Carbon Fiber Reinforced Polymer Sheets Research Articles

STUDIES OF INTERIOR SLAB-COLUMN CONNECTIONS STRENGTHENED WITH HEMP FIBER REINFORCED POLYMER SHEETS

With increasing environmental concerns, using natural materials in concrete, such as bio-based fibers, is now becoming popular. Recently, hemp fibers have been utilized in the production of composite materials that have the possibility to replace synthetic fibers. The main objective of the research reported in this paper was to investigate the feasibility of using externally bonded hemp fiber-reinforced polymer (HFRP) fabric sheets as an alternative to synthetic carbon fiber-reinforced polymer (CFRP) sheets for punching shear strengthening of reinforced concrete two-way slabs. The experimental program consisted of testing small-scale, interior slab-column connections, under monotonically increased load until failure. The main test parameters included the slab thickness, type of strengthening material (HFRP or CFRP sheets), the width of HFRP sheets, number of sheets layers, and the location of the HFRP sheets relative to the column face. Test results showed that HFRP strengthening sheets enhanced the structural behavior of slab-column connections.

Precise finite element verification of the unreliability of using multi-layers of FRP on CFRP-debonding in RC beams

The nonlinear behaviour of an adhesive material that connects layer of carbon fibre reinforced polymer (CFRP) to a reinforced concrete (RC) beam is numerically simulated in this study. To the author’s knowledge, how debonding increases significantly with increasing FRP thickness has not yet been studied theoretically only with few experimental studies that directly say this information. The work is conducted via a finite element approach using the commercially available software ABAQUS 6.13. Firstly, the 3D finite element model is introduced and all the suitable elements, material properties, damage initiation and evolution, and failure criteria are presented. Initially, the numerical model is validated by using the experimental study of a CFRP strengthened beam, which is chosen from literature. The model is shown to accurately capture slip at the interface of the strengthening material and resultant debonding. Furthermore, the tensile strain profile along the CFRP sheet is studied and, which has shown a reverse trend to the interfacial slip profile. Using the validated model, a detailed study is conducted with regards to the effects of multiple CFRP layers on the ultimate capacity and failure mode of the strengthened RC beam. It is found that adding two layers similar to the thickness of one layer will not change the response of the beam. However, this makes the beam behave with less ductility. Furthermore, the difference between the two cases is that the damage of one layer is concentrated at the FRP free end for a short distance. While, for two layers it is also at the free end but extended to a longer distance to the centre of the beam what causes earlier debonding. It is also found that adding one layer of CFRP to strengthen a RC beam can improve the ultimate capacity by 22%. But adding more CFRP layers does not increase the ultimate capacity or change the failure mode. In addition, it will reduce the total deflection of the beam. The study has also found that the interface bond-stresses are non-uniformly distributed along the reinforced boundaries and the shear stresses values exhibit peak values of 1 to 2 times greater than or 1 to 0.5 times less than the mean values predicted by the classical beam theory. Moreover, during the simulation, no de-lamination was observed between the superimposed CFRP plates for the two layers of CFRP.

Durability Investigation on CFRP Strengthened Cementitious Materials in Cold Region.

Epoxy resin, CFRP (Carbon Fiber Reinforced Polymer) sheet, and concrete flexural specimens are selected to study the durability of carbon fiber strengthened cementitious materials in a cold region. Two exposure environments, chloride immersion and salt-freeze coupling, are set up, and the mechanical deterioration is discussed utilizing a microscopic observation mechanical test and finite element analysis. The damage to the epoxy resin, CFRP sheet, and concrete exerts a more severe performance degradation in the salt-freeze coupling environment when compared with the chlorine salt immersion environment. The freeze–thaw action destroys the bonding surface of CFRP and concrete based on the microscope observation. The flexural strength of the specimens strengthened with CFRP is 3.6 times higher than that of the specimens without CFRP, while the degradation rate is only 50%. These observations show that the strengthened CFRP effectively improves the cementitious material’s flexural performance in the cold region. The finite element model of epoxy and CFRP subjected to chloride immersion and salt-freeze coupling environment is established. The degradation formula of bond performance between CFRP and concrete is proposed. In addition, the flexural mechanical numerical model is established with and without CFRP strengthened concrete, respectively. Research results provide a technical reference for applying CFRP reinforced cementitious materials in a cold region.

