# Shear Strengthening of Reinforced Concrete Beams Using Engineered Cementitious Composites and Carbon Fiber-Reinforced Polymer Sheets

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Material Properties and Mix Proportions

^{®}-300 C provided by Sika (El-Obour City, Egypt), was employed. The fabric sheet’s specifications based on the manufacturer’s datasheet are presented in Table 4 [47]. The adhesive responsible for bonding the CFRP sheets is a two-component epoxy resin, Sikadur

^{®}-330. According to its product datasheet, this adhesive boasts an elasticity modulus of 4.5 GPa and a tensile strength of 30 MPa [48].

#### 2.2. Details of the Tested Specimens and Investigated Parameters

#### 2.3. Strengthening Procedures

#### 2.4. Test Setup and Instrumentation

## 3. Test Results and Discussion

_{cr}) with its corresponding deflection (Δ

_{cr}), the yielding load (P

_{y}) with its associated deflection (Δ

_{y}), the ultimate load (Pu) with its respective deflection (Δ

_{u}), the ductility index (DI), and the failure mode.

#### 3.1. Load Capacities

#### 3.2. Load–Deflection Relationships

_{u}by approximately 6.5%, 7.2%, and 10.4% for specimens employing full wrapping, inclined strips, and vertical strips, respectively, as detailed in Table 6. Furthermore, an escalation in the values of Δ

_{u}by 47.9% and 59.4% was observed for specimens utilizing full wrapping and inclined strips, respectively, while a reduction of about 21.7% was noted for specimens employing the vertical strip strengthening configuration. Specimens E-40-F-C-2, E-40-V-C-2, and E-40-I-C-2 reached their maximum loads at deflections of 11.43 mm, 5.41 mm, and 13.87 mm, respectively. Notably, all three reinforced specimens—E-40-F-C-2, E-40-V-C-2, and E-40-I-C-2—exhibited nearly identical stiffness, surpassing that of the reference beam.

#### 3.3. Modes of Failure

#### 3.4. Ductility

_{u}) to the deflection at the yielding load (Δ

_{y}) [50]. Within the first group, the DI values for beams E-20-F and E-40-F rose by roughly 10% and 16.4%, respectively, compared to the control beam. This indicates that the introduction of ECC layers of varying thicknesses enhanced the specimens’ ductile performance. In the second group of beams, the enhancements in ductility were observed to be 11.8%, 10%, and 21% for the full wrapping, vertical strip, and inclined strip configurations, respectively. Among these beams, the inclined strengthening configuration demonstrated the most pronounced ductile behavior.

## 4. Theoretical Code Formulation

#### 4.1. According to ACI 549

_{n}) of the strengthened beams is obtained as follows:

_{n}= V

_{c}+ V

_{FRCM}

_{c}and V

_{FRCM}are the amount of shear strengths provided by concrete and the strengthening layers, respectively. V

_{c}is determined experimentally as the reaction at the support of the tested beams [52].

_{cr}is the shear critical span. The involvement of the strengthening layer to the shear strength (V

_{FRCM}) is expected by adding the contributions from the fiber sheets (V

_{f}) to the related ECC (V

_{ECC}) as follows:

_{FRCM}= F (V

_{ECC}+ V

_{f})

_{cm}, t

_{m}, and d

_{f}are the ECC compressive strength (in MPa), the thickness of the ECC strips (in mm) taken as 20 mm and 40 mm for the beam specimens, and the effective depth of the ECC-CFRP shear reinforcement (269 mm for the current study), respectively. To determine the contribution of the CFRP and ECC-CFRP composite to the shear strength (V

_{f}), the equivalent shear-effective area of the CFRP is calculated according to Equation (6).

_{fv}= A

_{f,wrap}(sinα

_{wrap}+ cosα

_{wrap}) + A

_{f,weft}(sinα

_{weft}+ cosα

_{weft})

_{f,warp}, A

_{f,weft}, α

_{warp}, and α

_{weft}are the area and the orientation angle for the textile in the warp and weft directions, respectively. So, the contribution of the CFRP and ECC-CFRP composite to the shear strength (Vf) is calculated as follows:

_{f}= 2n A

_{fv}σ

_{fv}d

_{f}

_{fv}, and ε

_{fv}are the number of fabric plies placed in the composite (1 or 2) for the beams of this study, the tensile strength, and the tensile strain of the composite, respectively. According to ACI 549 [24], the effective tensile stress is expressed in terms of the effective tensile strain (ε

_{fv}) and the cracked tensile elastic modulus (E

_{f}), as shown in Equation (8):

_{fv}= E

_{f}ε

_{fv}

_{fv}) is considered as 0.004. Finally, the theoretical-predicted ultimate load of the specimens (${\mathrm{P}}_{\mathrm{u}}^{\mathrm{Th}}$) can be calculated as shown in Equation (9):

#### 4.2. According to ACI 440.2R-17

_{n}) can be determined by adding the shear strength of the externally bonded fabrics (V

_{f}) to the concrete (Vc), and the ECC composite (V

_{ECC}), according to ACI 318M −19 provisions [53].

