# C-Anchor for Strengthening the Connection between Adhesively Bonded Laminates and Concrete Substrates

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## Abstract

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## 1. Introduction

## 2. FRP Plate Anchoring Systems

## 3. New C-Anchor Description

^{2}cross-sectional area with a rough surface finish. This grid has been extensively tested by both its manufacturer and by other investigators [34] to determine its mechanical properties. Its guaranteed tensile strength is 1200 MPa and its elastic modulus is 100 GPa. Due to its rough surface finish, it bonds very well with both concrete and the epoxy adhesive.

## 4. Experiential Program

#### 4.1. Test Specimens

_{y}= yield stress = 440 MPa, ε

_{y}= strain at yield = 0.0022, E

_{s}= modulus of elasticity of steel = 200 GPa, f

_{u}= ultimate strength = 680 MPa, ε

_{u}= ultimate strain = 0.056 and ε

_{sh}= strain corresponding to the beginning of strain hardening = 0.007. For the CFRP materials used in the current study, Table 1 shows the properties of the CFRP sheet and laminate, the primer and the two part epoxy adhesive as reported by their manufactures.

**Figure 2.**Typical beam dimensions, reinforcement and load configuration. (

**a**) elevation; (

**b**) cross-Section.

**Table 1.**Manufacturers’ specified properties of the carbon fiber reinforced polymer (CFRP) composites, primer and epoxy used in the current study.

Properties | CFRP Laminate | Epoxy | CFRP Sheet | Primer | Saturant |
---|---|---|---|---|---|

Tensile strength (MPa) | 2800 | 46.8 | 3800 | 14.5 | 54 |

Modulus of elasticity (GPa) | 165 | 4.5 | 227 | 0.717 | 3.034 |

Ultimate strain (%) | 1.90 | 1.0 | 1.67 | 40 | 3.50 |

Thickness (mm) | 1.2 | - | 0.165 per ply | - | - |

Width (mm) | 50 | - | 610 | - | - |

Type of CFRP | Beam | No. of Layers | Thickness per Layer | Width | Total Cross-Sectional Area |
---|---|---|---|---|---|

(mm) | (mm) | (mm^{2}) | |||

CB | 0 | - | - | - | |

CFRP Laminate | LN100 | 1 | 1.2 | 100 | 120 |

LA100 | 1 | 1.2 | 100 | 120 | |

LN50 | 1 | 1.2 | 50 | 60 | |

LA50 | 1 | 1.2 | 50 | 60 | |

CFRP Sheet | SN166 | 3 | 0.165 | 166 | 82.2 |

SA166 | 3 | 0.165 | 166 | 82.2 | |

SN83 | 3 | 0.165 | 83 | 41.1 | |

SA83 | 3 | 0.165 | 83 | 41.1 |

#### 4.2. External Shear Reinforcement

#### 4.3. Instrumentation and Test Method

## 5. Results and Discussion

#### 5.1. Load Deflection Behaviour

#### 5.2. Ultimate Flexural Strength

_{n}, of each beam was calculated based on the Canadian Standard CSA 23.3-04 (CSA 2004) [35] and is shown in Table 3. The calculated strength is based on the assumption of strain compatibility, i.e., the FRP laminate is assumed fully bonded until failure, and the concrete ultimate compressive strain is assumed equal to 0.0035.

_{F}, are presented in column 4 of Table 3. The control beam CB failed at 4% higher load than its theoretical strength value. This beam failed in a flexural-shear mode, i.e., high shear stresses contributed to its failure. Beam LN100 debonded at 260 kN.m, and the test was stopped immediately after. The theoretical ultimate moment capacity of this beam based on full bond is 270 kN.m. Beam LA100, which is the companion to LN100, failed at 3.5% higher load than its theoretical value. Hence, in comparison to LN100, which had no anchors, LA100 with anchors, achieved 7.5% higher moment. Similarly, Beam SN166 achieved 93% of its theoretical capacity while Beam SA166 reached 14.4% higher load compared to Beam SN166. It is clear that the higher capacity of SA166 is due to the anchors because the two beams were otherwise nominally identical. Comparing Beams LN50 and LA50, they failed at 11% and 16% higher load, respectively, than their corresponding theoretical values, and the beam with anchor had approximately 5% higher strength than the one without anchor. Finally, Beams SN83 and SA83 achieved failure moments 8.1% and 17.6% higher than their respective theoretical values. In this case, the beam with anchors achieved 9.5% higher moment than the one without anchor. Based on this discussion, in each case, the anchors allowed the beams to achieve higher strength. In the case of the beams with the larger amount of FRP, the actual failure load in all cases exceeded the corresponding theoretical value. This means that the anchors allowed the beams to reach their maximum theoretical capacity.

