# Influence of Cross-Section Shape and FRP Reinforcement Layout on Shear Capacity of Strengthened RC Beams

^{*}

## Abstract

**:**

## 1. Introduction

_{c}(shear resistance of concrete), V

_{s}(shear resistance of steel stirrups) and V

_{f}(shear resistance provided by FRP). Regarding the last two contributions, each of them is evaluated by separately taking into account the orientation of each reinforcement, namely (β) for the FRP and (α) for the transverse reinforcement.

_{f}and V

_{s}.

_{f}, V

_{s}, and V

_{c}and the total shear force. The experimental results show that there is a significant contribution of the flange to the shear strength in the case of T-cross-sectional members. In some cases, it was found to be up to 45% of the total shear strength. None of the code models recognizes the effect of the flange in a T cross section as relevant in modifying member shear resistance.

## 2. Shear Models

#### 2.1. ACI 440.2R-17

_{c}), steel stirrup (V

_{s}) and FRP (V

_{f}) contributions. According to the symbol notation in Figure 1 and Abbreviations, V

_{c}(nominal shear strength provided by shear reinforcement) is calculated as:

_{c}= 0.167 f′c

^{0.5}b

_{w}d

_{s}(nominal shear strength provided by shear reinforcement) is calculated as:

_{s}= (A

_{v}f

_{yt}d)/s

_{f}= (A

_{fv}d

_{fv}f

_{fe}(sin β + cos β))/s

_{f}

_{f}equation, A

_{fv}= 2nt

_{f}w

_{f}, f

_{fe}= ε

_{fe}E

_{f}and different safety factors are used for different wrapping schemes. The shear strength of the retrofitted RC beam is equal to:

_{c}+ V

_{s}+ ψ

_{f}V

_{f})

_{f}= 0.95 while for other schemes ψ

_{f}= 0.85, while φ is a strength-reduction factor. The effective strain of the FRP (ɛ

_{fe}) is calculated based on the different configurations. It should not be more than 0.75 of the ultimate strain ε

_{fu}, while for the design it should be limited to 4 × 10

^{−3}. The FRP effective depth is considered as the distance between the centroid of tensile reinforcement and the top free edge of the FRP. It must be stressed that the ACI model takes into account the actual height of the FRP reinforcement by the parameter d

_{fv}(Figure 1).

_{fe}of partly wrapped sections, the ultimate strain of the FRP is multiplied by a bond-reduction factor k

_{v,}as ε

_{fe}= k

_{v}ɛ

_{fu}≤ 4 × 10

^{−3}. k

_{v}can be calculated as k

_{v}= k

_{1}k

_{2}L

_{e}/(11,900ɛ

_{fu}) ≤ 0.75, where the modification factors k

_{1}and k

_{2}can be calculated by using k

_{1}= (f′

_{c}/27)

^{2/3}and k

_{2}= (d

_{fv}− γL

_{e})/d

_{fv}(γ = 1 for the U-wrapped scheme and γ = 2 when both sides are wrapped), where the effective length is L

_{e}= 23,300/ (E

_{f}t

_{f})

^{0.58}.

#### 2.2. CNR Model

_{Rd,f}= (1/γ

_{Rd}) 0.9 d f

_{fed}2 t

_{f}(cot θ + cot β) (b

_{f}/p

_{f})sin

^{2}β

_{f}= $\overline{p}$

_{f}sin β represents the spacing of the FRP measured perpendicular to the direction of fiber. The shear capacity of the stirrup and concrete strut is given as:

_{Rd,s}= 0.9 d (A

_{sw}/s) f

_{ywd}(cot θ + cot α) sin α

_{Rd,c}= 0.9 d b α

_{c}0.5 f

_{cd}(cot α + cot θ)/(1 + cot

^{2}θ)

_{c}= 1 has to be retained for the beam, and the angle ψ, yet to be determined, can be introduced by replacing the angle α listed in the code, in order to stress that the evaluation of the shear strength of the compressed concrete strut is not a trivial issue, as will be shown below. The strengthened member shear resistance is computed as:

_{Rd}= min (V

_{Rd,s}+ V

_{Rd,f,}V

_{Rd,c})

_{Rd,s}and V

_{Rd,f}are the weights.