Hysteresis behavior of 3D RC exterior beam-column joints strengthened with CFRP sheets and spike anchors

Full-scale 3D exterior beam-column joints lacking shear reinforcement but externally shear-strengthened with carbon fiber reinforced polymer (CFRP) sheets were investigated with respect to their behavior under both gravity and lateral cyclic loadings. For this purpose, three such joints including one control and two experimental ones (strengthened either with CFRP sheets or with both CFRP sheets and spike anchors) were subjected to relevant tests. Prior to CFRP installation, all the externally strengthened specimens were subjected to surface preparation and grooving in order to prevent possible CFRP debonding. The flexural capacity of both the non-strengthened and strengthened joints were estimated using a specially-developed analytical method. Comparisons of the lateral load–displacement hysteresis curves and in the test results revealed that, compared to the control, the externally strengthened joints showed enhancements of 30, 222, and 200% in lateral load-bearing capacity, energy dissipation, and secant stiffness, respectively. It was further found that despite the efficacy of the shear retrofit design proposed for 3D exterior connections, those strengthened with the combined CFRP sheets and spike anchors outperformed the ones solely strengthened with CFRP sheets. The sectional analysis results also revealed that the simple method proposed in this study is well capable of estimating bearing capacity in both the control and strengthened connections with reasonable accuracy.

Compression Performance of Square Steel Tubular Members Externally Enfolded with Carbon Fiber–Reinforced Polymer Sheet

Compression Performance of Square Steel Tubular Members Externally Enfolded with Carbon Fiber–Reinforced Polymer Sheet

Condition assessment and renovation of an aged precast reinforced concrete multi-storey building

This paper assesses the condition of a 45 years old precast reinforced concrete multistorey building and proposes innovative repair techniques for extending its service life. The residential building investigated consists of six floors, and each floor consists of 4 apartments with a total floor area of 900 m2. Initially, visual inspection was conducted to identify the extent of deterioration in all parts of the building, followed by field non-destructive and destructive tests to determine the root causes of the damage. Moreover, analytical tools such as ETABS and SAFE design softwares were used by applying the same loading assumptions and material properties given by the designer, to check the compliance of the building with the safety requirements specified in ACI 318-14/SBC 304-18 building codes. The field and laboratory checks confirmed the occurrence of considerable degree of deterioration in some elements of the building due to reinforcement corrosion, alkali silica reaction (ASR), salt–scaling and leaching. The analytical checks revealed excessive deflections, due to a design error. Several advanced repair techniques including carbon fiber reinforced polymer sheets (CFRP), and steel jackets were implemented to restore the structural load carrying capacity of the columns and beams that suffered extensive deterioration. The excessive deflections were reduced below the code limit by supporting the deflected slabs using wide flanged I-section steel beams. Moreover, the Repair strategy proposed included, removal of the deteriorated concrete, coating the exposed steel bars with a protective anti-corrosive coating, and cathodic protection of the steel bars followed by injecting high strength cementitious grout.

Strengthening of Reinforced Concrete Beams with Circular Opening at Flexure Zone by Various Types of Fiber Reinforced Polymer

This paper aims to investigate the flexural behaviour of reinforced concrete (RC) beams containing circular opening at mid-beam span and strengthened using externally bonded Textile Reinforced Concrete (TRC) sheets, Carbon Fibre Reinforced Polymer (CFRP) sheets and Carbon Fibre Reinforced Polymer (CFRP) plates. The flexural behaviour including ultimate load, deflection, crack pattern as well as failure mode was investigated. Five RC beams with the dimensions of 1700 mm length and cross section of 200 mm x 250 mm with design concrete strength of 64 N/mm2 were tested under 4-points loading. The tested RC beams consists of solid beam as a control beam, unstrengthened RC beam with circular opening and strengthened RC beams with circular opening. The circular opening with ratio of 0.32 is classified as small opening with diameter of 80 mm was kept constant for all beam specimens. The inclusions of circular opening at the middle of beam span slightly decreased the ultimate load of beam about 6.2% compared to control beam. The reduction of stiffness was also experienced in RC beam with opening. The application of strengthening in beams with circular openings manages to regain the beam capacity about 17.5 to 22.6% higher than the unstrengthened RC beams with opening.

