Flexural strength of low-strength RC beams using CFRP composite

As mentioned above, this study investigates the effects of CFRP on the structural behavior of LSC. Thus, several trial mixes were conducted to cast 17 MPa concrete. Then, 16 RC beams with dimensions of 2,200 mm × 200 mm × 150 mm were constructed with 17 MPa concrete. 3 m³ of concrete was batched to the laboratory via a mixer truck. The properties of concrete are listed in Table 1. The RC beams were designed to fail in a flexural manner, using a design based on the ACI-318-19 standard, and the predicted ultimate shear and flexural capacity loads were 147 and 46.9 kN, respectively. In this case, when the RC beam is subjected to a load gradually, the RC beam would fail in flexural, as the flexural capacity of the section is lower than the shear capacity. The section was reinforced with 2Ø12 mm bars at the bottom and 2Ø10 mm bars as longitudinal reinforcement. Shear reinforcement bars were Ø8 mm @ 150 mm c/c. Concrete cover was maintained at 25 mm along the entire beam, as presented in Figure 1.

Figure 1

RC beam detailing.

In this research, two types of CFRP were used: unidirectional CFRP fabric and CFRP laminate. Both types were tested according to ASTM D3039M [23]. Testing coupons went through several stages, including cutting the CFRP matrix into strips. The fabric CFRP coupons were fabricated by a wet lay-up application using Sikadur-330 epoxy adhesive. Steel plates with (50 × 50 × 3) mm dimensions were fabricated to form the required grips for tensile testing of CFRP coupons. The grips were bonded to each coupon on both sides. Moreover, to get precise results, two strain gauges were attached to each coupon (CFRP laminate and CFRP fabric) to evaluate strain and Poisson’s ratio while testing. A total of 12 coupons were fabricated for each of the CFRP fabric and CFRP laminate coupons. The coupons were 250 mm in length and 50 mm in width, with a clear span of 150 mm between the grips. Testing was conducted at a load rate of 2 mm/min, following the guidelines of ASTM D3039M [23]. The CFRP curing process was carried out for 7 days at 26°C in the laboratory environment, as recommended by the Sika manufacturer. Figure 2 illustrates a schematic view of a CFRP coupon testing. Furthermore, the material properties for the carbon fiber (single fiber) used in this research were provided by the manufacturer (Sika) for both types of CFRP fabric and CFRP laminate (Table 2). These results were compared to the experimental findings. Although the fabricated coupons are matrixed, in contrast to the single fiber provided by the manufacturer.

Figure 2

CFRP coupon testing: (a) universal machine test; (b) coupon under testing; (c) laminate CFRP coupons failure; and (d) fabric CFRP coupons failure.

Two beams served as control specimens (BF-L), only one representative sample was presented in this work. Seven RC beams were strengthened in flexure using CFRP composite (Figure 3). The first application was adding a layer of CFRP laminate with a 100 mm width at the bottom of the RC beam (BF-L-LB). The second scheme was adding a two-layer CFRP sheet with 100 mm in width placed at the bottom of the RC beam (BF-L-SB-2). The third scheme was a layer of CFRP laminate with a 100 mm width placed at the bottom of the RC beam, and provided a U-shaped CFRP sheet at both ends with a 100 mm width to increase the bonding between the CFRP composite and concrete surface (BF-L-LB-UE). The fourth scheme was adding a layer of CFRP laminate with 100 mm in width placed at the bottom of the RC beam and providing a U-shaped CFRP sheet at both ends with 500 mm in width to prevent debonding at the ends and investigate the performance of the thickness of U anchorage (BF-L-LB-UE5). The fifth scheme was adding a layer of CFRP sheet with 100 mm in width at the bottom of the RC beam and providing a U-shaped CFRP sheet at both ends with 100 mm in width to prevent debonding at the ends (BF-L-SB-UE). The sixth scheme was adding two layers of CFRP sheet with 100 mm width at the bottom of the RC beam and providing a U-shaped CFRP sheet at both ends with 100 mm in width to prevent debonding at ends (BF-L-SB-UE2). The seventh scheme was adding a layer of CFRP laminate with 100 mm in width at the bottom of the RC beam and another layer at the top face between the two applied loads, and providing a U-shaped CFRP sheet at both ends with 100 mm in width (BF-L-LBT-UE). Strengthening schemes' objectives are defined in Table 3.

