# Strengthening of RC Beams Using Externally Bonded Reinforcement Combined with Near-Surface Mounted Technique

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Test Matrix

#### 2.2. Specimens and Materials

^{2}. A unidirectional, woven CFRP fabric (SikaWrap

^{®}-301C) with a thickness of 0.17 mm was used as external strengthening material at the beam soffit. A two-part epoxy (Sikadur

^{®}30) was used as the adhesive filler to fix the CFRP bar inside the groove. The CFRP fabric was also soaked with epoxy resin (Sikadur

^{®}330) for proper bonding with the concrete substrate. These resins are available with a two-part adhesive based on a combination of epoxy resins and filler. Table 2 presents the properties of concrete, internal steel, strengthening steel, CFRP bar, CFRP fabric, and epoxy.

#### 2.3. Specimen Design and Preparation

^{®}30), which was prepared according to the directions of the manufacturers. The NSM CFRP bar was properly cleaned and gently pressed inside the groove until surrounded by an equal amount of epoxy. Then, a spatula was used to level the surface and clean the area. The whole preparation was left for standard curing time, as prescribed by the manufacturer.

## 3. Results and Discussion

#### 3.1. Load-Carrying Capacity

#### 3.2. Load–Deflection Diagram

#### 3.3. Failure Modes

#### 3.4. Cracking Behaviour

#### 3.4.1. Crack Spacing

_{r0}) spacing can be expressed as the nearest point to a present crack at which a fresh crack can develop, where the concrete again reaches the tensile strength (Equation (1)). It can be expressed as

_{r.min}= s

_{r0}and s

_{r,max}= 2s

_{r0}. Various researchers proposed different values of average (mean) crack spacing, which varied from 1.33 to 1.54 times the minimum value (Equations (2) and (3)), whilst maximum crack spacing can be expressed as s

_{r,max}= 2s

_{r,min}.

_{r.max}and 0.73 S

_{r.min}, which complies with the limit suggested in Equations (2) and (3). Moreover, the ratio of the average S

_{r.max}and S

_{r.min}was 1.94, which was close to the findings of Borosnyói [39].

#### 3.4.2. Crack Width

#### 3.5. Stiffness Assessment

_{eff}) after exceeding the cracking moment (M

_{cr}) instead of using the gross moment of inertia (I

_{g}). For the full crack formation of the beam, I

_{eff}should be referred to as the cracked moment of inertia (I

_{cr}) of the cracked transformed section. With the formation of flexural cracks, the neutral axis also keeps changing its position, which is also a significant challenge for the appropriate estimation of bending stiffness.

_{exp}represent the applied service load, clear span of the RC beam, shear span of the beam, and the maximum mid-span experimental deflection at service load, respectively.

^{2}. The initial stiffness values of the strengthened beams were 5203, 8042, 9653, and 15,453 N mm

^{2}for the CBC8P1-, CBC8P2-, CBC10P1-, and CBC10P2-strengthened beams, respectively.

^{2}. The intermediate stiffness at the first crack of the CEBNSM-strengthened beams was 2008, 3142, 2553, and 8637 N·mm

^{2}for the CBC8P1-, CBC8P2-, CBC10P1-, and CBC10P2-strengthened beams, respectively. No noticeable difference in stiffness was observed after the first crack, and a radical realignment was visualised for this curve. An almost straight vertical line was formed where the moment increased with a steady rate. The CBC10P2-strengthened beam showed a gradually-decreasing stiffness with the increase in the moment capacity from the crack moment to the yield moment.

^{2}. The stiffness at the yield moment of the CBC series beams was 983, 1292, 2002, and 5656 N·mm

^{2}for the CBC8P1-, CBC8P2-, CBC10P1-, and CBC10P2-strengthened beams. After crossing the yield moment point, the beams showed an almost constant decrease in stiffness with a negligible moment increment. Then, the moment capacity increased again without any appreciable change in stiffness up to failure.

## 4. Simulation Method and Verification

#### 4.1. Moment-Rotation Approach

#### 4.1.1. Tension Stiffening Analysis

_{def}located between two flexural cracks. The slip of reinforcements would be at maximum at the location of the flexural cracks. As the bond stress acting on the reinforcements reacts against the slip of the reinforcements, the slip of the reinforcements would be gradually reduced, as the force acting on the reinforcements would be transferred to the adjacent concrete. Due to symmetry of forces, the slip of reinforcements would tend to zero at the middle of the beam segment, as shown in Figure 11b. As such, the analysis area can be reduced to length L

_{def}.

