A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

An experimentally based analytical model for the shear capacity of FRP-strengthened reinforced concrete beams

This paper deals with the shear strengthening of Reinforced Concrete (RC) flexural members with externally bonded Fiber-Reinforced Polymers (FRPs). The interaction between an external FRP and an internal transverse steel reinforcement is not considered in actual code recommendations, but it strongly influences the efficiency of the shear strengthening rehabilitation technique and, as a consequence, the computation of interacting contributions to the nominal shear strength of beams. This circumstance is also discussed on the basis of the results of an experimental investigation of rectangular RC beams strengthened in shear with “U-jacketed” carbon FRP sheets. Based on experimental results of the present and other investigations, a new analytical model for describing the shear capacity of RC beams strengthened according to the most common schemes (side-bonded and “U-jacketed”), taking into account the interaction between steel and FRP shear strength contributions, is proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 339–356, May–June, 2008.     

Bond-slip behavior of CFRP plate-concrete interface

The paper deals with evaluation of the bond performance between a CFRP plate and concrete with respect to various compressive strengths of concrete and bond lengths of the CFRP plate as parameters. To consider stress conditions in the tensile zone of reinforced concrete (RC) structures, double-lap axial tension tests were conducted for eight specimens with CFRP plates bonded to concrete prisms. In addition, a simple linear bond-slip model for the CFRP plate/concrete joints, developed from the bond tests, was used. To verify the model proposed, a total of seven RC beams were strengthened with CFRP plates and tested in flexure employing various bond lengths, strengthening methods, and numbers of CFRP plates. A nonlinear finite-element analysis, with the bond–slip model incorporated in the DIANA program, was performed for the strengthened RC beams. Also, the results of flexural test and analytical predictions are found to be in close agreement in terms of yield and ultimate loads and ductility.     

Dynamic assessment of reinforced concrete beams repaired with externally bonded FRP sheets

This research deals with RC beams strengthened with FRP. An experimental research is presented which is aimed at evaluating the capability of an experimental modal analysis to assess the stiffness decrease due to damage, as well as the stiffness recovery due to strengthening. Ten beams were tested. All of them were subjected to loading cycles with increasing load levels in order to induce cracking of different severity in them. The beams were then retrofitted by externally bonded FRP sheets. Three types of composites were used. The number of layers was varied, too. Modal tests were carried out after each loading-unloading cycle. The modal frequencies and damping ratios were determined for the first four vibration modes. The results obtained indicate that an experimental modal analysis can give useful information on the severity of damage and the effectiveness of strengthening. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 3–20, January–February, 2006.     

Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates

The results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening, are presented. The internal flexural steel reinforcement was designed so that to allow steel yielding before the collapse of the beams. To prevent the shear failure, steel stirrups were used. The tests also included two nonstrengthened control beams; the other specimens were strengthened with different configurations of externally bonded carbon-fiber-reinforced polymer (CFRP) laminates. In order to prevent the premature failure from delamination of the CFRP strengthening, a wrapping was also applied. The experimental results obtained show that it is possible to achieve a sufficient degree of moment redistribution if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 667–686, September–October, 2007.     

An improved closed-form solution to interfacial stresses in rc beams strengthened with a composite plate

The strengthening of concrete structures in situ with externally bonded fiber-reinforced plastic (FRP) composite sheets is increasingly being used for the repair and rehabilitation of existing structures. However, debonding along the FRP-concrete interface can lead to premature failure of the structures. The interfacial stresses have played a significant role in understanding this premature debonding failure of such repaired structures. In this paper, an improved theoretical analysis of the interfacial stresses is presented for a simply supported concrete beam bonded with a FRP plate. The shear strains of the adherends have been included in the present theoretical analysis by assuming a parabolic distribution of shear stress across their thickness. Contrary to some existing studies, the assumption that both adherends have the same curvature is not used in the present investigation. The results of this numerical study are beneficial for understanding the mechanical behavior of material interfaces and for the design of hybrid FRP-reinforced concrete structures.     

Stability of round concrete columns confined by composite wrappings

External confinement by the wrapping of fiber-reinforced polymer (FRP) sheets is a very effective method for the strengthening and retrofit of round concrete columns. The stability and strength of concrete columns confined by carbon FRP jackets in which the fibers are oriented in the hoop direction was studied. Stability tests were conducted on hinged plain and confined concrete columns of different slenderness. The theoretically predicted critical stress at the on set of in stability was compared with that obtained experimentally, and a good agreement between them was observed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 657–666, September–October, 2007.     

