# Debonding Failure Analysis of Reinforced Concrete Beams Strengthened with CFRP Plates

^{*}

## Abstract

**:**

## 1. Introduction

_{f}

^{0.41}) when the attachment length of the plate was less than the effective attachment length, and tf to the power of 0.32 (t

_{f}

^{0.32}) when the attachment length was more significant than the effective attachment length.

## 2. Experimental Study

^{®}UC Composite Laminate Strip laminated by FYFE Co. LLC, USA. The CFRP plates were 1.9 mm thick and 50 mm wide. CFRP plates were glued to the tension face of the strengthened beams with epoxy adhesive by FYFE Co. LLC, as shown in Figure 1c and Figure 2. Tyfo

^{®}S Epoxy was applied as the main layer on the prepared concrete substrate and Tyfo

^{®}TC Epoxy was applied to a thickness of 2 mm on the substrate before applying the CFRP plate. Installation of CFRP plates on beams was carried out by certified applicators, as shown in Figure 2. The mechanical properties of the CFRP plate used were supplied by the manufacturer. The ultimate tensile strength in primary fiber direction and tensile modulus of the CFRP plates used were 2.51 GPa and 139 GPa, respectively.

## 3. Fiber Element Method

_{i}, in the concrete and reinforcement elements for an assumed value of curvature, φ, and the lever arm of each element, y

_{i}, can be calculated as:

_{i}, acting on each reinforcement layer, concrete element and the steel plate can be determined as:

_{i}, for each of the concrete elements and reinforcement layers with an area, A

_{i}, using:

_{o}, which fulfills the equilibrium condition of the internal forces.

## 4. Finite Element Method

## 5. Results and Discussion

#### 5.1. Experimental Results

#### 5.2. Parametric Study

#### 5.3. Debonding Failure Analysis

_{cr}) in a square cross-section of concrete, as shown in Equation (8), was used.

_{t}is the tensile strength of concrete, I is the moment of inertia, and y is the distance from the centroidal axis of the beam cross-section.

^{3}, we modified Equation (9) as;

_{c}) with that of the plate (E

_{p}) on the debonding load. Furthermore, Figure 16c plots the effect of the CFRP plate thickness on the debonding load using the data from the study by Kotynia et al. [13] and Ahmed et al. [15]. These plot results show that the longitudinal tensile reinforcement ratio, E

_{c}/E

_{p}, and plate thickness ratio significantly affect the debonding load.

_{c}/E

_{p}is expressed as β and (3) the effect of plate thickness as t

_{p}. The effect of these three variables is shown in Equation (10).

_{t}is the ratio of tensile reinforcement, $\beta $ = E

_{c}/E

_{p}, E

_{c}is the modulus of elasticity of concrete, E

_{p}is the modulus of elasticity of the plate, t

_{p}is the plate thickness, b

_{w}is the width of the RC beam, h is the height of the rectangular concrete member, and f

_{t}is the splitting tensile strength; if the splitting tensile strength is not determined from tests, then the value of the concrete tensile strength can be calculated as f

_{t}= f

_{c}’/10.

#### 5.4. Implementation of the Proposed Model on the RCCSA Software

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic pictures of the tested beams and their identifications (

**a**) beam dimension and loading position, (

**b**) cross section of control beams, and (

**c**) cross section of plated beams.

**Figure 4.**Analytical model using the fiber element method (

**a**) reinforced concrete cross section, (

**b**) fiber element model, and (

**c**) strain distribution.

**Figure 7.**Material stress-strain models used in finite element analysis (

**a**) concrete, (

**b**) steel reinforcement, and (

**c**) CFRP plate.

**Figure 8.**Crack patterns of the beams after the test (

**a**) G6C1, (

**b**) G6C2, (

**c**) G6C3, (

**d**) G6P1, (

**e**) G6P2, and (

**f**) G6P3.

**Figure 10.**Load-deflection curve from the tested beams (

**a**) control beams, and (

**b**) beams with CFRP plates.

**Figure 11.**Comparison between test results and the fiber element method (RCCSA) (

**a**) reinforcement ratio 1%, (

**b**) reinforcement ratio 1.5%, and (

**c**) reinforcement ratio 2.5%.

**Figure 12.**Comparison between test results and the finite element method (ATENA 2D) (

**a**) reinforcement ratio 1%, (

**b**) reinforcement ratio 1.5%, and (

**c**) reinforcement ratio 2.5%.

**Figure 13.**Effect of (

**a**) ratio of tensile reinforcement, (

**b**) the elastic modulus of the concrete, and (

**c**) plate thickness on the flexural capacity using RCCSA.

**Figure 15.**Effect of (

**a**) ratio of tensile reinforcement, (

**b**) the elastic modulus of the concrete, and (

**c**) plate thickness on the strain of tensile reinforcement using ATENA.

**Figure 16.**Effect of (

**a**) ratio of tensile reinforcement, (

**b**) E

_{c}/E

_{p}, and (

**c**) the plate thickness on the debonding loads.

**Figure 18.**Comparison of the debonding load between the proposed model ($\omega $ = 6) and the experimental results.

**Figure 19.**Comparison of the debonding load between the experimental results and the prediction (Type 1 debonding failure occurs before the experimental debonding load and after the yielding of tensile reinforcement) (

