Effect of bond enhancement using carbon nanotubes on flexural behavior of RC beams strengthened with externally bonded CFRP sheets

Abstract

This paper studied the effect of incorporation of carbon nanotubes (CNTs) in carbon fiber reinforced polymer (CFRP) on strengthening of reinforced concrete (RC) beams. The RC beams were prepared, strengthened in flexure by externally bonded CFRP or CNTs-modified CFRP sheets, and tested under four-point loading. The experimental results showed the ability of the CNTs to delay the initiation of the cracks and to enhance the flexural capacity of the beams strengthened with CFRP. A nonlinear finite element (FE) model was built, validated, and used to study the effect of various parameters on the strengthening efficiency of CNTs-modified CFRP. The studied parameters included concrete strength, flexural reinforcement ratio, and CFRP sheet configuration. The numerical results showed that utilization of CNTs in CFRP production improved the flexural capacity of the strengthened beams for U-shape and underside-strip configurations. The enhancement was more pronounced in the case of U-shape than in the case of use of sheet strip covers on the underside of the beam. In case of using underside-strip, the longer or the wider the sheet, the higher was the flexural capacity of the beams. The flexural enhancement of RC beams by strengthening with CNTs-modified CFRP decreased with increasing the rebar diameter and was not affected by concrete strength.

Graphical abstract

Keywords

RC beams / flexural / strengthening / CFRP / CNTs / finite element

1 Introduction

One of the most widely used methods in rehabilitation and strengthening of reinforced concrete (RC) members is the use of externally bonded (EB) fiber reinforced polymer (FRP) sheets [1–5]. FRP composites with their high strength to weight ratio and high corrosion resistance are usually attached to the bottom soffit of the RC beams to enhance their flexural capacity [3,6–8]. The EB technique usually relies on the adhesive layer to attach the FRP sheets to concrete surfaces thus to transfer load from the concrete substrate to the sheets. Most of the literatures has reported that debonding failure was the most common failure mode in this kind of applications [9–12], preventing full utilization of the FRP capacity [9–12]. A lot of research has been conducted to investigate the possibility of delaying or preventing the premature debonding failure. Most of the researchers have recommended using various types of anchors such as U-shaped FRP sheet strips in the transverse direction [13], mechanically fastened anchors [8,14,15], spiked fanning anchors [16], wave-shaped anchors [17], or self-locking anchors [9]. However, some problems are related to the use of anchorage system such as time-consuming onsite construction, and undue damage to the original member. Therefore, it is desirable to further investigate or try new techniques. An alternative way to delay the debonding failure is to enhance the properties of the adhesive materials, which is, in most cases, epoxy resin.

Carbon nanotubes (CNTs) with their excellent mechanical properties have been efficiently used to improve many properties of the epoxy resin such as stiffness, tensile strength, and fracture toughness [18,19]. The CNTs-modified epoxy has been used to produce FRP composites with better mechanical properties than conventional FRP. It has been reported that CNTs could enhance the interfacial shear strength and adhesion between the epoxy and the fibers thus improve the behavior of the composites [20,21]. The researchers tried to take advantage of the enhanced properties of the FRP composites made of CNTs-modified epoxy and use them with concrete. Rousakis et al. [22] showed an enhancement of the load capacity of confined concrete columns in the case of using CNTs-modified FRP compared to conventional FRP. Soliman et al. [23] showed that CNTs reduced the shear creep of the adhesive layer between FRP and concrete. The above-mentioned results encouraged the authors’ research group to explore the feasibility of using CNTs-modified FRP composites in strengthening applications of concrete structures. Irshidat et al. [11,12,25], Chen et al. [27], and Hawileh et al. [28] carried out comprehensive experimental work to explore the efficiency of CNTs in enhancing the repair and strengthening capability of the externally bonded CFRP sheets. Their results showed the ability of the CNTs to enhance the bond strength between CFRP sheets and concrete substrate [26] thus enhancing the flexural behavior [12,24] and the axial load carrying capacity [24,25] of strengthened and heat-damaged repaired beams and columns, respectively. However, experimental studies on using CNTs in strengthening application of RC structures are challenging due to the high cost of CNTs, especially when used in large quantity, and the introduction of CNTs into epoxy resin through appropriate sonication process. Finite element (FE) modelling represents a good alternative solution to overcome the above-mentioned challenges.