Mitigation of Concrete Cover Separation in Concrete Beams Strengthened with Fiber-reinforced Polymer Composites

Strengthening of reinforced concrete (RC) beams using fiber reinforced polymers (FRP) is an effective method that is gaining more acceptance worldwide. However, failure of the strengthened beams at the plate-end region by concrete cover separation (CCS) compromises the effectiveness of such a strengthening system. Among available anchorage systems to remedy such problem, the use of FRP U-wraps at the end region of the externally bonded FRP has the potential to prevent CCS failure. Most studies in the literature suffer from poor design of test specimens and the use of random amounts of FRP anchorage. This resulted in nonconclusive findings and contradicting results on the real effectiveness of FRP U-wraps as an anchorage to prevent plate-end debonding failure. That in turn has been reflected in the lack of reliable design methods for the design of FRP U-wrap anchorage. In this paper, the effect of FRP U-wraps on the mitigation of CCS failure in FRP-strengthened RC beams was experimentally examined and quantified. The study included full-scale RC beams strengthened in flexure using carbon FRP (CFRP) sheets and anchored at the plate-end region using vertical CFRP U-wraps. The test variable was the amount of CFRP U-wrap that is required to achieve complete mitigation of CCS. The test results indicated the effectiveness of FRP U-wraps on mitigating CCS failure once the required area of CFRP U-wrap was placed. Relevant design models were presented and assessed against the experimental results of the current study. The comparisons indicated inaccurate predictions for the area of FRP U-wrap that is required to prevent CCS. This sheds the light on the need for developing a more reliable and accurate method for the design of an end anchorage to prevent CCS failure.

Effects of resin pre-coating treatment and fibre reinforcement on adhesive bonding between CFRP sheet and concrete

Peeling of a concrete layer adjacent to the adhesive is a common failure mode in carbon-fibre-reinforced polymer (CFRP) sheet-strengthened concrete structures. The resistance to debonding depends on the concrete surface strength, which is often reduced by defects induced by material preparation and manual operation. In the present study, to address this issue, a resin pre-coating (RPC) treatment was employed to strengthen the concrete surface, and Kevlar fibres pretreated with the RPC were used to reinforce the adhesive layer. The effects of the interfacial treatment and bond length on the failure modes were investigated via single-lap shear tests. The results indicated that epoxy resin penetrated the defects near the concrete surface after the RPC treatment and that the adhesive layer was significantly reinforced by the fibres. To quantitatively investigate the effect of the proposed technique on the adhesive bonding, an analytical model was proposed for determining the shear strength τf and shear fracture energy GIIf by incorporating the interfacial heterogeneity and discontinuity for specimens with small bond lengths. Realistic τf and GIIf values were obtained via a normal-distribution analysis. The results indicated that the τf and GIIf values were increased by 25.1% and 21.4%, respectively, when both the RPC treatment and the fibre reinforcement were applied.

Behaviour of continuous steel–concrete composite beams strengthened with CFRP sheets at hogging-moment region

Although the use of carbon fibre reinforced polymer (CFRP) materials for strengthening reinforced concrete structures and steel structures is well established, relatively few works have been reported for the strengthening of steel–concrete composite structures, especially at their hogging-moment region. In this paper, an experimental program consists of eight beam specimens with different degrees of shear connection, numbers of layers of CFRP sheets and strengthening methods was conducted. The experimental results show that adding CFRP sheets on the top of the concrete slab at hogging-moment region has a great effect on the structural performance in terms of ultimate loading capacity, load–deflection and load-slip responses, crack propagation, ductility, and failure mode, etc. The hybrid bonded FRP (HB-FRP) technique is firstly applied for the strengthening of steel–concrete structures at hogging-moment region in this study, and the advantages of the HB-FRP technique is proved through the comparisons with the externally bonded (EB) method. Based on the experimental observations, an analytical method for estimating the ultimate moment capacity of the strengthened composite beam at hogging-moment region is developed, for which the validity is verified against the experiment results.