_{n}= φ (V

_{c}+FV

_{ECC}+ ψ

_{f}V

_{f})

_{f}is another reduction factor for the FRP fabrics’ shear strength (taken as 0.85). The values of V

_{c}, F, and V

_{ECC}are calculated as previously mentioned (Equations (2)–(4)). According to ACI 440.2R-17 [51], the FRP composites are employed as interrupted strips in different patterns or used as full strips along the studied span of the beam. For more details, Figure 8 explains the variables used in the calculation of the FRP fabrics’ shear strength. According to ACI 440 [51], the shear strength of FRP fabrics (V

_{f}) is given as follows:

_{fv}= 2 n t

_{f}W

_{f}

_{fv}represents the area of FRP shear reinforcement; n, t

_{f}, w

_{f}are the number, the thickness, and the breadth of the FRP sheets. The inclination angle of FRP fabric to the longitudinal axis of the beam is α, d

_{fv}represents the effective depth of the FRP fabric, s

_{f}represents the spacing between FRP strips center to center, as shown in Figure 8, and f

_{fe}represents the tensile stress for the FRP fabric. This stress can be considered from Hook’s law via Equation (13):

_{fe}= ε

_{fe}E

_{f}

_{f}represents the tensile elastic modulus of FRP. The strengthening and wrapping configuration affect the ε

_{fe}value. The ε

_{fe}value is considered using the bond-reduction constant k

_{v}for U-wraps or side-bonded wraps.

_{fe}= k

_{v}ε

_{fu}≤ 0.004

_{e}), and is given in the following equation:

_{v}depends on the compressive strength of concrete, the number of FRP fabrics, and the thickness of FRP fabric (f

_{c}, n, and t

_{f}). Finally, k

_{1}and k

_{2}are two modification factors and are calculated using the subsequent equations:

## 5. Conclusions

- The CFRP-ECC composites improved the shear capacity of the RC beams with a value ranging from 61.1% to 160.1% compared to the reference specimen.
- The deformation of the strengthened beams was 2.31 times that of the control beam, which demonstrates the higher ductile performance of these beams.
- The common type of failure mode for the strengthened beams was debonding or partial debonding of the strengthening layers ended with shear or flexural cracks. However, for reference one, a clear shear crack failure occurred.
- The fully strengthened configuration for beams in groups G2 and G3 showed more improvements in terms of load capacity with respect to the vertical or inclined schemes. However, the inclined scheme showed the highest values for beams of groups G4 and G5.
- Theoretical analysis using the two code provisions (ACI 549 and ACI 440.2R-17) was recommended to calculate the ultimate load capacity for the tested beams.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Strengthening and mid-span section layouts. (All dimensions are in mm). (

**a**) Full wrapping strengthening. (

**b**) Vertical strip strengthening. (

**c**) Inclined strip strengthening.

**Figure 2.**Strengthening procedures of tested beams. (

**a**) Casting ECC plates. (

**b**) Roughened surfaces. (

**c**) Installation of CFRP layers. (

**d**) Addition of weights on plates.

**Figure 4.**Applied load–deflection relationship measured under the loading point. (

**a**) Group G1. (

**b**) Group G2. (

**c**) Group G3. (

**d**) Group G4. (

**e**) Group G5.

**Figure 5.**Failure modes of the tested specimens. (

**a**) Reference. (

**b**) E-20-F. (

**c**) E-40-F. (

**d**) E-20-F-C-1. (

**e**) E-20-V-C-1. (

**f**) E-20-I-C-1. (

**g**) E-40-F-C-1. (

**h**) E-40-F-C-1. (

**i**) E-40-F-C-1. (

**j**) E-20-F-C-2. (

**k**) E-20-V-C-2. (

**l**) E-20-I-C-2. (

**m**) E-40-F-C-2. (

**n**) E-40-V-C-2. (

**o**) E-40-I-C-2.

**Figure 7.**FRP composites wrapping configurations [51]. (

**a**) Completely wrapped. (

**b**) Three-sided “U-wrap”. (

**c**) Two sides.

**Figure 8.**Parameters of FRP composites required for calculating shear strength [51].

Material | Cement | Fly Ash | Fine Aggregate | Coarse Aggregate | Water | HRWR * | PP Fibers | W/C |
---|---|---|---|---|---|---|---|---|