_{s}) taken as 0.1 mm, where the stress and strain acting in each element is assumed to be constant due to its small size. The maximum element for the analysis, i

_{max}= L

_{s}L

_{def}. The steel reinforcement is assumed to slip by a certain amount, and the load needed to cause this slip is assumed. The load and slip values for each element are then solved numerically and the load is adjusted until the slip is reduced to zero at the middle of the beam segment. The process is repeated until a load–slip relationship is obtained. The bond–slip model by CEB-FIP [49] was used to determine the bond force acting on the steel reinforcement.

_{max−n}is the maximum bond stress, δ is the slip, and δ

_{max−n}is slip corresponding to τ

_{max−n}. The full list of parameters used for the bond–slip model for NSM FRP bars is provided in Table 6, where the parameters are empirically derived by De Lorenzis [50] for RC beams strengthened with NSM FRP ribbed bars, with the exception of τ

_{max−n}, which was 21 MPa based on the value of bond strength given by the manufacturer of the Sikadur

^{®}30 epoxy adhesive.

#### 4.1.2. Moment-Rotation Analysis

_{def}. The concrete stress–strain model by Popovics [53] was used as the base model that was adjusted for concrete size:

_{c}is the concrete stress, f

_{c}is the concrete strength, ε

_{c}is the concrete strain. The parameters r and peak strain, ε

_{a}are determined as:

_{c}is the elastic modulus of concrete. It should be noted that Equation (19) was proposed by Chen, et al. [52], based on their research. To obtain the adjusted stress–strain relationship of concrete, σ

_{c}/ε

_{c-sd}—where ε

_{c-sd}is the size adjusted strain—the size dependent strain for concrete is then determined as:

_{NA}is then adjusted until an equilibrium of forces is achieved and the value of moment M is then determined from forces in Figure 12d.

_{def}. The load–deflection of the beam can then be determined from the moment-curvature relationship using the double integration method.

## 5. Conclusions

- The first crack, yield, and ultimate load of the CEBNSM-strengthened beams significantly increased compared with the control beam. The increment of the first crack load was the highest (230%) among the three load levels, which is particularly important for serviceability performance. The maximum ultimate load-carrying capacity increased to 170% over that of the control beam.
- A trilinear load–deflection response was detected, whereas a considerable reduction of the deflection for all of the strengthened beams was witnessed at the ultimate stage. The stiffness of the strengthened beam significantly increased at all levels of load compared with that of the control beam.
- All of the strengthened beams exhibited flexural failure, except for the CBC10P2-strengthened beam, which was strengthened using a double-ply CFRP fabric with a 10 mm-diameter NSM CFRP bar. However, this debonding failure was successfully eliminated by using CFRP U-Wrap anchorage at the fabric curtailment location.
- The average crack spacing of the strengthened beams was 64 to 77 mm, which was smaller than that of the control beam (109 mm). The number of cracks was also more significant (average of 35 cracks) than that of the control beam (21 cracks), which affirmed the enhanced energy dissipation of the strengthened beams. Furthermore, the crack width of the strengthened beams was significantly reduced.
- The strain value of steel and concrete for the strengthened beams was less than that of the control beam. The strain values of the NSM bar and the EBR fabric showed the perfect distribution of the strain by strengthening reinforcement after the yielding of the internal steel bar.
- The moment-rotation approach was applied to simulate the behaviour of CEBNSM-strengthened RC beams and was able to give good accuracy.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Beam details and test setup (all dimensions are in mm). CFRP: carbon fibre reinforced polymer; LVDT: linear variable differential transducer.

**Figure 2.**Sequence of specimen preparation and strengthening. Epoxy and CFRP fabric are colored green and light blue respectively.

**Figure 3.**Percentile increment of the first crack, yield, and ultimate load-carrying capacities of combined externally bonded and near-surface mounted (CEBNSM)-strengthened beams compared with the control beam.