#### 2.3. Colajanni et al. Model

_{f}= σ

_{f}/f

_{fu,}and $\tilde{\sigma}$

_{s}= σ

_{s}/f

_{yt}are the non-dimensional stresses of the FRP reinforcement and steel stirrups, respectively. R is the coefficient for effective strain and stress for the FRP at failure, where the effective stress is f

_{fe}= f

_{fu}R = E

_{f}ɛ

_{fe}and the effective strain is ɛ

_{fe}= ɛ

_{fu}R; f

_{fu}is the ultimate stress of the fiber; r is the efficiency coefficient for the steel stirrups, which considers the efficiency of the steel stirrups involved by the shear-critical crack; β represents the angle of the FRP and α represents the angle of the shear reinforcement with the beam axis.

_{fv}f

_{fu}/(b

_{w}s

_{f}0.5 f

_{c}) sin β + r A

_{v}f

_{yt}/(b

_{w}s 0.5 f

_{c}) sin α)

^{−1}– 1)

^{1/2}

_{sw}and ω

_{fw}, respectively.

_{sw}and ω

_{fw}values):

_{f}= $\tilde{\sigma}$

_{s}=1, while the stresses on the concrete strut can be obtained by using Equation (13).

_{sw}and ω

_{fw}values):

_{f}= $\tilde{\sigma}$

_{s}= $\tilde{\sigma}$

_{c}= 1.

_{sw}and ω

_{fw}values):

_{f}= 1 or by Equation (11), considering that the yielding in the steel stirrups is attained, having $\tilde{\sigma}$

_{s}= 1. In Appendix B, the above three different cases are elucidated by calculation examples.

## 3. Reduction Factors for Steel Stirrups “r”

_{fe,s}= ɛ

_{fe}cos(α − β) and the yield strain of the steel stirrup (ɛ

_{syw}). If ɛ

_{fe,s}/ɛ

_{syw}≤ 1.33, then r = 0.75 ɛ

_{fe,s}/ɛ

_{syw}, otherwise it is considered as r = 1.

## 4. Effectiveness Factor “R”

_{1}, R

_{2}, R

_{3}, R

_{4}), which represent different modes of failure. R

_{1}considers the tensile failure of the FRP, while R

_{2}and R

_{3}represent the debonding phenomenon and failure of the FRP due to shear crack width, respectively. Lastly, R

_{4}considers failure due to peeling of the concrete cover.

_{1}= 0.56(ρ

_{f}E

_{f})

^{2}− 1.22(ρ

_{f}E

_{f}) + 0.78

_{2}= [(f

_{ck})

^{2/3}(d

_{fv}− ηL

_{e}) [738.93 − 4.06(E

_{f}t

_{f})]]/ε

_{fu}d

_{fv}10

^{6}

_{3}= 6 × 10

^{−3}/ε

_{fu}

_{4}= (2f

_{ct}A

_{c}cos

^{2}βb

_{c,v})/(n

_{f}t

_{f}L

_{f}E

_{f}[(h

_{f}− L

_{e})/(h

_{f})]b

_{f}ε

_{fu})

_{5}and R

_{6}). One represents the tensile rupture of the FRP across the crack, and the other represents the debonding failure of the FRP due to insufficient bond length.

_{5}= (1 + (d − d

_{fv})/z)/2

_{max}/L

_{e})

_{6}= (σ

_{f,max}/E

_{f}ε

_{fu}) × (2/π λ × ((1−cos π λ/2)/(sin π λ /2)))

_{6}= (σ

_{f,max}

_{/}E

_{f}ε

_{fu}) × (1 − (π−2)/π λ)

## 5. Description of Data Sets and Analysis Steps

_{exp}of the data sets was used. v

_{the}is the analytical assessment of dimensionless shear, which for each model was calculated using all six different R-factor models, while v

_{exp}is the experimental value which can be expressed as v

_{exp}= V

_{exp}/(b

_{w}0.9d 0.5 f

_{c}). τ

_{avg}is the average value of the ratio τ

_{avg}= V

_{exp}/V

_{the}.