Figure 3

Flexural strengthening program.

The selection of CFRP widths and anchorage lengths followed established guidelines and prior experimental findings to ensure adequate load transfer and prevent premature debonding. Recommendations from ACI 440.2R-17 (ACI Committee 440, 2017) [24] and fib Bulletin No. 14 (fib, 2001) [25] were adopted for determining the effective bond length, beyond which additional bonded length provides negligible strength gain. Preliminary bond stress and strain transfer checks confirmed that the chosen CFRP widths adequately cover the tensile zone and that the anchorage lengths exceed the effective bond length estimated by these models. Previous studies (Grelle and Sneed [26]; Li et al. [27]; Anil and Belgin [28]) further supported the role of proper anchorage and U-wrap configurations in enhancing bond performance and delaying debonding.

All the tests were conducted at the College of Engineering lab, Duhok University. Tow-point test loading was performed to load the specimens up to failure. A flexural machine with 400 kN capacity was used. The RC beams were tested under the load control test method at a rate of 0.2 kN/s using a 400 kN flexural testing machine, in which the control RC beam took about 5 min from starting the loading up to failure. A series of 100 mm linear variable differential transformers was used to record the deflection at mid-span, under the loads, and at a distance d from the support. Moreover, strain gauges were used to measure strains at the tension zone at mid-span, the compression zone at mid-span, and at a distance d from the support. Digital image correlation (DIC) technique was also used using a Canon D90 camera to capture the distortion of the RC beam during loading. All RC specimens were painted with white paint on one side to capture the initiation of cracks conveniently while loading. Another side was painted with white and black dots for the DIC test procedure. Cracks were marked on the RC specimens with a pencil while loading, and cracking loads were recorded. A controlling computer with a data logger was used to collect all data from the bonded strain gauges, dial gauges, and load cell. DIC was also used to record the RC specimens while loading, and all recorded data were analyzed using GOM correlate software, and the results were then evaluated by comparing them with the experimental results and numerical models. Figure 4 illustrates the test setup, including the flexural machine, data logger, DIC camera, and tested sample.

Figure 4

Test set-up.

Test results for all the coupons are illustrated in Table 4. Figure 5 shows the linear elastic properties of the CFRP stress–strain curves acquired from the foil strain gauges. According to ASTM D3039/D3039M, the elastic modulus throughout the strain range of 0.001–0.003 was calculated using the CFRP stress-strain response. Numerous studies have discovered that there are differences in strength between the manufacturer's nominal qualities and the properties of materials that were tested as composite material (CFRP and epoxy) [29,30,31,32,33,34,35]. This is because evaluating a single fiber (based on the manufacturer's data) and testing a real-world tensile coupon are two different things. To prevent issues with stress concentrations at the grips and misalignment, as well as to allow for accurate strain readings, this testing must be performed on a composite CFRP and epoxy tensile specimen. Instead of using the thickness of the coupon, the maximum tensile stress and elastic modulus are based on the thickness of the fiber (i.e., epoxy plus fiber) [36].

Figure 5

CFRP mechanical properties.

Eight RC beams were tested under a flexural machine test, and the results have been listed and analyzed. The design of the samples ensured that flexural failure would occur before any shear failure. The flexural behavior of the RC beams is summarized in Table 5.

3.2.1

Load–deflection relationship

Eight RC beams were designed to be weak in flexural strength and were cast with LSCO (F1–F8). F1 served as a control sample. F2, F3, F4, F5, F6, F7, and F8 represent strengthened RC beams with different CFRP strengthening schemes. The load–deflection curves were recorded at mid-span with dial gauges as described earlier in the test set-up section. The load–deflection curves at mid-span are presented in Figure 6.

Figure 6

Load–deflection curves.