**Figure 6.**Failure modes of the control beam and the strengthened RC beams with close-up pictures at failure locations. (

**a**) Control beam; (

**b**) CBC8P1 beam; (

**c**) CBC8P2 beam; (

**d**) CBC10P1 beam; (

**e**) CBC10P2 beam; (

**f**) CBC10P2A beam.

**Figure 9.**Cross-sectional view of the strengthened beamshowing neutral axis (NS) location and curvature. b is the width of the beam, d is the effective depth of the beam, df is the effective depth of the NSM reinforcement, A

_{s}is the area of the main reinforcement, A

_{f}is the area of the NSM reinforcement, A

_{f}

_{.}

_{eb}is the area of the externally bonded reinforcement, N.A is the neutral axis of the section, c is the depth of the neutral axis, ε

_{c}is the compressive strain of the concrete, ε

_{s.y}is the tensile strain of the main reinforcement and φ

_{y}is the curvature of the section.

Serial. No. | Notation | Description | Strengthening details |
---|---|---|---|

1 | CB | Control RC beam | Without strengthening |

2 | CBC8P1 | 8 mm φ NSM CFRP bar and 1 ply of EBR CFRP fabric | CFRP bar: 1–8 mm φ (L = 2900 mm) CFRP fabric: 2900 × 125 × 0.17 mm ^{3} |

3 | CBC8P2 | 8 mm φ NSM CFRP bar and 2 ply of EBR CFRP fabric | CFRP bar: 1–8 mm φ (L = 2900 mm) CFRP 1st fabric: 2900 × 125 × 0.17 mm ^{3} CFRP 2nd fabric: 2600 × 125 × 0.17 mm ^{3} |

4 | CBC10P1 | 10 mm φ NSM CFRP bar and 1 ply of EBR CFRP fabric | CFRP bar: 1–10 mm φ (L = 2900 mm) CFRP fabric: 2900 × 125 × 0.17 mm ^{3} |

5 | CBC10P2 | 10 mm φ NSM CFRP bar and 2 ply of EBR CFRP fabric | CFRP bar: 1–10 mm φ (L = 2900 mm) CFRP 1st fabric: 2900 × 125 × 0.17 mm ^{3} CFRP 2nd fabric: 2600 × 125 × 0.17 mm ^{3} |

6 | CBC10P2A | NSM CFRP bar, EB 2 ply CFRP fabric and 2 ply U-wrap end anchorage | CFRP bar: 1–10 mm φ (2900 mm) CFRP fabric: 2900 × 125 × 0.34 mm ^{3} CFRP U-wrap anchorage: 2 ply (625 × 125 × 0.34 mm ^{3}) |

Material | Mechanical property | Result |
---|---|---|

Concrete | Compressive strength (MPa) | 50.1 |

Flexure strength (MPa) | 5.5 | |

Elastic modulus (GPa) | 33.26 | |

Steel 12 mm φ (Internal bottom reinforcement) | Yield stress (MPa) | 529 |

Ultimate strength (MPa) | 587 | |

Elastic modulus (GPa) | 200 | |

Elongation (%) | 21 | |

Steel 10 mm φ (Internal top reinforcement) | Yield stress (MPa) | 521 |

Ultimate strength (MPa) | 578 | |

Elastic modulus (GPa) | 200 | |

Elongation (%) | 20 | |

Steel 8 mm φ (Internal shear reinforcement) | Yield stress (MPa) | 380 |

Ultimate strength (MPa) | 450 | |

Elastic modulus (GPa) | 200 | |

Elongation (%) | 29 | |

CFRP bar-12 mm φ | Ultimate strength (MPa) | 2,400 |

Elastic modulus (GPa) | 165 | |

Ultimate strain (%) | 1.6 | |

CFRP Fabric (SikaWrap-301C) [35] | Ultimate strength (MPa) | 4,900 |

Elastic modulus (GPa) | 230 | |

Ultimate strain (%) | 2.1 | |

Epoxy (Sikadur^{®}) 30 [36] | Compressive strength | 70–80 MPa (15 °C); 85–95 MPa (35 °C) |