**a**) Thamrin et al. [1], (

**b**) Garden & Hollaway [2], (

**c**) Ross et al. [4], (

**d**) Khomwan et al. [11], (

**e**) Ahmed et al. [15], and (

**f**) Bilotta et al. [16].

Literature | Empirical Equations for Debonding Moment | |
---|---|---|

Oehlers [21] | ${M}_{db,f}=\frac{{E}_{c}{I}_{tr,c}{f}_{ct}}{0.901{E}_{frp}{t}_{frp}}$ | Equation (6) |

Teng & Chen [22] | ${M}_{db,f}=\frac{0.488{M}_{u,0}}{{\left({\alpha}_{flex}{\alpha}_{axial}{\alpha}_{w}\right)}^{1/9}}$ | Equation (7) |

_{db,f}means flexural debonding moment, E

_{c}and E

_{frp}are the elastic modulus of the concrete and the elastic modulus of the FRP, respectively, I

_{tr,c}is the cracked second moment of the area of the plated section transformed to concrete, f

_{ct}is the cylinder splitting tensile strength of concrete, b

_{frp}and t

_{frp}are the width and thickness of the FRP plate, respectively, and M

_{u,0}is the theoretical ultimate moment of the unplated section, which is also the upper bound of the flexural debonding moment M

_{db,f}. α

_{flex}, α

_{axial}and α

_{w}are three dimensionless variables, (EI)

_{c,frp}and (EI)

_{c,0}are the flexural rigidities of the cracked section with and without an FRP plate, respectively, and b

_{c}and d are the widths and effective depth of the RC beam, respectively.

Specimen | fc’ | ft | E_{c} | b_{w} | h | a | ρ_{t} | t_{p} | E_{p} | Oehlers [21] | Teng&Chen [22] | Proposed Model | P_{exp} |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

(MPa) | (MPa) | (GPa) | (mm) | (mm) | (mm) | (mm) | (GPa) | (kN) | (kN) | (kN) | (kN) | ||

Thamrin et al. [1] | |||||||||||||

G6P1 | 20 | 2.0 | 21 | 125 | 250 | 800 | 0.009 | 1.90 | 139 | 22.77 | 21.27 | 32.71 | 48.90 |

G6P2 | 20 | 2.0 | 21 | 125 | 250 | 800 | 0.014 | 1.90 | 139 | 28.35 | 31.19 | 49.06 | 63.10 |

G6P3 | 20 | 2.0 | 21 | 125 | 250 | 800 | 0.023 | 1.90 | 139 | 37.35 | 47.15 | 81.77 | 71.15 |

Garden & Hollaway [2] | |||||||||||||

Beam 1 U,1.0 m | 44.8 | 4.5 | 31 | 100 | 100 | 300 | 0.01 | 0.82 | 110 | 15.35 | 5.96 | 21.22 | 36.50 |

Beam 2 U,1.0 m | 44.8 | 4.5 | 31 | 100 | 100 | 300 | 0.01 | 0.82 | 110 | 15.35 | 5.96 | 21.22 | 32.00 |

Beam 3 U,1.0 m | 44.8 | 4.5 | 31 | 100 | 100 | 220 | 0.01 | 0.82 | 110 | 20.93 | 8.12 | 28.94 | 34.00 |

Beam 4 U,1.0 m | 44.8 | 4.5 | 31 | 100 | 100 | 100 | 0.01 | 0.82 | 110 | 46.04 | 17.87 | 63.66 | 34.50 |

Beam 5 U,1.0 m | 44.8 | 4.5 | 31 | 100 | 100 | 100 | 0.01 | 0.82 | 110 | 46.04 | 17.87 | 63.66 | 34.60 |

Spadea et al. [3] | |||||||||||||

A3.1 | 24.9 | 2.5 | 23 | 140 | 300 | 1800 | 0.011 | 1.20 | 152 | 32.22 | 18.47 | 21.14 | 37.40 |

Ross et al. [4] | |||||||||||||

1B | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0047 | 0.45 | 138 | 60.01 | 7.92 | 15.19 | 40.05 |

1C | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0047 | 0.45 | 138 | 60.01 | 7.92 | 15.19 | 35.60 |

2B | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0085 | 0.45 | 138 | 80.06 | 15.10 | 27.57 | 48.95 |