3.2.2

Load–strain relationship

The load–strain relationships for the steel reinforcement, concrete, and CFRP were recorded at mid-span, with strain gauges positioned along the CFRP strips. Figure 7 presents these relationships, showing that the steel strain increased progressively with the applied load until reaching the ultimate capacity. A comparable trend was observed for the CFRP, indicating that both materials effectively shared the flexural stresses during loading. This similarity in behavior confirms the efficiency of the strengthening system, as the CFRP contributed significantly to resisting tensile strains that would otherwise be concentrated in the steel reinforcement. Moreover, the smooth transfer of strain between the CFRP and steel suggests good bonding performance and adequate composite action, which is essential for achieving the desired flexural enhancement.

Figure 7

Strain–load relationship at mid-span.

3.2.3

Failure modes of RC beams

The failure modes of all RC beams critical in flexural are illustrated in Figure 8. The figure demonstrates the crack patterns and associated failure modes observed in the specimens. The figure highlights the main failure mechanisms, the paths and distribution of cracks, and the number of cracks developed under loading. This visual representation helps to better understand the structural response and the progression of damage leading to failure. Control RC beams critical in flexural F1 (BF-L) failed in typical flexural tension failure. Flexural failure happened in a ductile manner, as was supposed by the design. Sample F1 (BF-L) suffered from flexural-compression block failure. Flexural failure, in all RC beams critical in flexural, happened gradually as the flexural stresses were resisted by steel reinforcement, and this led to steel yielding, and ductile failure was observed. This failure mode occurs when the steel reinforcement reaches its yielding point, leading to excessive deflection and potentially compromising the beam's load-carrying capacity.

Figure 8

Crack pattern and associated modes of failure.

Flexural failure, in strengthened RC beams, failed due to CFRP debonding or cover separation, which agrees with the common failure mode in CFRP-strengthened RC beams described in detail in Section 3.3.2 [22]. The strengthened RC beams showed excellent performance under applied load in terms of escalating ultimate load and ductility (Table 5).

3.2.4

DIC for sample F1 (BF-L) and F2 (BF-L-LB)

DIC testing is used, as described earlier in Section 3.2.9, to measure deflection and strain at mid-span. Recorded data were analyzed using GOM Correlate software. Figure 9-a1 presents the first crack initiation when the load reached 11 kN in sample F1 (BF-L), while Figure 9-a2 illustrates crack widening at the ultimate load when the load reached 51 kN.

Figure 9

DIC frame illustrates crack initiating at different stages; (a) sample F1 (BF-L); and (b) sample F2 (BF-L-LB).

According to the data from DIC in Figure 9, F2 (BF-L-LB) sample first flexural crack was 21 kN compared to 11 kN in the F1 (BF-L) sample. This result is normal as the flexural capacity of the strengthened RC beam increased after CFRP application. This result clarifies the experimental results in Table 5, in which the first flexural crack was 22 kN in the F2 (BF-L-LB) sample and 9 kN in the F1 (BF-L) sample. The first crack in the experimental result was observed by eye, simultaneously on another side of the sample, using DIC, cracks were recorded; the results showed excellent agreement between the two results. Deflection at first crack was also compared between DIC and experimental results, in which in the sample F1 (BF-L), Δ _DIC was 1.1 mm while it was 0.7 mm in the experimental result, and in the sample F2 (BF-L-LB), Δ _DIC was 2 mm while it was 2 mm in the experimental result. This close agreement between the DIC records and experimental results strengthens the data obtained and makes it more realistic (Figure 10).

Figure 10

Comparison in ultimate deflection between experimental and DIC test for samples F1 (BF-L) and F2 (BF-L-LB).

3.2.6

Effects of CFRP application on moment and shear vs deflection

Strengthened RC beams that were critical in flexural and cast with LSC showed an increase in the ultimate moment and shear capacities after CFRP strengthening, in which the total increase in the ultimate moment and shear capacities increased by 40–120% depending on the specific scheme used. Moment and shear behavior were extremely affected by the scheme of the CFRP strengthening, as presented in Figure 11.

Figure 11

Increase in ultimate moment capacity according to different CFRP schemes.

Figure 12 presents a comparison of the moment and shear between samples F2 and F3. Results reveal that in flexural application, both the CFRP sheet and CFRP laminate got close upgrade value in total load capacity. However, CFRP laminate increases RC beam stiffness while CFRP sheets increase beam ductility.

Figure 12

Comparison between F2 (BF-L-LB) and F3 (BF-L-SB-2) in moment and shear vs deflection.