FE modelling showed the ability to predict the flexural behavior of RC beams strengthened or repaired with FRP sheets [27–29]. Hawileh et al. [28] conducted FE simulations to study the behavior of RC beams strengthened with EB CFRP plates. Their FE model could predict the experimental failure modes and load-deflection curves. Zhang and Teng [29] used FE modelling to predict the end cover separation of flexural strengthened RC beams with FRP. Chen et al. [27] successfully examined the feasibility of using a dynamic approach to predict debonding failure in RC beams externally strengthened with FRP.

The capability of FE modeling to predict the flexural behavior of RC beams strengthened with EBFRP sheets, and the above-mentioned challenges of using CNTs in large-scale strengthening application, encouraged the authors to use nonlinear FE analysis to study the effect of bond enhancement using CNTs on the flexural capacity of the strengthened RC beams. This paper reports on experimental work that was performed by testing six RC beams strengthened in flexure with either conventional or CNTs-modified CFRP sheets. The primary purpose of the experimental work was to validate the FE results. After that, 3D nonlinear FE models were developed using ANSYS software and used to conduct comprehensive parametric study to investigate the effect of various parameters on the flexural behavior of the strengthened beams. The parameters included concrete strength, flexural reinforcement ratio, CNTs-modified CFRP sheet length, width, and configuration.

2 Experimental work

2.1 Test specimens

Six simply supported RC beams were cast with concrete of 40 MPa compressive strength. The beams had rectangular cross section with dimensions and reinforcements presented in Fig. 1. Four beams were strengthened with one layer of either CFRP sheet or CNTs-modified CFRP sheet attached to the bottom soffit of the beams as shown in Fig. 1. The other two beams were left without strengthening as control beams.

2.2 Materials properties

All beams were cast with the same batch of concrete. The 28 d compressive strength of the concrete was 40 MPa. The longitudinal steel reinforcing bars had 418 MPa yield stress and diameters of 10 and 12 mm. The shear rectangular stirrups were made of steel with 290 MPa yield stress and 6 mm diameter. Unidirectional CFRP sheets (MBrace CF 230/4900) and (MBrace Saturant) epoxy resin were used for strengthening. The CF sheet had 0.34 mm thickness, 4900 MPa tensile strength, 28 GPa tensile elastic modulus, and 2.1% strain at break. A master-batch (MB) of epoxy with CNTs (EpoCyl™ NC R128-02) was used as a source of CNTs. This MB contained Bisphenol-A epoxy resin reinforced with NC7000 multi-walled CNTs. According to the manufacturer (Nanocyl, Belgium), the CNTs had 9.5 nm diameter and were 1.5 μm in length. The MB was diluted with the epoxy resin according to the manufacturer recommendations to get epoxy with 3.4 wt.% of CNTs. To ensure of good dispersion of the CNTs within the epoxy, a sonication process was carried out on the mixture for 30 min using Qsonica Q700 sonicator.

2.3 Strengthening process

The RC beams were strengthened with one layer of either conventional or CNTs-modified CFRP composites. At the beginning, one layer of epoxy or CNTs-modified epoxy was applied to the bottom soffit of the beams. Then, the CF sheet was attached to the epoxy and pushed until it was saturated with the epoxy. A second layer of the epoxy was applied. The beams were left at room temperature for 7 d to be cured.

2.4 Test procedure

The control and strengthened beams were tested under four-point flexural loading with displacement control using a universal testing machine. To avoid stress concentration under the load, the boundary conditions and the load were applied through steel plates as shown in Fig. 1. A linear variable displacement transducer (LVDT) was used to monitor the vertical deflection at the midspan of the beams. Figure 1 shows the test setup and loading configuration.