- Every model + R factor deals with six different member sets, which differ in the type of cross section (R and T) and wrapping scheme (U, U*, F and U/F).
- For each data set, the results provided by the Colajanni et al. model with the six different formulations of the R effectiveness factor are discussed.
- For each of the three models: in the first approach, to cover the influence of the cross-section shape, a comparison is made between the R and T sections (i.e., between RU and TU, between RU* and TU*, between RF and TU/F within Data Set 1 and within Data Set 2).
- For each of the three models: in the second approach, to recognize the influence of the FRP inclination angle, a comparison is made of Data Set 1 against Data Set 2 for the effectiveness of each model in the strength assessment of members having the same cross-section shape but with different inclination angles (i.e., RU of DS1 and RU of DS2, RU*of DS1 and RU* of DS2, RF of DS1 and RF of DS2).

## 6. Results and Discussion

_{Avg}= V

_{exp}/V

_{the}and its CoV are analyzed. In the reliability assessment, R as proposed by ACI [18], CNR [21], fib [35] and Mofidi and Challaal [36] (M&C) is used in its original form, considering the steel-stirrup reduction factor equal to r = 1, as well as two R-factor models proposed in Colajanni et al. [19] including the steel-stirrup reduction factor.

_{avg}= 0.97) were obtained, while the worst results were obtained in the case of using the R factor of fib.

_{avg}= 0.95, very close to the best ones.

_{avg}= 0.61) as well as the largest scattering of data was observed when the R factor proposed by the fib model was used. Similar results can be observed in the case of α = β.

_{avg}= 0.87, CoV = 0.14) was observed for the effectiveness factor proposed by Chen and Teng. This unfavorable large overestimation was less marked in the models with the effectiveness factors of Khalifa and Nanni + Pellegrino and Modena, or Chen and Teng because of the introduction of the “r” factor. In Table 2, the results are further subdivided into the two databases described in Section 6.1, Section 6.2 and Section 6.3.

#### 6.1. Conclusion Based on 1st Approach for DS1 (α = β)

**τ**was close to unity. This is due to the fact that for RF and TU/F, some approaches underestimated while others overestimated the shear strength. It was observed that overall, more accurate estimation of the shear strength was obtained for RF and TU/F as compared to the previous comparisons, with less dispersion. This is due to the fact that the effective fiber strength of the completely wrapped sections was more accurately estimated than that of the partially wrapped ones, and possibly the partial ineffectiveness of the anchorage in the TU/F section was compensated by the flange contribution.

_{avg}#### 6.2. Conclusion Based on First Approach for DS 2 (α ≠ β)

#### 6.3. Conclusion Based on the 2nd Approach

**τ**in DS2 than in DS1, but with less of a dispersion of the data, while the average overestimation for RU* was larger in the CNR model than in the Colajanni one. This is due to the ability of the Colajanni et al. model to take into account the difference of steel and FRP reinforcement orientation, and to properly evaluate their contributions in determining the inclination of the concrete strut.

_{avg}**τ**, but more scattering of the data as compared to DS2. In the case of TU, excellent results were achieved in DS2.