Beam | Theoretical Failure Moment, M_{u} (kN.m) | Experimental | $\frac{{\text{M}}_{\text{F}}}{{\text{M}}_{\text{F}}^{\mathrm{control}}}$ | $\frac{{\text{M}}_{\text{F}}}{{\text{M}}_{\text{u}}}$ | |
---|---|---|---|---|---|

Debonding Moment M_{db} (kN.m) | Failure Moment M_{F} (kN.m) | ||||

CB | 180 | - | 187.9 | 1.00 | 1.04 |

LN100 | 270 | 260.1 | - | - | - |

LA100 | 257.0 | 279.6 | 1.49 | 1.04 | |

SN166 | 263 | 260.0 | 244.7 | 1.30 | 0.93 |

SA166 | 288.6 | 279.9 | 1.49 | 1.06 | |

LN50 | 235 | 223.9 | 260.8 | 1.39 | 1.11 |

LA50 | 240.9 | 271.9 | 1.45 | 1.16 | |

SN83 | 232 | 237.7 | 250.8 | 1.33 | 1.08 |

SA83 | 251.3 | 272.9 | 1.45 | 1.18 |

#### 5.3. Debonding Load

_{db}, of the test beams are shown in column 2 of Table 4. In each case, comparison can be made between the debonding load of the beam without and with anchor. Comparing Beam LN100 and LA100, the anchor did not increase the debonding capacity of the beam. As for Beam SN166 and Beam SA166, the anchor increased the debonding load of the beam by 11%. Similarly, considering LN50 and LA50, the beam with anchor achieved 7.6% higher debonding load. Finally, comparing Beams SN83 and SA83, one observes that the beam with anchor debonded at 5.7% higher load. Based on the preceding loads, it can be stated that in general the anchors were able to delay debonding.

Beam | P_{db} (kN) | P_{drop} (kN) | P_{F} (kN) | ΔP_{drop} (kN) | ΔP_{drop}/P_{db} (%) | P_{F}/P_{db} (%) |
---|---|---|---|---|---|---|

CB | - | - | 250.5 | - | - | - |

LN100 | 346.8 | 293.8 | - | 53.0 | 15.3 | - |

LA100 | 342.6 | 276.3 | 372.8 | 66.3 | 19.4 | 108.8 |

SN166 | 346.8 | 245.5 | 326.2 | 101.3 | 29.2 | 94.1 |

SA166 | 384.8 | 319.9 | 373.1 | 64.9 | 16.9 | 97.0 |

LN50 | 298.5 | 262.6 | 347.7 | 35.9 | 12.0 | 116.5 |

LA50 | 321.2 | 274.0 | 362.5 | 47.2 | 14.7 | 112.9 |

SN83 | 316.9 | 273.4 | 334.4 | 43.5 | 13.7 | 105.5 |

SA831 | 335.1 | 298.5 | 363.8 | 36.6 | 10.9 | 108.6 |

#### 5.4. Load Drop after Debonding

_{drop}, for all the beams is shown in column 5 of Table 4.