3 Numerical simulations

3.1 FE model

Three-dimensional FE models were generated using commercially available software ANSYS. Similar geometry, support conditions, and loading to that used in the experimental work were applied to the beam FE model, as shown in Fig. 2. Due to the symmetry and in order to save computational time, a quarter model of the tested beams was modeled and simulated. Mesh sensitivity and convergence analyses were performed by testing different FE models with various meshes. Typical FE model configurations including the FE mesh, boundary conditions, and the applied load are shown in Fig. 2.

3.2 Elements selection

The elements were carefully selected from the ANSYS library to simulate the advanced nonlinear behavior of the strengthened beams such as concrete cracking and crushing, steel rebars yielding, elastic behavior of CFRP, and the interfacial bond between FRP composites and concrete. The SOLID65 3D brick element was used to model the concrete. The SOLID65 element was defined using eight nodes located at its edges having three degrees of freedom (DOF) at each node, with capability of plastic deformation and creep. This element had the capability to predict concrete cracking in tension as well as concrete crushing in compression in the three orthogonal directions. Steel rebars were modeled using LINK180. This element was a three-dimensional spar with uniaxial tension and compression properties. LINK180 was defined using two nodes located at its edges having three DOFs at each node, with capability of plasticity, rotation, creep, deflection, and large strain. CFRP and CNTs-modified CFRP composites were modeled using the SOLID185 element. Similar to the SOLID65 element, SOLID185 has 8 nodes with 3 DOF for each node. This element has the capability to model materials with orthotropic properties, which make it suitable for FRP composites.

3.3 Constitutive relations

3.3.1 Concrete

Concrete with 40 MPa compressive strength, 0.2 Poisson’s ratio, and 29.7 GPa modulus of elasticity were used for this model. The nonlinear compressive behavior of concrete was modeled by employed the strain-stress equation proposed by Hognestad et al. [30] as given in Eqs. (1) and (2), and shown in Fig. 3(a).

(1)f_{\text{c}} ={f_{\text{c}}}^{\mathrm{\prime }}\left(2\left(\frac{{\epsilon }_{\text{c}}}{{\epsilon }_{\text{co}}}\right)-{\left(\frac{{\epsilon }_{\text{c}}}{{\epsilon }_{\text{co}}}\right)}^2\right), {\epsilon }_{\text{c}}⩽{\epsilon }_{\text{co}},

(2)f_{\text{c}} ={f_{\text{c}}}^{\mathrm{\prime }}\left(1-\frac{0.15}{{\epsilon }_{\text{c}}-{\epsilon }_{\text{co}}}\left({\epsilon }_{\text{c}}-{\epsilon }_{\text{co}}\right)\right),{\epsilon }_{\text{c}} >{\epsilon }_{\text{co}},

where f_{\text{c}} and {\epsilon }_{\text{c}} are the concrete stress and corresponding strain, {f_{\text{c}}}^{\mathrm{\prime }} and {\epsilon }_{\text{co}} are the concrete strength and corresponding strain. The nonlinear tensile behavior of concrete was defined based on the William and Warnke model [31]. The tensile strength of concrete ( f_{\text{t}}) was calculated using Eq. (3) as per the ACI318-14 design guidelines to be 3.92 MPa.

(3)f_{\text{t}} =0.62\sqrt{f_{\text{c}}^{\mathrm{\prime }}} .

The condition of the crack surface was defined through the shear transfer coefficient (β_t) with a value of 0.3.

3.3.2 Steel reinforcement

The steel rebars were modeled as elastic-perfectly plastic in both tension and compression as shown in Fig. 3(b). The Young’s modulus, yield stress, and Poisson’s ratio of 200 GPa, 418 MPa, and 0.3 were considered as reported in the experimental work.

3.3.3 CFRP composites

The CFRP composites were modeled as linear elastic orthotropic materials. The orthotropic mechanical properties of the CFRP and CNTs-modified CFRP composites are listed in Table 1.