Tensile strength | 14–17 MPa (15 °C); 16–19 MPa (35 °C) | |

Shear strength | 24–27 MPa (15 °C); 26–31 MPa (35 °C) | |

Epoxy (Sikadur^{®}) 330 [37] | Tensile strength (MPa) | 30 |

Elastic modulus–Flexural (MPa) | 3,800 | |

Elastic modulus–Tensile (MPa) | 4,500 |

Beam ID | P_{cr} (kN) | Δ_{cr} (mm) | P_{y} (kN) | Δ_{y} (mm) | P_{u} (kN) | Δ_{u} (mm) | Failure modes |
---|---|---|---|---|---|---|---|

CB | 5 | 0.5 | 36 | 15.0 | 39 | 34.3 | FFC |

CBC8P1 | 11 | 1.5 | 50 | 14.9 | 71 | 39.7 | FFF |

CBC8P2 | 13 | 1.9 | 55 | 15.2 | 77 | 31.3 | FFF |

CBC10P1 | 13 | 1.6 | 54 | 16.6 | 82 | 43.3 | FFF |

CBC10P2 | 15 | 2.3 | 69 | 23.7 | 87 | 42.7 | CFD |

CBC10P2A | 16 | 2.8 | 80 | 24.7 | 105 | 47.9 | FFC |

_{cr}= first crack load; P

_{y}= yield load; P

_{u}= ultimate load; ∆

_{cr}= deflection at 1st crack; ∆

_{y}= deflection at yield of steel; ∆

_{u}= mid-span deflection at failure load; FFC = flexural failure (concrete crushing after steel yielding); FFF = flexure failure due to FRP rupture; CFD = CFRP fabric delamination.

Beam No. | S_{r.max} (mm) | S_{r.min} (mm) | S_{r.mean} (mm) | No. cracks |
---|---|---|---|---|

CB | 140 | 75 | 109 | 21 |

CBC8P1 | 85 | 45 | 64 | 39 |

CBC8P2 | 110 | 50 | 77 | 31 |

CBC10P1 | 95 | 50 | 70 | 38 |

CBC10P2 | 90 | 48 | 65 | 34 |

CBC10P2A | 110 | 60 | 70 | 33 |

_{r.max}denotes the maximum crack spacing, S

_{r.min}denotes the minimum crack spacing and S

_{r.mean}denotes the mean crack spacing.

Beam ID | P_{cr} (kN) | P_{serv} (kN) | w_{serv} (mm) | Load (kN) at w = 0.33 mm | % of Pu |
---|---|---|---|---|---|

Control | 5.0 | 23.4 | 0.34 | 22 | 56 |

CBC8P1 | 10.9 | 42.5 | 0.18 | 56 | 79 |

CBC8P2 | 13.0 | 46.1 | 0.31 | 54 | 70 |

CBC10P1 | 12.6 | 49.0 | 0.28 | 58 | 71 |

CBC10P2 | 15.0 | 52.4 | 0.19 | 74 | 85 |

CBC10P2A | 16.5 | 63.1 | 0.21 | 76 | 72 |

_{cr}= 1st crack load, P

_{serv}= Service load (60% of the ultimate load), w

_{serv}= crack width at service load.

Parameter | Value |
---|---|

δ_{max} (mm) | 0.319 |

τ_{max−n} (mm) | 21 |

α | 0.65 |

α’ | −0.88 |

© 2016 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Darain, K.M.u.; Jumaat, M.Z.; Shukri, A.A.; Obaydullah, M.; Huda, M.N.; Hosen, M.A.; Hoque, N.
Strengthening of RC Beams Using Externally Bonded Reinforcement Combined with Near-Surface Mounted Technique. *Polymers* **2016**, *8*, 261.
https://doi.org/10.3390/polym8070261

**AMA Style**

Darain KMu, Jumaat MZ, Shukri AA, Obaydullah M, Huda MN, Hosen MA, Hoque N.
Strengthening of RC Beams Using Externally Bonded Reinforcement Combined with Near-Surface Mounted Technique. *Polymers*. 2016; 8(7):261.
https://doi.org/10.3390/polym8070261

**Chicago/Turabian Style**

Darain, Kh Mahfuz ud, Mohd Zamin Jumaat, Ahmad Azim Shukri, M. Obaydullah, Md. Nazmul Huda, Md. Akter Hosen, and Nusrat Hoque.
2016. "Strengthening of RC Beams Using Externally Bonded Reinforcement Combined with Near-Surface Mounted Technique" *Polymers* 8, no. 7: 261.
https://doi.org/10.3390/polym8070261