Adding a two-layer CFRP sheet at the bottom of the beam increased the ultimate moment and shear capacity. It also increased the stiffness of the strengthened beam, leading to a reduction in total deflection. Figure 13 presents a comparison between two different CFRP applications: the F6 sample, which features one CFRP layer at the soffit, and the F7 sample, which has two CFRP layers.

Figure 13

Comparison between F6 (BF-L-SB-UE) and F7 (BF-L-SB-UE2) in moment and shear vs deflection.

Adding a two-layer CFRP sheet at the bottom of the beam results in an increase in the ultimate moment and shear capacity. Additionally, it enhances the stiffness of the strengthened beam, resulting in a reduction in total deflection. Figure 13 presents a comparative analysis between two different CFRP applications: the F6 sample with one CFRP layer at the soffit and the F7 sample incorporating two CFRP layers.

3.2.7

Effects of CFRP anchorage on CFRP application

As mentioned in the literature, CFRP debonding and separation of concrete cover are the most common flexural failures when an RC beam is strengthened with CFRP composite. Thus, in this research, several types of anchorage were investigated to study the effects of anchorage on the load-carrying capacity of strengthened RC beams. Figure 14 presents a comparison between different types of anchorage, in which load-carrying capacity increased with the presence of CFRP laminate at the RC beam soffit without CFRP U anchorage by 44%, by 63% when anchored at both ends with a 100 mm CFRP U jacket, and by 119% when anchored at both ends with a 500 mm CFRP U jacket. In the case of strengthening with a two-layer of CFRP sheets without anchorage, the ultimate load capacity increased by 44% while it went to 53% when anchored at both ends using 100 mm wide CFRP U jackets. These findings are significant as they reveal the effects of adding an anchorage system to the flexural strengthening program using CFRP.

Figure 14

Increase in ultimate load capacity according to different CFRP schemes.

3.2.8

Effects of CFRP application on ductility of RC beams critical in flexural

The ductility index, according to the experimental results for all RC beams, is presented in Table 6. Ductility was found using the ductility index factor (μd) method and the area under the curve at ultimate load (P _u). The area under the curve was calculated using SketchAndCalc software.

Table 6

Beam symbol	Beam ID	P y (kN)	Δ y (mm)	P u (kN)	Δ u (mm)	μ ε u (steel-tension)	P u /Δ u	Ductility index Δ u /Δ y (μd)	Increase in μd %	Area under curve (kN mm)	Increase in area under curve %
BF-L	F1	48.4	6.7	51	16	2,364	3.2	2.39	—	138	—
BF-L-LB	F2	58.2	7	73.4	10.8	3,398	6.8	1.54	−36%	192	39%
BF-L-SB-2	F3	46	5.9	73.4	20.1	2,871	3.7	3.41	43%	413	199%
BF-L-LB-UE	F4	67.2	6.4	76.4	17.6	2,942	4.7	2.75	15%	411	198%
BF-L-LB-UE5	F5	104	7.2	111.8	18.6	3,580	6.0	2.58	8%	510	270%
BF-L-SB-UE	F6	60.8	11.1	71.6	30.2	2,900	2.4	2.72	14%	696	404%
BF-L-SB-UE2	F7	67	10.7	78.2	22.8	—	3.4	2.13	−11%	547	296%
BF-L-LBT-UE	F8	60.6	6.1	72.8	11.3	2,872	6.4	1.85	−23%	195	41%

Ductility can be measured by finding the area under the curve at ultimate load, as illustrated in Table 6. The ductility index reference is the area under the curve of the F1 (BF-L) sample. The ductility of RC beams with fiber addition increased by 291% compared to RC beams without fiber additions, which agreed with the study by Al-Hadithi et al. [37]. Moreover, RC beams strengthened with CFRP composite showed a significant increase in ductility, ranging from 39% in sample F2 to 404% in sample F6. Figure 15 illustrates the area under the curve for all RC beams critical in flexural.

Figure 15

Ductility index.