3.3.4 Bond between steel rebars and concrete

The COMB39 element was used to define the bond between steel rebars and concrete. This element is a unidirectional spring element with nonlinear generalized force-deflection capability. COMB39 is defined at any node with up to three DOFs at each node, with capability of large displacement.

3.4 CFRP/ concrete interface models

The INTER205 cohesive element was used to model the bond behavior between concrete and CFRP composites in order to capture the debonding failure that was observed in the experimental work. The INTER205 is a 3D linear interface element defined by eight nodes. This element simulates the interface between two surfaces. It has the ability to simulate the delamination process. A cohesive zone (CZM) model is required to define the debonding process by the INTER205 element. In this study, the implemented CZM started with an increasing segment up to certain value of the shear stress ( {\tau }_{\text{o}}) and the corresponding slip value ( s_{\text{o}}) as shown in Fig. 3(c). Then, a second increasing segment started with much lower slope up to the maximum shear stress ( {\tau }_{\text{max}}) and the corresponding maximum slip ( s_{max}). The first part of the bond-slip curve was modeled using the model developed by Lu et al. [32] and described in Eq. (4). The second part of the model was formulated as shown in Eq. (5).

(4)\tau ={\tau }_{\text{o}}\sqrt{\frac{s}{s_{\text{o}}}},

(5)\tau ={\tau }_{\text{o}}+\frac{\left({\tau }_{\text{max}}-{\tau }_{\text{o}}\right)}{\left(s_{max}-s_{\text{o}}\right)}s.

The values of ( {\tau }_{\text{o}}, {\tau }_{\text{max}}, s_{\text{o}}, and s_{max}) were extracted from experimental work conducted by the authors [26] and listed in Fig. 3(c) for convenience. The values of ( {\tau }_{\text{o}}, {\tau }_{\text{max}}, s_{\text{o}}, and s_{max}) for neat CFRP and CNTs-modified CFRP were equal to (1.885, 2.226, 0.044, and 0.4497) and (2.501, 3.014, 0.0183, and 0.6837), respectively.

4 Experimental results and model validation

4.1 Cracks pattern and failure mode

For unstrengthened beams, the first crack appeared at a load value of 5.85 kN at the midspan of the beam. More cracks were initiated at the high moment zone with increasing load. These cracks propagated toward the compression zone of the beam. With applying further load, concrete crushing was observed and the beam failed at a load of 44.5 kN. The FE model was able to predict the first crack initiation, cracks distribution, and failure mode as illustrated in Fig. 4. In the FE simulation, the first crack appeared at 5.89 kN whereas the failure happened at 45.5 kN with uncertainty of 1% and 2%, respectively.

On the other hand, the same crack pattern and failure mode were experimentally observed for beams strengthened with either CFRP or CNTs-modified CFRP sheets. The first crack appeared at a load of 11.5 and 12.5 kN, respectively. With further applied load, more cracks were initiated at the high moment zone and extended toward the compression zone of the beams. The cracks started widening, leading to concrete crushing and delamination of the sheets as depicted in Fig. 5. The FE model showed good efficacy in predicting crack initiation, crack pattern, and failure mode of the strengthened beams as shown in Fig. 5. The model predicted the initiation of the cracks at the exact location and with percentage difference of 4% and 3% for beams strengthened with CFRP and CNTs-modified CFRP, respectively. In addition, the FE-predicted crack pattern followed the experimental one, where heavy flexural cracks developed at the midspan of the beams combined with shear cracks at both ends as exhibited in Fig. 5. Finally, the FE-predicted failure mode was very close to the experimentally captured one. Concrete spalling combined with FRP sheet delamination were predicted using the FE model for beams strengthened with either CFRP or CNTs-modified CFRP as shown in Fig. 5.