_{avg}## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

A_{fv}, A_{sw} | Area of steel stirrups |

R | Reduction coefficient (ratio of effective average stress/strain in FRP sheet to its ultimate strength) |

R | Rectangular beam |

T | T beam |

V_{c} | Shear resistance of concrete |

V_{s} | Shear resistance of steel stirrups |

V_{f} | Shear resistance provided by FRP |

V_{Rd,f} | FRP contribution to the shear capacity |

V_{Rd,s} | Steel contribution to the shear capacity |

V_{Rd,c} | Steel contribution to the shear capacity |

τ_{avg} | Average shear strength (τ_{avg} = V_{exp}/V_{the}) |

α, β | Angle of steel and FRP transverse reinforcement |

a | Shear span |

b_{f}, b_{w} | Web widths of FRP and concrete |

d, d_{fv} | Effective depth of beam and FRP |

f_{c}, f′_{c} | Characteristic compressive strength of concrete |

E_{f}, E_{sw} | FRP and steel elastic modulus |

f_{bd} | Design resistance of the adhesion between FRP and concrete |

f_{ywd} | Design steel stirrup strength |

f_{fed} | Effective design strength of the FRP shear reinforcement |

f_{yt} | Characteristic yield strength of transverse reinforcement |

f_{fe} | Effective stress in the FRP; stress level attained at section failure |

f_{fu} | Design ultimate tensile strength of FRP |

f_{ck}, f_{ctm} | Characteristic cylinder compressive and mean concrete tensile strength of concrete |

f_{sy}, f_{yt} | Yielding stresses of longitudinal steel reinforcement and steel stirrups |

h_{w} | Beam cross-section height |

k_{v}, k_{1}, k_{2} | Bond-reduction coefficient and modification factors |

L_{max}, L_{e} | Maximum and effective length |

r | Reduction factor for steel stirrups |

w_{f} | Spacing, thickness, and width of the FRP strip |

s_{f}, t_{f} | Spacing and thickness of FRP strip |

$\overline{s}$_{f} | Spacing of FRP strips measured perpendicular to FRP strip axis |

s | Spacing of the steel stirrups |

V, V_{n} | External, and nominal shear forces |

v_{exp}, v_{the} | Experimental and theoretical nondimensional shear strengths, where v _{exp} = (V_{exp}/(b_{w} 0.9d 0.5 f_{c})) |

z | Inner lever arm |

ɛ_{syw} | Yield strain of steel stirrup |

ɛ_{fe} | Effective FRP strain |

ɛ_{fu} | Nominal FRP strain |

ɛ_{fe,s} | Effective strain in the direction of transverse steel reinforcement |

θ | Angle between member axis and concrete stress |

λ | Maximum bond length (normalized) |

$\tilde{\sigma}$_{c} | Stress of the web concrete (non-dimensional) |

$\tilde{\sigma}$_{f} | Tensile stress of transverse FRP (non-dimensional) |

$\tilde{\sigma}$_{s} | Stress in transverse reinforcement (non-dimensional) |

φ | Angle between the FRP reinforcement direction and steel stirrups |

ρ_{f}, ρ_{s} | Transverse geometrical ratio of fiber and steel reinforcement |

σ_{f,max} | Maximum stress along the bond length |

ψ | Fictitious angle of reinforcement incorporating FRP and transverse steel reinforcement |

ψ_{f}ω _{fw,} ω_{sw}ω _{fw}ω _{sw} | Reduction factor equal to 0.95 in case of wrapping scheme, 0.85 for the other schemes Mechanical ratio of transverse FRP and stirrups reinforcement (2b _{f}t_{f}f_{fu})/(b_{w} s_{f} sin β f_{c})(A _{v} f_{yt})/(b_{w} s sin α f_{c}) |

## Appendix A. Specimen Details and Experimental Results

f_{c} | b_{w} | d | ρ_{s} | f_{yt} | E_{sw} | t_{f} | β | ρ_{f} | f_{fu} | E_{f} | wrap | v_{exp} | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Specimen no. | (MPa) | (mm) | (mm) | a/d | (%) | (MPa) | (GPa) | (mm) | (°) | (%) | (MPa) | (GPa) | U,C | (-) | |

Sato et al. (1997) [37] | No.2 | 35.7 | 150 | 240 | 2.5 | 0.42 | 387 | 183 | 0.11 | 90 | 0.15 | 3480 | 230 | T, U | 0.39 |