_{db}is the maximum load before debonding, P

_{drop}is the load immediately after debonding, and ΔP

_{drop}= P

_{db}− P

_{drop}. Beam LN50 compared to LA50 debonded at 7.6% higher load. If we look at the load drop for the two beams (column 5 of Table 4), it is 35.9 kN and 47.2 kN, respectively. Hence, in this case, the beam with anchors debonded over a slightly higher length, and the anchors were not able to prevent the propagation of debonding. Finally, comparing Beam SN83 and SA83, one can observe that the anchors in Beam SA83 delayed debonding and increased the debonding load by 5.7%. It can be stated that generally the anchors delayed debonding and increased the debonding load, but they did not substantially limit the propagation of the debonding zone along the concrete-FRP interface.

**Figure 7.**Typical failure for beams with and without anchors. (

**a**) Debonding in Beam SN166; (

**b**) Sheet end slippage in Beam SA166; (

**c**) Slippage happened in Beam LA100; (

**d**) Debonding in Beam LN100.

#### 5.5. Strain Profile

#### 5.6. Ductility and Energy Absorption

_{max}, achieved just before debonding. In the case of load-deflection curves with a descending portion after P

_{max}, it is defined as the deflection corresponding to 0.85 P

_{max}on the descending part of the curve, divided by the deflection corresponding to P

_{max}. Hence, in the case of the control beam, the failure load was taken as 0.85 of the maximum load reached. The area under the complete load- deflection curve represents the total energy absorbed by the beam up to failure. The energy absorption index, η, may be defined as the calculated area under the load deflection curve of the strengthened beam to the area under the load deflection curve of the control beam. All the strengthened beams with anchors show higher energy absorption compared to the ones without anchor, except beam LN100, which shows very low energy absorption. The latter is due to the fact that the test was stopped in the case of this beam, but, had loading been continued after debonding, the beam would have followed the load-deflection curve of the control beam.

Beam | Max. Load at Failure (kN) | Deflection at Debonding Load (mm) | Deflection at Failure Load (mm) | Ductility Index (μ) | Energy Absorbed (kN.m) | Energy Absorption Index (η) |
---|---|---|---|---|---|---|

CB | 212.5 | 29.6 * | 37.6 | 1.27 | 7.8 | 1.00 |

LN100 | 344.5 | 13.2 | 13.2 | 1.00 | 3.3 | 0.43 |

LA100 | 371.0 | 10.5 | 93.2 | 8.88 | 32.2 | 4.11 |

SN166 | 342.0 | 12.2 | 65.6 | 5.38 | 19.2 | 2.45 |

SA166 | 368.5 | 18.9 | 71.3 | 3.77 | 23.3 | 2.98 |

LN50 | 338.1 | 9.2 | 114.4 | 12.43 | 36.4 | 4.65 |

LA50 | 354.7 | 25.8 | 124.4 | 4.82 | 39.6 | 5.06 |

SN83 | 328.1 | 20.1 | 94.8 | 4.72 | 29.1 | 3.71 |

SA83 | 361.3 | 29.8 | 123.4 | 4.14 | 40.0 | 5.11 |

#### 5.7. Maximum Strain Attained in FRP versus Its Rupture and Allowable Strains

_{F}, in each beam and the corresponding allowable strain, ${\mathsf{\epsilon}}_{\text{F}}^{\text{ACI}}$, recommended by the American Concrete Institute (ACI) 440 [9] and CSA S806 [8] for the particular retrofit scheme. The quantity ${\mathsf{\epsilon}}_{\text{F}}^{\text{ACI}}$ is calculated as

_{c}, is the concrete strength (MPa), n is the number of FRP laminate plies or layers used, t

_{F}is the thickness of each ply (mm) and E

_{F}is the elastic modulus of the FRP (MPa). The table also shows the ratio of ε

_{F}to the FRP rupture strain, ε

_{Fu}, and the ratio of ε

_{F}to ${\mathsf{\epsilon}}_{\text{F}}^{\text{ACI}}$. The latter ratio has been referred to as the anchor efficiency factor by Kalfat et al. [13]. In fact, both ratios are indicator of the efficient utilization of the FRP strength in retrofit works. It can be observed that in none of the beams, the FRP reached its tensile rupture strain, but the beams with anchor achieved higher strain compared to their companion beams without anchor. Therefore, the anchors in these cases increased the maximum achievable strain in the FRP. According to Kalfat et al. [13], the highest average efficiency factor achieved by existing anchors is 1.87, and this was achieved by using steel plates and anchor bolts. It is important to observe that the ACI allowable FRP strain value for beams without anchor was not achieved in any of the current test beams. In the case of beams with anchor, except beam LA100, the anchor allowed the laminate/sheet to surpass its theoretical strain value based on the ACI equation. Therefore, using the anchor allows one to conservatively estimate the ultimate strength of CFRP strengthened beams based on the ACI 440 Committee recommendation for allowable FRP strain. Without the anchor, the ACI recommended alue may not be reached in some cases.