4.2 Load-deflection relationship

The experimental load versus midspan deflection curves for all tested beams are plotted in Fig. 6. The unstrengthened beams showed typical bilinear response. The beams strengthened with either CFRP or CNTs-modified CFRP sheets exhibited behavior that was almost the same. The characteristics of the load-deflection curves are summarized in Table 2. It is clear that strengthening the beams with CFRP enhanced their ultimate load by almost 49% but reduced their toughness by 42%. The improvement in beams’ flexural capacity could be attributed to the role of the CFRP in enhancing their tensile strength at their tension zones [6,10]. The reduction in the beams’ toughness could be ascribed to the low ductility of the CFRP sheets attached to the bottom soffit of the beams [11,33]. Modifying the CFRP sheets by CNTs improved the beams’ toughness and ultimate load by 28% and 6%. The above-mentioned enhancements could be attributed to the ability of the CNTs to: (1) enhancement of the adhesion between the carbon fiber and epoxy resin [34,35] and the adhesion between epoxy resin and concrete substrate [26] thus improving the load transfer process between the composite sheets and the strengthened beams; (2) mitigation of the micro cracks within the matrix thus enhancing energy absorption by the system before failure [11].

The FE model of the control beam was able to predict its bilinear response as shown in Fig. 6. The model was also able to accurately predict the values of the first crack load, ultimate load, and toughness of the beams with 2% variation as presented in Table 2. Good agreement was also noticed between the FE and experimental results for beams strengthened by either CFRP or CNTs-modified CFRP. The predicted load-deflection curves followed the experimental ones at all stages of loading as illustrated in Fig. 6. The developed model had the ability to predict the first crack load, ultimate load, and toughness of CFRP and CNTs-modified CFRP strengthened beams with difference percentages of (2.2% and 4%) and (3.2% and 4%), respectively.

The above-mentioned results reflected the efficacy of the CNTs in enhancing the strengthening process of RC beams using CFRP composites. The results also reflected the ability of the FE models to predict with reasonable accuracy the flexural behavior of the strengthened RC beams, and to capture their fracture behavior. Based on that, comprehensive parametric study was conducted herein using FE simulations to explore the effect of various parameters on the flexural capacity of RC beams strengthened with CNTs-modified CFRP. The studied parameters included the length of the CFRP sheet, the width of the CFRP sheet, the CFRP sheet configuration, the concrete strength, and the flexural steel reinforcement.

5 Parametric study

5.1 Effect of CNTs-modified CFRP sheet length

Three different sheet-length-values were considered in this study: 50 cm to cover the high-moment zone (CNT-L50), 100 cm to cover two third of the beam span (CNT-L100), and 150 cm to cover the full length of the beam span (CNT-L150). The layout and the FE models of the strengthened beams are presented in Fig. 7. The load-deflection curves, cracks patterns, and failure modes for CNT-L50, CNT-L100, and CNT-L150 specimens are shown in Fig. 8. It is clear that the length of the CNTs-modified CFRP sheet highly influenced the flexural behavior of the strengthened beams. Figure 8(a) reflects that the longer the sheet, the higher is the flexural capacity of the beams. Strengthening RC beam with CNTs-modified CFRP sheet covering only the high-moment zone did not enhance its ultimate load. Extending the length of the sheet to cover two-third of the beams’ span increased the ultimate load by 14% compared to the control beam. Further enhancement in the ultimate load by 56% compared to the control beam was noticed when the span length was fully covered by the sheet. A similar trend has previously been experimentally discovered and reported in [11,36]. In addition, the toughness of the strengthened beams increased with the length of the sheet. Beam CNT-L50 had toughness of 781 N∙m. This value was increased by 26% and 89% when the length of the sheet was extended to cover two-third and full length of the beams’ span, respectively. However, all strengthened beams had less toughness than the control beam. The reduction in the toughness is attributed to the huge reduction in the maximum deflection of the beams when strengthened by the CNTs-modified CFRP sheets.

On the other hand, the length of the CNTs-modified CFRP sheet clearly affected the crack pattern and the failure mode of the strengthened beams. The first crack was initiated at load of 7.2, 9.7, and 12.9 kN for beams strengthened with 50, 100 and 150 cm sheet, respectively, as shown in Fig. 8(b). With load increase, more cracks appeared and extended toward the compression zone as shown in Fig. 8(c). Then, flexural cracks started widening leading to cover separation in beams CNT-L50 and CNT-L100. For beam CNT-L150, concrete crushing near the sheet led to its delamination.