2C | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0085 | 0.45 | 138 | 80.06 | 15.10 | 27.57 | 35.60 |

2D | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0085 | 0.45 | 138 | 80.06 | 15.10 | 27.57 | 40.05 |

3B | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0132 | 0.45 | 138 | 101.33 | 23.96 | 42.58 | 54.52 |

3C | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0132 | 0.45 | 138 | 101.33 | 23.96 | 42.58 | 54.07 |

3D | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0132 | 0.45 | 138 | 101.33 | 23.96 | 42.58 | 54.29 |

4B | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0187 | 0.45 | 138 | 123.76 | 34.60 | 60.68 | 53.82 |

4C | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0187 | 0.45 | 138 | 123.76 | 34.60 | 60.68 | 52.29 |

4D | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0187 | 0.45 | 138 | 123.76 | 34.60 | 60.68 | 55.63 |

5B | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0201 | 0.45 | 138 | 128.85 | 37.19 | 65.15 | 73.43 |

5C | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0201 | 0.45 | 138 | 128.85 | 37.19 | 65.15 | 73.43 |

5D | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0201 | 0.45 | 138 | 128.85 | 37.19 | 65.15 | 72.76 |

6B | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0335 | 0.45 | 138 | 171.54 | 61.32 | 108.47 | 84.55 |