Experimental study on torsional behaviour of square concrete filled CFRP-steel tube (S-CF-CFRP-ST)

In this study, the torsional behaviour of square concrete filled carbon fiber reinforced polymer (CFRP) steel tube is revealed by experimental study. Taking the confinement factor of transverse CFRP, strengthening factor of longitudinal CFRP and the compressive strength of cubic concrete as principal factors, total 18 specimens were designed and tested under torsional load. Based on the tests, a numerical simulation method is firstly proposed to estimate the torsional performance of square concrete filled CFRP steel tube (S-CF-CFRP-ST), and then validated against the representative tests results, such as the failure modes, torque-rotation angle curves, and torque-shear strain curves. The test results reveal that the CFRP sheets are all under tension during loading and can cooperate well with steel tube as strains measured on CFRPs are almost same with the ones on steel tube. The failure mode of S-CF-CFRP-ST, such as cracked concrete, ruptured CFRP and torsional deformation of steel tube, belongs to ductile failure. The obtained torque-rotation angle and torque-shear strain curves of tested specimens have similar characteristics and can be divided into elastic stage, elasto-plastic stage and plastic stage. Additionally, the torsional deformation of S-CF-CFRP-ST is in line with plane section assumption before the specimen gets into plastic stage. The good consistence between numerical results and experimental ones reveals that the proposed simulation method can predict the torsional behaviour of S-CF-CFRP-ST reasonably and accurately. Using this verified numerical models, parametric study is conducted to explore the influence of principle factors (e.g. CFPR layers, strength of concrete and steel, and steel ratio) on torsional behaviour of S-CF-CFRP-ST. It is found that the torsional bearing capacity of S-CF-CFRP-ST is slightly improved with the increase of CFRP layers and significantly affected by the strength of the used square steel tube. Additionally, the increase of steel ratio for CF-CFRP-ST member enhances not only the torsional strength but also the initial stiffness.

Mechanical behavior and recoverable properties of CFRP shape memory alloy composite under different prestrains

This paper explored a prestressed CFRP/SMA composite system, which can be applied to add prestress to the civil structural members. The composite system was composed of carbon fiber reinforced polymer (CFRP) sheets and the embedded shape memory alloy (SMA) wires. The prestress in CFRP sheets was formed by the recovery of SMA wires. Four groups of fully composite (Type I) specimens were fabricated to bear a unidirectional static load to investigate their tensile mechanical properties. Three groups of partial composite (Type II) specimens and five groups of SMA wire specimens were used to study their recoverability. The static test results showed that two main failure modes of the Type I specimens were observed, and the strength of the material was affected by the structural form of the composite. The recovery test results showed that the SMA wire could generate different levels of recovery stress under various amounts of prestrain, and the maximum recovery stress can reach 394.2 MPa for the SMA wire with 6% prestrain by heating it to 131℃. More importantly, the recovery stress can be introduced into the CFRP sheets. In addition, an analytical model for predicting the stress–strain relationship and material strength of the fully composite was proposed, and an improved segmented recovery stress–temperature model of the SMA wire under constraint conditions was also put forward. The results indicated that the calculated values are in good agreement with the experimental values, and the proposed model can effectively predict the mechanical and recoverable properties of the composites.

Seismic Retrofitting Method Using CFRP Sheets for H-Section Steel Beam with Variable Cross Section

Severe damage to steel bridge piers and steel rigid-frame piers starting from regions of abrupt change in cross section has been widely reported. Therefore, finding a simple and effective seismic retrofitting method for steel structural members with variable cross sections to improve their plastic deformation performance is currently an urgent concern. The objective of this study was to establish an effective seismic retrofitting method for H-section steel beams with abruptly variable cross sections using a carbon fiber–reinforced plastic (CFRP) sheet because of its outstanding properties such as light weight, high strength, and superior durability. Bending and bending-shear cyclic loading tests were conducted with two parameters, including the type of CFRP sheets, and whether or not polyurea putty was inserted between the CFRP sheet and steel beam. The test results indicate that the proposed retrofitting method using intermediate-modulus CFRP and polyurea putty increases the load-carrying capacity, ductility, energy dissipation capacity, and bending stiffness of H-section steel beams significantly without any failure. Further, by implementing finite-element (FE) analyses considering the actual cyclic plasticity properties of steel, anisotropic performance of the CFRP sheets, and nonlinear bond-slip properties of the polyurea putty layer, the cyclic loading test results were reproduced accurately. Moreover, in the cases in which the polyurea putty was applied, parametric FE analysis of the CFRP bonding method with and without creating a stepped length at the top of each CFRP sheet showed that the retrofitting method without the stepped length was similar in effectiveness to the method with the stepped length.