5.2 Effect of CNTs-modified CFRP sheet width

Three different sheet strips with varied width were considered: 2 (CNT-W2), 6 (CNT-W6), and 10 cm to cover the full width of the beam (CNT-W10). All sheets had same length of 150 cm (full span length of the beam). The FE models of the strengthened beams are shown in Fig. 9. It is clear in Fig. 10(a) and Table 3 that the ultimate load of the strengthened beams increased with increasing width of the sheet. The control beam had an ultimate load of 45.5 kN. Strengthening the beam with 2 cm sheet strip enhanced its ultimate load by almost 11%. Using wider strips increased the ultimate load of the beams by 27% and 55% for specimens CNT-W6 and CNT-W10, respectively. In addition, the toughness of the strengthened beams enhanced by increasing width of the strips. CNT-W2 beam had a toughness of 950 N·m. Using 6 and 10 cm strips enhanced the toughness of the beam by 21% and 55%, respectively. However, all strengthened beams had less toughness than the control beam.

In addition, the width of the CNTs-modified CFRP sheet strip affected the crack pattern of the strengthened beams. Intensive cracks were developed near the end of the CFRP strips which led to concrete spalling for beams CNT-W2 and CNT-W6 as shown in Fig. 10(b). When the strip covered the entire width of the beam (CNT-W10), less concrete spalling was noticed.

5.3 Effect of CNTs-modified CFRP sheet configuration

U-shape CNTs-modified CFRP sheet covered the bottom soffit and the two sides of the beam were considered herein. Three different lengths of the U-shape composites were studied: 50 (CNT-U50), 100 (CNT-U100), and 150 cm (CNT-U150) as shown in Fig. 11. Figure 12(a) shows that using U-shape CNTs-modified CFRP composite extended in the high moment zone of the beam and enhanced its ultimate load by 25% compared to the control beam. Increasing the length of the U-shape composite to cover two-third and entire length of the beam span improved its ultimate load by 62% and 106%, respectively as shown in Table 3. These results are consistent with other results reported in the literature for conventional CFRP composites [37,38]. In addition, increasing the length of the U-shape composites delayed the initiation of the first crack. The first crack was initiated at 7.7, 10.9, and 14.5 kN for beams CNT-U50, CNT-U100, and CNT-U150, respectively. The cracks pattern and failure mode of the beams are illustrated in Fig. 12(b). It is clear that due to stress concentration, intensive cracks were developed at the ends of the composites, which led to concrete spalling at those locations.

To highlight the superiority of using U-shape instead of sheet strip covering the bottom side of the beam, the results of specimens CNT-U50, CNT-U100, and CNT-U150 summarized in Table 3 were compared with the results of specimen CNT-L50, CNT-L100, and CNT-L150. It is clear that using U-shape CNTs-modified composites is much more efficient in enhancing the flexural capacity of the strengthened beams regardless of the length of the composites. This finding could be attributed to the confinement effect of the U-shape compared to the underside strip [39,40].

To highlight the effect of CNTs on the strengthening efficiency of CFRP composites, the FE results of beams strengthened with either U-shape or underside strip made of conventional CFRP (NE-U150 or NE-L150) and CNTs-modified CFRP (CNT-U150 or CNT-L150) composites listed in Table 3 are compared. The results show that utilization of CNTs in the CFRP production improved the flexural capacity of the strengthened beams for both configurations (U-shape and underside strip). The enhancement was more pronounced in the case of U-shape where the enhancement due to CNTs incorporation reached 34% compare to only 9% in the case of underside sheet strip.