6C | 54.8 | 5.5 | 35 | 200 | 200 | 914 | 0.0335 | 0.45 | 138 | 171.54 | 61.32 | 108.47 | 76.55 |

Shehata et al. [5] | |||||||||||||

V1 | 33.3 | 3.3 | 27 | 150 | 450 | 1350 | 0.010 | 1.20 | 165 | 180.83 | 95.39 | 84.87 | 140.00 |

V3 | 34.3 | 3.4 | 28 | 150 | 450 | 1350 | 0.010 | 1.20 | 165 | 195.75 | 96.01 | 88.73 | 150.00 |

Nguyen et al. [6] | |||||||||||||

A950 | 26.6 | 2.7 | 24 | 120 | 150 | 440 | 0.016 | 1.20 | 181 | 15.61 | 14.34 | 25.80 | 28.10 |

A1100 | 26.6 | 2.7 | 24 | 120 | 150 | 440 | 0.016 | 1.20 | 181 | 15.61 | 14.34 | 25.80 | 28.65 |

A1150 | 26.6 | 2.7 | 24 | 120 | 150 | 440 | 0.016 | 1.20 | 181 | 15.61 | 14.34 | 25.80 | 29.45 |

B1 | 37.0 | 3.7 | 29 | 120 | 150 | 440 | 0.004 | 1.20 | 181 | 12.73 | 3.53 | 10.14 | 24.60 |

B2 | 37.0 | 3.7 | 29 | 120 | 150 | 440 | 0.044 | 1.20 | 181 | 28.95 | 41.41 | 112.69 | 65.05 |

C5 | 20.8 | 2.1 | 21 | 120 | 150 | 440 | 0.014 | 1.20 | 181 | 16.67 | 17.41 | 15.29 | 35.50 |

C10 | 20.8 | 2.1 | 21 | 120 | 150 | 440 | 0.015 | 1.20 | 181 | 15.74 | 16.41 | 15.86 | 34.00 |

C20 | 20.8 | 2.1 | 21 | 120 | 150 | 440 | 0.016 | 1.20 | 181 | 14.02 | 14.47 | 17.13 | 31.50 |

Fanning & Kelly [7] | |||||||||||||

F5 | 80 | 5.0 | 39 | 155 | 240 | 1100 | 0.011 | 1.20 | 155 | 69.59 | 25.51 | 79.64 | 50.00 |

F6 | 80 | 5.0 | 39 | 155 | 240 | 1100 | 0.011 | 1.20 | 155 | 69.59 | 25.51 | 79.64 | 51.50 |

F7 | 80 | 5.0 | 39 | 155 | 240 | 1100 | 0.011 | 1.20 | 155 | 69.59 | 25.51 | 79.64 | 48.75 |

F8 | 80 | 5.0 | 39 | 155 | 240 | 1100 | 0.011 | 1.20 | 155 | 69.59 | 25.51 | 79.64 | 32.00 |

F9 | 80 | 5.0 | 39 | 155 | 240 | 1100 | 0.011 | 1.20 | 155 | 69.59 | 25.51 | 79.64 | 31.00 |

F10 | 80 | 5.0 | 39 | 155 | 240 | 1100 | 0.011 | 1.20 | 155 | 69.59 | 25.51 | 79.64 | 41.00 |

Breña et al. [8] | |||||||||||||

D1 | 37.2 | 3.7 | 29 | 203 | 406 | 1220 | 0.005 | 1.19 | 155 | 128.10 | 41.78 | 72.10 | 64.05 |

D2 | 37.2 | 3.7 | 29 | 203 | 406 | 1220 | 0.005 | 1.19 | 155 | 128.10 | 41.78 | 72.10 | 66.95 |

Breña et al. [9] | |||||||||||||

A6-I | 47.7 | 4.8 | 33 | 100 | 100 | 330 | 0.008 | 1.19 | 155 | 7.98 | 5.14 | 17.44 | 34.80 |

Pimanmas et al. [10] | |||||||||||||

B-200P | 44 | 4.4 | 31 | 120 | 220 | 700 | 0.033 | 1.20 | 150 | 51.45 | 51.12 | 180.95 | 117.79 |

Khomwan et al. [11] | |||||||||||||

B2 | 37 | 3.7 | 25 | 350 | 700 | 2500 | 0.006 | 1.40 | 165 | 467.07 | 142.64 | 191.97 | 223.50 |

B6 | 53 | 5.3 | 29 | 350 | 700 | 2500 | 0.006 | 1.40 | 165 | 574.57 | 147.06 | 315.70 | 238.50 |

Benjeddou et al. [12] | |||||||||||||

RB1 | 21 | 1.86 | 30 | 120 | 150 | 600 | 0.010 | 1.20 | 165 | 9.20 | 7.91 | 11.47 | 20.06 |

Kotynia et al. [13] | |||||||||||||

B-08 S | 32.3 | 2.8 | 27 | 150 | 300 | 1400 | 0.008 | 1.20 | 172 | 38.35 | 23.28 | 25.28 | 46.30 |

B-08 M | 37.3 | 3.5 | 29 | 150 | 300 | 1400 | 0.008 | 1.40 | 220 | 43.51 | 21.83 | 30.97 | 70.00 |

Al-Tamimi et al. [14] | |||||||||||||

B85P | 54 | 5.4 | 35 | 110 | 180 | 562 | 0.009 | 1.40 | 215 | 24.21 | 16.50 | 42.59 | 30.35 |

B25P | 54 | 5.4 | 35 | 110 | 180 | 562 | 0.009 | 1.40 | 215 | 24.21 | 16.50 | 42.59 | 25.97 |

B70P | 54 | 5.4 | 35 | 110 | 180 | 562 | 0.009 | 1.40 | 215 | 24.21 | 16.50 | 42.59 | 23.54 |

Ahmed et al. [15] | |||||||||||||

FB-1L | 36 | 3.0 | 29 | 150 | 200 | 700 | 0.006 | 1.20 | 165 | 24.85 | 11.81 | 19.66 | 31.00 |

FB-2L | 36 | 3.0 | 29 | 150 | 200 | 700 | 0.006 | 2.40 | 165 | 17.30 | 10.18 | 39.32 | 34.88 |

FB-3L | 36 | 3.0 | 29 | 150 | 200 | 700 | 0.006 | 3.60 | 165 | 14.52 | 9.35 | 58.98 | 37.20 |

Bilotta et al. [16] | |||||||||||||

EBR_c_1.4x40_1 | 17.43 | 1.74 | 20 | 120 | 160 | 925 | 0.013 | 1.40 | 171 | 3.23 | 4.17 | 7.02 | 18.25 |

EBR_c_1.4x40_2 | 17.43 | 1.74 | 20 | 120 | 160 | 925 | 0.013 | 1.40 | 171 | 4.42 | 4.20 | 7.02 | 17.60 |

Fu et al. [17] | |||||||||||||

B1S1 | 49 | 4.9 | 33 | 200 | 450 | 1300 | 0.008 | 0.67 | 251 | 286.39 | 83.90 | 61.75 | 137.70 |

B1S2 | 25.9 | 2.6 | 24 | 200 | 450 | 1300 | 0.005 | 0.67 | 251 | 149.99 | 50.20 | 15.82 | 121.20 |

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**MDPI and ACS Style**

Thamrin, R.; Zaidir, Z.; Desharma, S.
Debonding Failure Analysis of Reinforced Concrete Beams Strengthened with CFRP Plates. *Polymers* **2021**, *13*, 2738.
https://doi.org/10.3390/polym13162738

**AMA Style**

Thamrin R, Zaidir Z, Desharma S.
Debonding Failure Analysis of Reinforced Concrete Beams Strengthened with CFRP Plates. *Polymers*. 2021; 13(16):2738.
https://doi.org/10.3390/polym13162738

**Chicago/Turabian Style**

Thamrin, Rendy, Zaidir Zaidir, and Silvy Desharma.
2021. "Debonding Failure Analysis of Reinforced Concrete Beams Strengthened with CFRP Plates" *Polymers* 13, no. 16: 2738.
https://doi.org/10.3390/polym13162738