Bond of FRP Reinforcement in Concrete - a Challenge

The bond of ordinary steel reinforcement in concrete depends on many factors, such as the pullout resistance, the geometry of a concrete member, the placement of a bar in the member cross section, the cover splitting, the confinement caused by concrete and the surrounding reinforcement, the order of bond-crack appearance, and the bond-stress distribution along the bond length. The bond of FRP reinforcement depends on even a greater number of factors. Moreover, the types of FRP bars are numerous. Their surface is weaker than that of steel bars and may fracture by bond forces. The surface of FRP bars is softer and does not create as high local stress concentrations in bond contact points to concrete as the harder steel bars do. This fact often delays the appearance of cover splitting cracks along the bars. However, the load necessary for developing the crack pattern of ultimate splitting failure in concrete is then very dependent on whether the bar surface is glossy or rough. The FRP reinforcement can also be used for external shear and/or flexural strengthening of existing members. For this application, FRP bars are placed in grooves cut on the surface of the member to be strengthened and are fixed there with a cement mortar or epoxy paste. In such an application, the performance of bond between the FRP rod and the mortar or resin and then between the mortar or resin and concrete is critical for the effectiveness of the technique. The presence of two interfaces increases the number of parameters needed to characterize the global joint behavior and introduces new possible failure modes. The fundament for the bond resistance estimation should be an accepted bond philosophy linked to appropriate models. A system of bond tests should provide necessary coefficients for the models.     

An analysis of the joint operation of a CFRP concrete in flexural elements

The strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated. Two methods for calculating the shear force in the contact zone are considered, one of which takes into account the compliance of the zone and gives results agreeing rather well with experimental data for beams, regardless of the way the CFRP is fastened to concrete. The method of shear stresses is good for beams with in significant shear strains between CFRP and concrete. A method allowing for hardening of the contact zone is suggested. It is shown that the fracture mechanism of the zone depends on the way of fastening the CFRP and the depth the adhesive penetrates into concrete. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 687–700, September–October, 2007.     

HB-FRP加固混凝土结构的粘结滑移统一模型

为了进一步简化HB-FRP(hybrid bonding FRP)加固技术的粘结滑移模型, 并基于先期研究的HB-FRP粘结滑移分区模型开展研究.在假定HB-FRP加固技术的粘结滑移统一模型表达式的基础上,推导了钢扣件部位的粘结应力分布系数.将HB-FRP加固作用分为普通FRP粘结性能和钢扣件产生的粘结性能两部分,依据能量方法,推导了FRP张拉力与滑移量的表达式.基于理论分析和数值求解,研究了界面滑移量的分布特征.基于模型试验测试结果,研究了粘结滑移统一模型中的待定系数表达式.研究结果表明:建立的HB-FRP加固混凝土结构的粘结滑移统一模型能有效预测加固界面的剥离承载力及有效粘结长度.     

Anchorage strength models for end-debonding predictions in RC beams strengthened with FRP composites

The increase in the flexural capacity of RC beams obtained by externally bonding FRP composites to their tension side is often limited by the premature and brittle debonding of the external reinforcement. An in-depth understanding of this complex failure mechanism, however, has not yet been achieved. With specific regard to end-debonding failure modes, extensive experimental observations reported in the literature highlight the important distinction, often neglected in strength models proposed by researchers, between the peel-off and rip-off end-debonding types of failure. The peel-off failure is generally characterized by a failure plane located within the first few millimetres of the concrete cover, whilst the rip-off failure penetrates deeper into the concrete cover and propagates along the tensile steel reinforcement. A new rip-off strength model is described in this paper. The model proposed is based on the Chen and Teng peel-off model and relies upon additional theoretical considerations. The influence of the amount of the internal tensile steel reinforcement and the effective anchorage length of FRP are considered and discussed. The validity of the new model is analyzed further through comparisons with test results, findings of a numerical investigation, and a parametric study. The new rip-off strength model is assessed against a database comprising results from 62 beams tested by various researchers and is shown to yield less conservative results. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 373–388, May–June, 2008.     

A method for predicting the deflection of reinforced concrete beams strengthened with carbon plates

For strengthening bent beams, plates of reinforced plastics are glued to their tensioned surface. As s result, the beam becomes layered, and it is possible to control its rigidity and deflection. Based on the methods of structural mechanics of layered media, a method is elaborated for determining the deflection of such beams on the entire range of loading up to their ultimate failure. A comparison between the theoretical and experimental results is carried out. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 45–60, January–February, 2006.     

Strengthening of RC beams with an innovative timber-FRP composite system

The results of a theoretical and experimental research project on the use of an innovative technique for strengthening concrete beams are presented. A spacer element is inserted between the tension side of a beam and the composite material to increase its lever arm and to enhance the over all stiffness of the strengthened beam. The main aim of this exploratory project was to increase the ultimate failure load of strengthened beam specimens, whilst guaranteeing acceptable over all deflections at the serviceability limit states. This resulted into a significant reduction in the amount of FPR required and in a better utilization of the materials employed. A preliminary theoretical study was carried out to investigate the effect of Young’s modulus, failure strain, and thickness of the element to be used as a spacer in order to determine the best possible candidate material. Three tests on 2.5-m-long beams were carried out, and different anchorage techniques were used to try and prevent the debonding of the strengthening system. The results from this pilot study are very promising, as the strengthening system ensures an adequate initial stiffness along with an improved ultimate flexural capacity. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 403–416, May–June, 2008.     