The observed increase in ductility, up to 400% compared with the control beam, has significant implications for practical structural performance. Such an improvement means that the strengthened beams can undergo substantially greater deformations before failure, indicating enhanced energy absorption and post-yield behavior. In real structures, this translates to improved warning before collapse, greater resilience under overload or seismic actions, and a shift from a brittle to a more ductile failure mode. From a design standpoint, this level of ductility improvement suggests that CFRP strengthening not only restores or increases flexural capacity but also enhances the deformation capacity and safety margin, allowing engineers to achieve more reliable and damage-tolerant structural systems.

Another ductility indication is the ductility index factor (μd). In order to find the index factor, the yielding of the steel was significant to record. Yielding of the steel was found based on the data from strain gauges bonded to the steel rebar (Table 6). Yield steel strain was estimated to be equal to (0.67ε _u = 0.23%). Samples F1 (BF-L) and F9 (BF-LP) behave as a ductile beam. All strengthened RC beams showed an increase in ductility index according to the index factor (μd) except F2, F7, and F8, in which ductility was reduced by 36 and 23%, respectively. The increasing range is between 8% in the F5 sample and 43% in the F3 sample. Figure 15 illustrates the index factor for all RC beams critical in shear. The results of the ductility index from the area under the curve and ductility factor showed an increase in ductility.

The failure moments (M _u), cracking moment (M _cr), and deflection (Δ) of two RC beams were calculated based on the ACI 318M-14 [38] and ACI 440.2R-17 [24]. The analyzed beams were F1 and F2). A bi-linear stress–strain curve was adopted for modeling steel and CFRP reinforcement. Stress and strain distributions were drawn, as in Figure 16. Whitney rectangular stress block was used to model the concrete compressive block. For accurate analysis, compression block coefficients (α ₁ and β ₁) were computed based on Collins and Mitchell [39] and Park and Paulay [40]. Compressive concrete cylinder strength (f _c′) and failure compressive concrete strains (ε _cu) were measured based on test results of concrete cylindrical samples.

• E _c is calculated according to ACI 318M-14 [38].

• Maximum compressive concrete strain ε _cu is computed from experimental test results.

• α ₁ and β ₁ were calculated based on equations (‎1) and (2).

• Based on the linear relationship, strains of compression steel, tension steel, and CFRP are given by (1) ε st = ε cu d − c c , {\varepsilon }_{{\rm{st}}}={\varepsilon }_{{\rm{cu}}}\left(\frac{d-c}{c}\right), (2) ε sc = ε cu d sc − c c , {\varepsilon }_{{\rm{sc}}}={\varepsilon }_{{\rm{cu}}}\left(\frac{{d}_{{\rm{sc}}}-c}{c}\right), (3) ε fe = ε cu d f − c c − ε bi ≤ ε fd . {\varepsilon }_{{\rm{fe}}}={\varepsilon }_{{\rm{cu}}}\left(\frac{{d}_{{\rm{f}}}-c}{c}\right)-{\varepsilon }_{{\rm{bi}}}\le {\varepsilon }_{{\rm{fd}}}.

• Determine FRP strain to prevent intermediate crack-induced debonding failure ACI 440.2R-17 [24]. (4) ε fd = 0.41 f c ′ n t f E f ≤ 0.9 ε fu . {\varepsilon }_{{\rm{fd}}}=0.41\sqrt{\frac{{f}_{{\rm{c}}}^{^{\prime} }}{n{t}_{{\rm{f}}}{E}_{{\rm{f}}}}}\le 0.9{\varepsilon }_{{\rm{fu}}}.

• Computing maximum steel and CFRP stresses that are equal to the maximum level of stress at the failure of section 440.2R-17 [24]. (5) f st = E st ε st ( ε st < ε y ) , f st = f y ( ε st ≥ ε y ) , {f}_{{st}}={E}_{{st}}{\varepsilon }_{{st}}({\varepsilon }_{{st}}\lt {\varepsilon }_{y}),{\rm{\ }}{f}_{{st}}={f}_{y}({\varepsilon }_{{st}}\ge {\varepsilon }_{y}), (6) f sc = E sc ε sc ( ε sc < ε y ) , f sc = f y ( ε sc ≥ ε y ) , {f}_{{sc}}\left={E}_{{sc}}{\varepsilon }_{{sc}}({\varepsilon }_{{sc}}\left\lt {\varepsilon }_{y}),{\rm{\ }}{f}_{{sc}}={f}_{y}({\varepsilon }_{{sc}}\ge {\varepsilon }_{y}), (7) f fe = E f ε fe ( ε fe < ε fu ) , f fe = f fu ( ε fe ≥ ε fu ) . {f}_{{fe}}\left={E}_{f}{\varepsilon }_{{fe}}\hspace{1em}({\varepsilon }_{{fe}}\left\lt {\varepsilon }_{{fu}}),{\rm{\ }}{f}_{{fe}}={f}_{{fu}}({\varepsilon }_{{fe}}\ge {\varepsilon }_{{fu}}).