No.3 | 35.3 | 150 | 240 | 2.5 | 0.42 | 387 | 183 | 0.11 | 90 | 0.15 | 3480 | 230 | T, U/C | 0.46 | |

Deniaud & Cheng (2001) [38] | T6S4-C90 | 44.1 | 140 | 528 | 2.8 | 0.10 | 520 | 260 | 0.11 | 90 | 0.08 | 3400 | 230 | T, U | 0.19 |

T6S4-G90 | 44.1 | 140 | 528 | 2.8 | 0.10 | 520 | 260 | 1.80 | 90 | 2.57 | 106 | 18 | T, U | 0.20 | |

T6S2-C90 | 44.1 | 140 | 528 | 2.8 | 0.20 | 520 | 260 | 0.11 | 90 | 0.08 | 3400 | 230 | T, U | 0.21 | |

Deniaud & Cheng (2003) [39] | T4S4-G90 | 30.0 | 140 | 362 | 3.0 | 0.10 | 520 | 200 | 1.80 | 90 | 2.57 | 106 | 18 | T, U | 0.30 |

T4S2-G90 | 30.3 | 140 | 362 | 3.0 | 0.20 | 520 | 200 | 1.80 | 90 | 2.57 | 106 | 18 | T, U | 0.33 | |

T4S2-C45 | 29.4 | 140 | 362 | 3.0 | 0.20 | 520 | 200 | 0.70 | 45 | 0.50 | 442 | 45 | T, U | 0.33 | |

T4S2-Tri | 30.4 | 140 | 362 | 3.0 | 0.20 | 520 | 200 | 2.10 | 60 | 3.00 | 124 | 8 | T, U | 0.35 | |

Bousselham & Chaallal (2006) [40] | SB-S1-0.5L | 25.0 | 152 | 356 | 3.0 | 0.38 | 650 | 215 | 0.06 | 90 | 0.08 | 3100 | 243 | T,U | 0.46 |

SB-S1-1L | 25.0 | 152 | 356 | 3.0 | 0.38 | 650 | 215 | 0.11 | 90 | 0.14 | 3100 | 243 | T, U | 0.42 | |

SB-S1-2L | 25.0 | 152 | 356 | 3.0 | 0.38 | 650 | 215 | 0.21 | 90 | 0.28 | 3100 | 243 | T, U | 0.44 | |

Pellegrino & Modena (2006) [24] | A-U1-C-17 | 41.4 | 150 | 250 | 3.0 | 0.39 | 534 | 210 | 0.17 | 90 | 0.22 | 3450 | 230 | R, U | 0.34 |

A-U1-C-20 | 41.4 | 150 | 250 | 3.0 | 0.34 | 534 | 210 | 0.17 | 90 | 0.22 | 3450 | 230 | R, U | 0.32 | |

A-U1-S-17 | 41.4 | 150 | 250 | 3.0 | 0.39 | 534 | 210 | 0.17 | 90 | 0.22 | 3450 | 230 | R, U | 0.35 | |

A-U1-S-20 | 41.4 | 150 | 250 | 3.0 | 0.34 | 534 | 210 | 0.17 | 90 | 0.22 | 3450 | 230 | R, U | 0.34 | |

A-U2-C-17 | 41.4 | 150 | 250 | 3.0 | 0.39 | 534 | 210 | 0.33 | 90 | 0.44 | 3450 | 230 | R, U | 0.35 | |

A-U2-C-20 | 41.4 | 150 | 250 | 3.0 | 0.34 | 534 | 210 | 0.33 | 90 | 0.44 | 3450 | 230 | R, U | 0.33 | |

A-U2-S-17 | 41.4 | 150 | 250 | 3.0 | 0.39 | 534 | 210 | 0.33 | 90 | 0.44 | 3450 | 230 | R, U | 0.31 | |

A-U2-S-20 | 41.4 | 150 | 250 | 3.0 | 0.34 | 534 | 210 | 0.33 | 90 | 0.44 | 3450 | 230 | R, U | 0.30 | |

Leung et al. (2007) [41] | SB-U1 | 27.4 | 75 | 155 | 2.9 | 0.28 | 550 | 210 | 0.11 | 90 | 0.10 | 4200 | 235 | R, U | 0.45 |

