexural failure occurred for these beams.
Article
Incrementally linear constitutive equations that are characterized by an orthotropic tangential stiffness or compliance matrix have recently become widely used in finite element analysis of concrete structures and soils. It does not seem to be, however, widely appreciated that such constitutive equations are limited to loading histories in which the prinicipal stress directions do not rotate, and that a violation of this condition can sometimes have serious consequences. It is demonstrated that in such a case the orthotropic models do not satisfy the form-invariance condition for initially isotropic solids, i.e., the condition that the response predicted by the model must be the same for any choice of coordinate axes in the initial stress-free state. An example shows that the results obtained for various such choices can be rather different. The problem cannot be avoided by rotating the axes of orthotropy during the loading process so as to keep them parallel to the principal stress axes, first, because this would imply rotating against the material, the defects that cause material anisotropy, such as microcracks, and, second, because the principal directions of stress and strain cease to coincide. The recently popular cubic triaxial tests do not give information on loading with rotating principal stress directions.
Article
In this paper a nonlinear sectional formulation to account for full 3D stress–strain states on frame elements is presented, by means of a special cross-section model which allows for warping and section’s shape distortion. This formulation allows using a 3D constitutive model for concrete. Subsequently, the approach is applied it to the nonlinear coupled behaviour of RC sections under multiaxial internal forces considering inclined cracking pattern and failure stages. The applicability of the model to RC sections is validated by means of combined tangential-normal loading case studies. The presented formulation uses the traditional six generalized strains 3D sectional analysis; therefore it can be implemented on any 3D frame element without introducing additional degrees of freedom on the frame element.
Article
Modeling the response of reinforced concrete structures under combined shear and normal forces involves handling the anisotropic behavior that takes place in the post-cracked and ultimate ranges. Current 2D (plane-stress and plane-strain) and 3D (solid) non-linear finite element formulations capable of modeling such response are too costly and not suitable for daily engineering practice. In this paper a new developed frame element model which combines an efficient fully coupled in-plane shear–normal sectional model with a beam–column element, suitable for structural analysis applications is described and verified with tests results.Both normal and shear stresses and strains are involved in the sectional equilibrium and compatibility equations, respectively. The shear and vertical strain distributions are assumed to be composed by a series of polynomial shape functions; each one is affected by a constant whose value is internally calculated according to the materials state. The non-linear analysis of the frame structure is carried out using the Generalized Matrix Formulation, which is a force-based approach with “exact” interpolation of forces along the element and implicitly accounts for the shear deformation of the element.The model has been verified using the results of selected well documented tests, in which the influence of the level of shear stresses on the structure response is experimentally evidenced. Good agreement has been obtained between the experimental and the theoretical results provided by the model, showing its capability to reproduce displacements, stresses and strains in the concrete and in the reinforcements, and different types of failure, with more accuracy than previous models.
Article
A nonlinear and time-dependent fibre beam element model able to simulate the response of existing reinforced concrete (RC) frame structures subjected to repair and strengthening interventions is presented in this paper. The relevant attributes of the proposed formulation are: (i) its capability for considering shear effects in both service and ultimate levels and (ii) the step-by-step nonlinear sequential type of analysis, which allows capturing the strengthening effects, accounting for the state of the structure prior to the intervention. The 2D fibre beam element developed is based on the Timoshenko theory and a hybrid (kinematic/force) formulation is used to simulate the response of RC sections under combined normal and shear stresses. Biaxial constitutive equations assuming smeared rotating cracks are used to describe the behaviour of cracked concrete. The proposed model is validated with experimental results of a shear damaged and subsequently strengthened RC beam, available in the literature. An alternative shear strengthening solution with the use of prestressed stirrups is also presented. The importance of considering shear-bending interaction and previous damage in the numerical assessment of strengthened RC beams is highlighted.
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An analytical model for the nonlinear and time-dependent analysis of segmentally constructed three dimensional concrete frames is presented. The structural effects of the load and temperature histories, materials nonlinear behaviour, creep, shrinkage, aging of concrete and relaxation of prestressing steel are considered, as well as the nonlinear geometric effects. The step by step analysis procedure allows us to simulate most of current construction processes of bridges and buildings. Possible changes on the structural configuration and loading at any time include variations on the longitudinal scheme and cross section, restraining and releasing boundary conditions or stressing and removing prestressing tendons, among others. Numerical results are compared with those obtained from a large scale laboratory test, showing the capability of the analytical model to reproduce the structural effects of a complex evolutionary construction process along with the nonlinear and time dependent behaviour of the materials.
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This paper presents the shear performance of reinforced concrete (RC) beams with T-section. Different configurations of externally bonded carbon fiber-reinforced polymer (CFRP) sheets were used to strengthen the specimens in shear. The experimental program consisted of six full-scale, simply supported beams. One beam was used as a bench mark and five beams were strengthened using different configurations of CFRP. The parameters investigated in this study included wrapping schemes, CFRP amount, 90°/0° ply combination, and CFRP end anchorage. The experimental results show that externally bonded CFRP can increase the shear capacity of the beam significantly. In addition, the results indicated that the most effective configuration was the U-wrap with end anchorage. Design algorithms in ACI code format as well as Eurocode format are proposed to predict the capacity of referred members. Results showed that the proposed design approach is conservative and acceptable.
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The present study examines the shear performance and modes of failure of rectangular simply supported reinforced concrete (RC) beams designed with shear deficiencies. These members were strengthened with externally bonded carbon fiber reinforced polymer (CFRP) sheets and evaluated in the laboratory. The experimental program consisted of twelve full-scale RC beams tested to fail in shear. The variables investigated within this program included steel stirrups, and the shear span-to-effective depth ratio, as well as amount and distribution of CFRP. The experimental results indicated that the contribution of externally bonded CFRP to the shear capacity was significant. The shear capacity was also shown to be dependent upon the variables investigated. Test results were used to validate a shear design approach, which showed conservative and acceptable predictions.
Análisis de los modelos de comportamiento de vigas de hormigón armado reforzadas a cortante con polímeros armados con fibras (FRP). Validación y calibración experimental
  • A Alzate
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Shear response of continuous RC beams strengthened with carbon FRP sheets
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Arduini, M., Nanni, A., Di Tommaso, A., and Focacci, F. (1997). "Shear response of continuous RC beams strengthened with carbon FRP sheets." Proc., 3rd Int. Symp. on Non-metallic (FRP) Reinforcement for Concrete Structures, Vol. 1, Japan Concrete Institute, Tokyo, 459-466.
Collasso di travi in C.A. per taglio e utilizzo di FRCM per l'adeguamento
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Caiazza, R., Recupero, A., and Scilipoti, C. D. (2006). "Collasso di travi in C.A. per taglio e utilizzo di FRCM per l'adeguamento." Proc., Convenio Nazionale Crolli e Affidabilita delle strutture civili (CRASC'06), Università degli Studi di Messina, Italy (in Italian).
A model for the nonlinear, time-dependent and strengthening analysis of shear critical frame concrete structures
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Ferreira, D. (2013). "A model for the nonlinear, time-dependent and strengthening analysis of shear critical frame concrete structures." Ph.D. thesis, Dept. of Construction Engineering, Universitat Politècnica de Catalunya, Barcelona, Spain.
The finite element method
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Zienkiewicz, O. C. (1977). The finite element method, McGraw-Hill, London.