RC | 360 | ---- | 670 | 1277 | 151 | ---- | ---- | 0.42 |

ECC | 877 | 598 | ---- | ---- | 420 | 12 | 16.5 | 0.48 |

Specimen | Compressive Strength (MPa) | Tensile Strength (MPa) |
---|---|---|

1 | 67.5 | 7.16 |

2 | 67 | 5.57 |

3 | 62.5 | 5.73 |

Mean | 65.67 | 6.15 |

Steel | Yield Strength Fy (MPa) | Ultimate Strength Fu (MPa) | Ultimate/Yield Strength | Modulus of Elasticity Es (GPa) |
---|---|---|---|---|

Stirrups | 299 | 458 | 1.53 | 196 |

Main reinforcement | 509 | 688 | 1.35 | 200 |

**Table 4.**Properties of CFRP [47].

Material | Area Density (Kg/m^{2}) | Nominal Thickness (mm) | Tensile Strength (MPa) | Elongation (%) | Elasticity Modulus (GPa) |
---|---|---|---|---|---|

SikaWrap^{®}-300 C | 0.304 | 0.167 | 4000 | 1.7% | 230 |

Group | Specimen | ECC Thickness (mm) | Matrix | CFRP Layers | Strengthening Scheme |
---|---|---|---|---|---|

Control | Reference | ---- | ---- | ---- | ---- |

G1 | E-20-F | 20 | ECC | ---- | Full |

E-40-F | 40 | ECC | ---- | Full | |

G2 | E-20-F-C-1 | 20 | CFRP-ECC | 1 | Full |

E-20-V-C-1 | 20 | CFRP-ECC | 1 | Vertical strips | |

E-20-I-C-1 | 20 | CFRP-ECC | 1 | Inclined strips | |

G3 | E-40-F-C-1 | 40 | CFRP-ECC | 1 | Full |

E-40-V-C-1 | 40 | CFRP-ECC | 1 | Vertical strips | |

E-40-I-C-1 | 40 | CFRP-ECC | 1 | Inclined strips | |

G4 | E-20-F-C-2 | 20 | CFRP-ECC | 2 | Full |

E-20-V-C-2 | 20 | CFRP-ECC | 2 | Vertical strips | |

E-20-I-C-2 | 20 | CFRP-ECC | 2 | Inclined strips | |

G5 | E-40-F-C-2 | 40 | CFRP-ECC | 2 | Full |

E-40-V-C-2 | 40 | CFRP-ECC | 2 | Vertical strips | |

E-40-I-C-2 | 40 | CFRP-ECC | 2 | Inclined strips |

Group | Specimen | P_{cr} (kN) | Δ_{cr} (mm) | P_{y} (kN) | Δ_{y} (mm) | P_{u} (kN) | Δ_{u} (mm) | DI | Mode of Failure |
---|---|---|---|---|---|---|---|---|---|

Control | Reference | 47.90 | 2.36 | 65.00 | 3.40 | 69.48 | 3.76 | 1.10 | Shear |

G1 | E-20-F | 53.60 | 2.51 | 96.47 | 4.46 | 111.90 | 5.40 | 1.21 | P. D |

E-40-F | 69.77 | 3.23 | 116.00 | 4.90 | 139.70 | 6.30 | 1.28 | P. D + Shear | |

G2 | E-20-F-C-1 | 62.25 | 3.09 | 127.80 | 6.43 | 143.00 | 7.90 | 1.23 | D + Shear |

E-20-V-C-1 | 62.48 | 3.11 | 112.50 | 5.21 | 122.50 | 6.31 | 1.21 | P. D in strips + Shear | |

E-20-I-C-1 | 61.07 | 3.98 | 105.40 | 5.97 | 136.80 | 7.96 | 1.33 | P. D in strips + Shear | |

G3 | E-40-F-C-1 | 83.20 | 4.34 | 135.00 | 6.63 | 168.80 | 13.50 | 2.04 | Flexural under the load |

E-40-V-C-1 | 80.61 | 3.61 | 112.80 | 5.20 | 131.20 | 6.56 | 1.26 | P. D in strips + Shear | |

E-40-I-C-1 | 75.42 | 2.82 | 127.30 | 5.24 | 168.20 | 13.48 | 2.57 | P. D in strips + Flexural | |

G4 | E-20-F-C-2 | 83.55 | 2.48 | 139.50 | 5.37 | 159.90 | 7.73 | 1.44 | P. D + Shear |