Flat friction spot joining of aluminum alloy to carbon fiber reinforced polymer sheets: Experiment and simulation

The Al alloy and carbon fiber reinforced polymer (CFRP) hybrid structures, incorporating the performance advantages of the two materials, have been attracting more attention in high-end manufacturing fields. In the current investigation, the flat friction spot joining (FSJ) was employed in joining the AA6061-T6 alloy and CFRP sheets. The significance of temperature distribution in influencing joint quality was highlighted through analyzing interface microstructural features, weld defect formation as well as fractography. To understand the role of thermal energy generation and conduction in the process comprehensively, a 3D thermal-mechanical coupling finite element model was established. The interfacial temperature was characterized by an uneven distribution behavior due to the inhomogeneous heat distribution. The peak temperatures on the top surface and Al alloy to CFRP interface at 1500 rpm rotational speed with 0.1 mm/s plunging speed were 498 °C and 489 °C, respectively. The peak interface temperature was reduced to 286 °C at 250 rpm, which produced an extremely small melted area. Compared with the plunging speed, rotational speed was found to be the predominant parameter for determining the joint property, which could be optimized to simultaneously realize the avoidance of thermal decomposition of CFRP, the sufficient melting duration time, and the wide enough melted area. Simulated thermal histories and melted area profiles were in agreement with experimental ones. The findings could be utilized to provide some feasible guidance for process optimization of dissimilar FSJ of metals and composites.

Flexural Behavior on Damaged Steel Beams Strengthened with CFRP Sheets Subjected to Overloading

This paper presents results of testing and numerical analyses of damaged steel beams strengthened with carbon-fiber reinforced polymer (CFRP) sheet and subjected to overloading. The test results showed that as cyclic times increase, the yield load and stiffness increase, but the ultimate bearing capacity decreases to a certain extent. Applying prestress could improve the ductility of the girder. The damage level greatly influenced the girders with overloading, and the increase in damage degree reduced the stiffness, yield load and ultimate load. The numerical calculation showed that the yield load would decrease by 0.4–0.8 kN when the cyclic times increase by 100 times. The yield load would increase by 1–2 kN and the ultimate bearing capacity would decrease by 0.6–1.2 kN when the overloading amplitude increased by 0.02 Pu. The increase in damage degree would obviously reduce the yield load and ultimate bearing capacity of the steel beam after overloading. The yield load and ultimate bearing capacity could be increased by approximately 3 kN when the CFRP sheet thickness increases by 0.05 mm.

Effectiveness and Efficiency of Externally Bonded CFRP Sheets for Shear Strengthening of RC Beam-Column Joints.

To develop feasible carbon fiber reinforced polymer (CFRP) retrofit schemes for the shear strengthening of real three-dimensional reinforced concrete (RC) beam-column joints, a series of parameters in relation to the contributions of the CFRP sheets externally bonded to joint panels was numerically investigated in this study. The parameters include CFRP reinforcement ratio, CFRP layout, transverse beam-to-joint panel width ratio, transverse beam-to-joint panel height ratio, location of transverse beam, and number of transverse beams. Strengthening efficiency, a new dimensionless index, was introduced to evaluate the residual effect of a CFRP-strengthening system weakened by the presence of transverse beams in comparison with the increase in joint shear capacity in relation to the one-way counterpart. The results obtained from 44 nonlinear finite element models, which were calibrated against experimental observations, confirmed the effectiveness of the CFRP strengthening technique with regard to the relatively wide ranges of the parameters. The significant differences among the roles of the parameters were revealed, and the reasons behind the differences were analyzed. Furthermore, the shear mechanism of the CFRP-retrofitted joint panels was discussed with the proposed strut-and-tie model.

Experimental and numerical evaluation of compression confinement techniques for HSC beams reinforced with different ratios of high strength steel reinforcement

This work presents experimental and numerical research to evaluate the compression confinement techniques of HSC beams reinforced with different ratios of high-strength steel reinforcement. Twelve specimens of high-strength reinforced concrete beams with two different compression confinement techniques were tested experimentally. The first method is used carbon fiber reinforced polymers sheets (CFRPs) around the compression zone, CF, and the steel fibers reinforced concrete is used in the compression zone by 1% of volume fraction, SF, in the second case. A 3-D finite element analysis was done; using the ANSYS program to simulate and idealize all experimental specimens. The numerical and experimental results of the RC beams were validated and compared in this work. The results showed that there is a good idealization using 3-D finite element models with the experimental specimens. Also, it was found that using the suggested techniques can increase the strength ratio and increase the ductility index depending on the tensile reinforcement ratios. Moreover, the energy absorption and the mode of failure were enhanced.