• Neutral axis (c) is computed based on equilibrium using second-degree equations ACI 318M-14 [38] and 440.2R-17 [24]. (8) α 1 f c ′ β 1 bc + A sc f sc = A st f st + A f f fe . {\alpha }_{1}{f}_{c}^{^{\prime} }{\beta }_{1}{bc}+{A}_{{sc}}{f}_{{sc}}={A}_{{st}}{f}_{{st}}+{A}_{f}{f}_{{fe}}.

• Determine moment failure based on the following equation, where ψ _f is the additional reduction factor assigned by 440.2R-17 [24] equal to 0.85. (9) M n = A st f st d − β 1 c 2 + Ψ f A f f fe d f − β 1 c 2 − A sc f sc β 1 c 2 − d sc . {M}_{n}={A}_{{\rm{st}}}{f}_{{\rm{st}}}\left(d-\frac{{\beta }_{1}c}{2}\right)+{\Psi }_{f}{A}_{f}{f}_{{\rm{fe}}}\left({d}_{f}-\frac{{\beta }_{1}c}{2}\right)-{A}_{{\rm{sc}}}{f}_{{\rm{sc}}}\left(\frac{{\beta }_{1}c}{2}-{d}_{{\rm{sc}}}\right).

• Computing load failure based on the bending moment formula for a simply supported beam

(10) P u = 2 M u − W l 2 8 / a . {P}_{u}=2\left({M}_{u}-\frac{W{l}^{2}}{8}\right)/a.

Figure 16

Section force distribution without CFRP.

Numerical analysis was carried out using GiD and ATENA software. The main parameters obtained from numerical analysis were load vs deflection at mid-span, crack pattern, fracture strain, strains, and stresses in entities. Additionally, an analytical analysis was conducted, and load vs deflection curves were obtained. All materials were assigned in the software (Figure 17).

Figure 17

GiD 3D model.

Load versus deflection was obtained from ATENA software and analytical analysis (Figures 18–20). The maximum applied load was well-matched curve obtained by experimental results. The variation was less than 5% with exceptional precision. The initial slope showed that the model had the same stiffness behavior as the experimental sample stiffness. However, the total displacement in the finite element (FE) model was about 20% less compared with the experimental sample. This result agrees with previous studies [1,41], which claim FE models show about 5–10% more stiffness and 5–20% less total deflection. The deflection at maximum load was predicted. The FE load–deflection and load–strain curves and the experimental findings matched rather well, as did the initial slope of the rising section of the curves. An analytical analysis was also conducted, and the results showed excellent agreement between both experimental and GiD results; the experimental strain–load curve beyond 22.4 kN went vertical due to strain gauge rupture.

Figure 18

Load–deflection comparison between experimental, analytical, and GiD results for sample F1 (BF-L).

Figure 19

Load–deflection comparison between experimental, analytical, and GiD results for sample F2 (BF-L-LB).

Figure 20

Load–deflection comparison between experimental, analytical, and GiD results for sample F5 (BF-L-LB-UE5).

GiD and ATENA software were used to capture and obtain crack patterns. A comparison of the crack pattern between the experimental and nonlinear finite element software results is shown in Figure 21. It is evident that the finite element model and the one from the lab result accord rather well. All modeled samples indicated flexural cracks due to high flexural stresses near mid-span. In sample F1 (BF-L), the model showed compression cracks at mid-span, which validated the results because the control sample, in the experimental study, suffered from compression failure after bending cracks.

Figure 21

Crack pattern comparison between experimental and GiD.