**Table 6.**Maximum recorded fiber reinforced polymers (FRP) strain in test beams compared to its rupture strain and to the maximum strain allowed by the American Concrete Institute (ACI) Committee 440 Guidelines (ACI 440.2R-08) [9].

Beam Designation | Maximum Strain Recorded in FRP, ε_{F}(microstrain) | ${\mathsf{\epsilon}}_{\text{F}}^{\text{ACI}}$ (microstrain) | $\frac{{\mathsf{\epsilon}}_{\text{F}}}{{\mathsf{\epsilon}}_{\text{Fu}}}$ | Efficiency Factor = $\frac{{\mathsf{\epsilon}}_{\text{F}}}{{\mathsf{\epsilon}}_{\text{F}}^{\text{ACI}}}$ |
---|---|---|---|---|

LN100 | 5750 | 6640 | 0.30 | 0.87 |

LA100 | 5790 | 0.31 | 0.87 | |

LN50 | 5760 | 0.30 | 0.87 | |

LA50 | 9370 | 0.49 | 1.41 | |

SN166 | 5760 | 8820 | 0.35 | 0.65 |

SA166 | 9300 | 0.56 | 1.05 | |

SN83 | 8320 | 0.50 | 0.94 | |

SA83 | 9820 | 0.59 | 1.08 |

## 6. Conclusions

- (1)
- Beams outfitted with the proposed C-anchor had generally 5%–10% higher debonding load and reached higher maximum load and corresponding deflection than the companion beams without anchor.
- (2)
- Beams with anchor reached higher strain in the FRP compared to their companion beams without anchor and the maximum strain exceeded the theoretical strain based on the ACI 440 equation.
- (3)
- Although complete separation of the laminate/sheet from the concrete was not observed in any of the beams with anchor, substantial slip was noticed at one end of the FRP laminate.
- (4)
- Despite the fact that some of the strengthened beams were over-reinforced, they failed in a ductile fashion because the failure was initiated by debonding and thereafter they reverted to their un-strengthened under-reinforced behavior.
- (5)
- The anchor was found to be effective in limiting the extent of debonding along the laminate, thus indirectly contributing to the beam flexural stiffness by limiting its crack width.
- (6)
- The anchor significantly increased the energy absorption or toughness of the strengthened beams, but further investigation is needed to optimize the number and location of the anchors.
- (7)
- The proposed C-anchor shows promise, but its performance can be improved by increasing its contact surface with the concrete and the FRP laminate. In other words, the anchor spine width needs to be much larger than its thickness in order to increase its surface area for resisting interfacial shear.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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## Share and Cite

**MDPI and ACS Style**

Razaqpur, G.; Mostafa, A.B.
C-Anchor for Strengthening the Connection between Adhesively Bonded Laminates and Concrete Substrates. *Technologies* **2015**, *3*, 238-258.
https://doi.org/10.3390/technologies3040238

**AMA Style**

Razaqpur G, Mostafa AB.
C-Anchor for Strengthening the Connection between Adhesively Bonded Laminates and Concrete Substrates. *Technologies*. 2015; 3(4):238-258.
https://doi.org/10.3390/technologies3040238

**Chicago/Turabian Style**

Razaqpur, Ghani, and Ahmed B. Mostafa.
2015. "C-Anchor for Strengthening the Connection between Adhesively Bonded Laminates and Concrete Substrates" *Technologies* 3, no. 4: 238-258.
https://doi.org/10.3390/technologies3040238