5.4 Effect of concrete strength

Four beams made of different concrete grades (25 (CNT-C25), 30 (CNT-C30), 40 (CNT-40), and 50 MPa (CNT-C50)) and strengthened with similar CNTs-modified CFRP composites (10 cm sheet strip attached to the bottom side) were modeled. The load-deflection curves for these beams are plotted in Fig. 13(a). It is clear that the flexural capacity of the beams increased with concrete compressive strength. A similar trend was reported in [41] for beams strengthened with conventional CFRP. The ultimate load of beams CNT-C25, CNT-C30, CNT-C40, and CNT-C50 were equal to 50.5, 60.6, 69.9, and 77.5 MPa, respectively. In addition, increasing concrete strength delayed the first crack initiation and reduced the number of the developed cracks especially at the ends of the beams, thus reduced the possibility of concrete crushing and composites delamination, as shown in Fig. 14.

Four more control (unstrengthened) beams made of different concrete grades (25 (Control-C25), 30 (Control-C30), 40 (Control-40), and 50 MPa (Control-C50)) were modeled. The FE results of these beams are summarized in Table 3. In order to focus on the effect of concrete strength on strengthening efficiency of CNTs-modified CFRP, the ultimate load of strengthened beams was divided by the ultimate load of the corresponding control beams. The normalized values are plotted in Fig. 13(b). It is clear that concrete strength has negligible effect on the strengthening efficiency. Similar conclusion was drawn by Ref. [39] for beams strengthened with conventional CFRP composites.

5.5 Effect of flexural reinforcement ratio

Three FE models were generated to study the effect of steel rebar diameters on the flexural capacity of RC beams strengthened with CNTs-modified CFRP. The bar diameters for the additional models were 10 (CNT-D10), 12 (CNT-D12), and 14 mm (CNT-D14). The load-deflection curves for all models are plotted in Fig. 15(a). It is clear that, increasing steel bar diameter led to increase of the flexural capacity of the strengthened beam and delay of the first crack initiation. The ultimate loads of beams (CNT-D10), (CNT-D12), and (CNT-D14) were equal to 59.8, 69.9, and 76.5 kN, respectively. A similar trend for beams strengthened with conventional CFRP was reported in Ref. [28]. Three additional models were developed for control-unstrengthened beams to investigate the effect of steel diameter on strengthening efficiency. The results of the FE analysis of these models are summarized in Table 3. The ultimate load of the strengthened beams was divided by the ultimate load of the corresponding control beam. The normalized values are plotted in Fig. 15(b). It is clear that the enhancement in flexural capacity by strengthening the beams with CNTs-modified CFRP was decreased by increasing the bar diameter. Finally, the steel bar diameter slightly affected the crack pattern of the strengthened beams. Increasing the bar diameter reduced the shear crack development near the ends of the beams as shown in Fig. 16, and delayed the delamination of the sheets.

6 Conclusions

The effect of CNTs on flexural behavior of RC beams strengthened with externally bonded CFRP sheets was examined experimentally and numerically. A nonlinear FE model was built, validated, and then used to run parametric study to investigate the effect of various parameters on the strengthening efficiency of the CNTs-modified CFRP composites. The parameters included concrete strength, flexural reinforcement ratio, the length, width, and configuration of the CFRP sheet. The following conclusions could be drawn.

1) Using CNTs improved the strengthening of RC beams with externally bonded CFRP composites. CNTs incorporation delayed the initiation of the cracks, and enhanced the flexural capacity and toughness of the strengthened beams.

2) The nonlinear FE model predicted with reasonable accuracy the flexural behavior of the strengthened RC beams, and captured their fracture behavior.

3) The length and the width of the CNTs-modified CFRP sheet highly influenced the flexural behavior of the strengthened beams. The longer or the wider the sheet, the higher was the flexural capacity of the beams. In the case of using sheets with smaller dimensions than the beam soffit, stress concentration was noticed near the ends of the sheets, and led to sheet delamination.

4) Utilization of CNTs in the CFRP production improved the flexural capacity of the strengthened beams for both configurations (U-shape and strip). The enhancement was more pronounced in the case of U-shape than underside strip.

5) The enhancement in flexural capacity of RC beams by strengthening with CNTs-modified CFRP decreased with increasing the steel rebar diameter and did not affect concrete strength.

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