Experimental study on the eccentric performances of high predamaged rectangular reinforced concrete columns strengthened with carbon fiber reinforced polymer

The mechanical behaviors of 12 high predamaged reinforced concrete (RC) rectangular columns strengthened with carbon fiber reinforced polymer (CFRP) under eccentric compression were experimentally investigated. The effects of the predamaged degree ( δ), CFRP strips spacing ( s f ) and eccentricity ( e) on failure mode, bearing capacity, strain behaviors of CFRP strengthened predamaged columns were examined systematically. Test results demonstrated that the strengthened RC columns with small-eccentricity were destroyed by the yielding of compressive longitudinal steel bars and the crushing of compression concrete while the transverse CFRP strips were not ruptured. The failure mode of the strengthened RC columns with large-eccentricity was distinguished by the yielding of tensile and compressive longitudinal steel bars, the rupturing of longitudinal CFRP sheet, and the crushing of compressive concrete. With the increase of predamaged degree or eccentricity, the maximum bearing capacity of specimens decreased. In contrast, CFRP strips spacing had little effect on bearing capacity. Considering the effect of predamaged degree and eccentricity, a modified model for conveniently predicting the stress–strain relationship of CFRP strengthened predamaged RC columns under eccentric compression was proposed. On the basis of experimental study, the influence coefficients of predamaged degree and eccentricity and a strain distribution coefficient of CFRP strips were introduced, a calculation formula for predicting bearing capacity of high predamaged rectangular RC columns strengthened with CFRP under eccentric compression was proposed and validated test data with good agreement.

Flexural behavior of all lightweight reinforced concrete beams externally strengthened with CFRP sheets

The usage of structural Lightweight concrete (LWC) has increased over the years and received significant attention owing to its lower density, better economical design, and mechanical properties as compared to conventional normal weight concrete (NWC). However, limited research efforts and codes provisions deal with retrofitting and strengthening of lightweight concrete structures. Therefore, the main objective of this investigation is to evaluate the flexural performance of all lightweight concrete (ALWC) beams externally strengthened using Carbon Fibre Reinforced Polymer (CFRP) sheets. A total of fifteen ALWC beams were divided into three series based on their reinforcement ratio and strengthened with externally bonded CFRP sheets. The test variables studied in the experimental program were the effective reinforcement ratio, number of CFRP layers, and the percentage of pre-loading. All the beams were tested under four-point bending and the experimental results show that the CFRP sheet has significantly increased the ultimate load carrying capacity of pre-loaded and non-preloaded strengthened specimens. The increase in flexural capacity ranged from 28% to 102% over the unstrengthened control specimen. The ultimate load capacity was also predicted using different design standards and compared with the experimental load. The comparison showed that the current design standards have overestimated the flexural capacity of CFRP strengthened ALWC specimens.

Flexural strengthening of fire-damaged GFRP-reinforced concrete beams using CFRP sheet: Experimental and analytical study

Since the strengthening of fiber-reinforced polymer (FRP) bar-reinforced structures after a fire incident has rarely been considered in research works, in this work, the flexural response of plain and fiber-reinforced concrete beam specimens with embedded glass FRP (GFRP) bars strengthened with carbon FRP (CFRP) sheets was examined after a fire. Variables understudy in 10 GFRP bar-reinforced concrete beams included the exposure temperature (20, 400, and 600 °C), percentage of steel fiber in volume (0 and 1%), ratio of rebars (0.00314 and 0.00872), and CFRP sheet layers (0, 1, and 2), together with the presence or absence of the U-shaped anchorage. After conducting the four-point quasi-static bending experiment on the non-heated and heated beams, several parameters including the ductility, cracking pattern, and failure mode of the beams, together with their load–deflection diagrams, were assessed. The results showed that the flexural strengthening using CFRP sheets improved the flexural capacity of the specimens and this performance improvement became more notable with an increase in the exposure temperature. In the end, the sectional analysis method was utilized to propose an analytical model capable of estimating the load–deflection response of beams strengthened with CFRP sheets; this model properly estimated the test results.