E-20-V-C-2 | 70.66 | 3.04 | 112.50 | 4.95 | 134.20 | 6.91 | 1.40 | D in strips + Shear | |

E-20-I-C-2 | 75.97 | 3.40 | 126.80 | 5.77 | 168.60 | 8.70 | 1.51 | P. D in strips + Flexural | |

G5 | E-40-F-C-2 | 99.67 | 3.33 | 132.80 | 4.61 | 170.30 | 11.43 | 2.48 | Flexural under the load |

E-40-V-C-2 | 85.34 | 2.53 | 122.30 | 3.76 | 148.20 | 5.41 | 1.44 | D in strips + Shear | |

E-40-I-C-2 | 81.40 | 2.70 | 140.70 | 4.66 | 180.70 | 13.87 | 2.98 | C.C + P. D in strips + Flexural |

_{cr}: cracking load; P

_{y}: yield load; P

_{u}: ultimate load; Δ

_{cr}: cracking deflection; Δ

_{y}: yield deflection; Δ

_{u}: ultimate deflection; DI: the ductility index; P. D: partial debonding; D: debonding; C.C: concrete crushing.

Group | Specimen | Experimental (P_{u}) | Theoretical (P_{u}) ACI 549 [24] | Theoretical (P_{u})ACI 440 [51] | ${\mathbf{P}}_{\mathbf{u}}/{\mathbf{P}}_{\mathbf{u}}^{\mathbf{T}\mathbf{h}}$ ACI 549 [24] | ${\mathbf{P}}_{\mathbf{u}}/{\mathbf{P}}_{\mathbf{u}}^{\mathbf{T}\mathbf{h}}$ ACI 440 [51] |
---|---|---|---|---|---|---|

Control | Reference | 69.48 | ---- | --- | ---- | --- |

G1 | E-20-F | 111.90 | 91.72 | 91.71 | 1.220 | 1.220 |

E-40-F | 139.70 | 113.96 | 113.95 | 1.226 | 1.226 | |

G2 | E-20-F-C-1 | 143.00 | 154.965 | 160.47 | 0.923 | 0.891 |

E-20-V-C-1 | 122.50 | 120.80 | 117.20 | 1.014 | 1.045 | |

E-20-I-C-1 | 136.80 | 128.32 | 134.99 | 1.066 | 1.013 | |

G3 | E-40-F-C-1 | 168.80 | 177.20 | 182.71 | 0.953 | 0.924 |

E-40-V-C-1 | 131.20 | 134.10 | 130.54 | 0.978 | 1.005 | |

E-40-I-C-1 | 168.20 | 140.00 | 146.71 | 1.200 | 1.146 | |

G4 | E-20-F-C-2 | 159.90 | 218.20 | 183.39 | 0.733 | 0.872 |

E-20-V-C-2 | 134.20 | 158.70 | 128.66 | 0.846 | 1.043 | |

E-20-I-C-2 | 168.6 | 175.41 | 152.92 | 0.961 | 1.103 | |

G5 | E-40-F-C-2 | 170.30 | 240.40 | 205.63 | 0.710 | 0.828 |

E-40-V-C-2 | 148.20 | 172.00 | 142.00 | 0.862 | 1.044 | |

E-40-I-C-2 | 180.70 | 187.14 | 164.64 | 0.966 | 1.098 |

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## Share and Cite

**MDPI and ACS Style**

Emara, M.; Salem, M.A.; Mohamed, H.A.; Shehab, H.A.; El-Zohairy, A.
Shear Strengthening of Reinforced Concrete Beams Using Engineered Cementitious Composites and Carbon Fiber-Reinforced Polymer Sheets. *Fibers* **2023**, *11*, 98.
https://doi.org/10.3390/fib11110098

**AMA Style**

Emara M, Salem MA, Mohamed HA, Shehab HA, El-Zohairy A.
Shear Strengthening of Reinforced Concrete Beams Using Engineered Cementitious Composites and Carbon Fiber-Reinforced Polymer Sheets. *Fibers*. 2023; 11(11):98.
https://doi.org/10.3390/fib11110098

**Chicago/Turabian Style**

Emara, Mohamed, Mohamed A. Salem, Heba A. Mohamed, Hamdy A. Shehab, and Ayman El-Zohairy.
2023. "Shear Strengthening of Reinforced Concrete Beams Using Engineered Cementitious Composites and Carbon Fiber-Reinforced Polymer Sheets" *Fibers* 11, no. 11: 98.
https://doi.org/10.3390/fib11110098