Cracking Analysis of FRP-Reinforced Concrete Flexural Members

The paper is dedicated to the cracking analysis of FRP (Fiber-Reinforced Polymer)-reinforced concrete elements. A general nonlinear calculation procedure, based on the slip and bond stresses, is described and adopted for the prediction of the crack width and crack spacing in FRP-reinforced concrete beams. An analytical expression of the bond-slip law is estimated using the corresponding experimental results available in the literature. A numerical investigation is carried out and the influence of the mechanical and geometrical parameters of the material (bond-slip law, reinforcement ratio, concrete strength, diameter of rebars, etc.) on the crack formation is investigated. Referring to glass-FRP-reinforced concrete beams, a comparison between the theoretical predictions and experimental results is made. The results obtained are presented and discussed.     

FRP-strengthened reinforced concrete beams: a review and the assessment of cracking and deflection models

A review of some cracking and deflection models used for a structural analysis of FRP-strengthened reinforced concrete beams is presented, and, with reference to short-term deflections, a comparison between model predictions and experimental results is made. By using predictions provided by a nonlinear model derived from a cracking analysis, founded on slip and bond stresses, and experimental results for 63 FRP-strengthened beams, a modification of the well-known semi-empirical Branson’s formula to compute beam deflections is proposed. Finally, the efficiency of the modification is evaluated by comparison with experimental results.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.     

Finite-element modeling of the interaction of reinforcement with concrete matrix

A finite-element model of a reinforced concrete beam with rebars modeled by a 3-D deformable body has been developed. An analysis of the stress-strain state of the beam allowed us to determine the stress distribution on cross sections of the rebars and the location of zones with cracks in concrete. It is found that the break of bond between the reinforcement and concrete goes outside the areas of intensely cracked concrete matrix. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 309–316, May–June, 2008.     

Design equations for the assessment and FRP-strengthening of reinforced rectangular concrete columns under combined biaxial bending and axial loads

A simple procedure is proposed for the assessment of reinforced rectangular concrete columns under combined biaxial bending and axial loads and for the design of a correct amount of FRP-strengthening for underdesigned concrete sections. Approximate closed-form equations are developed based on the load contour method originally proposed by Bresler for reinforced concrete sections. The 3D failure surface is approximated along its contours, at a constant axial load, by means of equations given as the sum of the acting/resisting moment ratio in the directions of principal axes of the sections, raised to a power depending on the axial load, the steel reinforcement ratio, and the section shape. The method is extended to FRP-strengthened sections. Moreover, to make it possible to apply the load contour method in a more practical way, simple closed-form equations are developed for rectangular reinforced concrete sections with a two-way steel reinforcement and FRP strengthenings on each side. A comparison between the approach proposed and the fiber method (which is considered exact) shows that the simplified equations correctly represent the section interaction diagram. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 443–462, May–June, 2008.     

Load-deflection analysis of concrete elements reinforced with FRP rebars

The behavior of fiber reinforced plastic (FRP) concrete elements under service conditions is analyzed. Taking into account the real constitutive law of materials and local bond-slip law which adequately describes the interaction between the FRP reinforcement and concrete, a numerical procedure is proposed for obtaining moment-curvature relationships for a cracked beam element. Using the moment-curvature laws, the load-deflection analysis of FRP concrete beams is carried out. To study the influence of geometric and mechanical parameters, a numerical investigation was carried out and the results obtained were compared with those from other methods and Codes. The results of the experimental investigation are described and compared with those of the proposed procedure; the comparison shows good agreement between the theoretical and experimental results.Department of Materials Science, University of Lecce, Via per Arnesano, 73100 Lecce, Italy. Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 163–172, March–April, 1999.     

Estudio numérico-experimental de la interfaz hormigón-epoxi-FRP para una estructura reforzada sometida a doble corte

The strengthening of concrete structures with laminates of carbon fibers CFRP (Carbon Fibers Reinforced Polymer) began in the 1980's. Nowdays, this technology is one of the most promising one because of the good mechanical properties of laminates and their easy hand-work. Laminates are bonded to the concrete structure by means of epoxy resins. The load-carrying capacity of the strengthening depends directly on the proper behavior of the interface laminate-concrete. While the concrete is capable of transferring stresses to the laminate, this one becomes in charge and collaborates to the strength mechanism of the structure. The safety factor of the reinforcement can be guaranteed if we can predict the behavior at the interface between both materials. In this work we present a pure shear test and a simulation three-dimensional to characterize the behavior of the interface between the laminate and the concrete.