SB-F1 | 27.4 | 75 | 155 | 2.9 | 0.28 | 550 | 210 | 0.11 | 90 | 0.10 | 4200 | 235 | R, C | 0.46 | |

SB-F2 | 27.4 | 75 | 155 | 2.9 | 0.28 | 550 | 210 | 0.11 | 90 | 0.10 | 4200 | 235 | R, C | 0.46 | |

MB-U1 | 27.4 | 150 | 305 | 3.0 | 0.28 | 550 | 210 | 0.22 | 90 | 0.10 | 4200 | 235 | R, U | 0.27 | |

MB-U2 | 27.4 | 150 | 305 | 3.0 | 0.28 | 550 | 210 | 0.22 | 90 | 0.10 | 4200 | 235 | R, U | 0.28 | |

MB-F1 | 27.4 | 150 | 305 | 3.0 | 0.28 | 550 | 210 | 0.22 | 90 | 0.10 | 4200 | 235 | R, C | 0.42 | |

MB-F2 | 27.4 | 150 | 305 | 3.0 | 0.28 | 550 | 210 | 0.22 | 90 | 0.10 | 4200 | 235 | R, C | 0.44 | |

LB-U1 | 27.4 | 300 | 660 | 2.7 | 0.14 | 550 | 210 | 0.44 | 90 | 0.10 | 4200 | 235 | R, U | 0.23 | |

LB-U2 | 27.4 | 300 | 660 | 2.7 | 0.14 | 550 | 210 | 0.44 | 90 | 0.10 | 4200 | 235 | R, U | 0.23 | |

LB-F1 | 27.4 | 300 | 660 | 2.7 | 0.14 | 550 | 210 | 0.44 | 90 | 0.10 | 4200 | 235 | R, C | 0.36 | |

LB-F2 | 27.4 | 300 | 660 | 2.7 | 0.14 | 550 | 210 | 0.44 | 90 | 0.10 | 4200 | 235 | R, C | 0.36 | |

Monti & Liotta (2007) [12] | UF90 | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 90 | 0.18 | 2600 | 390 | R, U | 0.25 |

US60 | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 60 | 0.08 | 2600 | 390 | R, U | 0.22 | |

US45+ | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.09 | 2600 | 390 | R, U | 0.25 | |

US45++ | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.06 | 2600 | 390 | R, U* | 0.26 | |

UF45+ A | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.12 | 2600 | 390 | R, U* | 0.33 | |

UF45++ B | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.12 | 2600 | 390 | R, U* | 0.34 | |

UF45++ C | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.12 | 2600 | 390 | R, U* | 0.36 | |

US45+ D | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.09 | 2600 | 390 | R, U* | 0.32 | |

US45++ E | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.09 | 2600 | 390 | R, U* | 0.32 | |

US45++ F | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.09 | 2600 | 390 | R, U* | 0.29 | |

WS45+ | 11.0 | 250 | 410 | 3.5 | 0.10 | 500 | 210 | 0.22 | 45 | 0.06 | 2600 | 390 | R, C | 0.31 | |

USVA | 10.6 | 250 | 400 | 3.5 | 0.10 | 500 | 200 | 0.22 | 45 | 0.09 | 3000 | 390 | R, U | 0.25 | |

USVA+ | 10.6 | 250 | 400 | 3.5 | 0.10 | 500 | 200 | 0.22 | 45 | 0.09 | 3000 | 390 | R, U | 0.28 | |

Pellegrino & Modena (2008) [32] | B-U1-C-14 | 46.2 | 150 | 240 | 3.0 | 0.48 | 534 | 210 | 0.17 | 90 | 0.22 | 3450 | 230 | R,U | 0.34 |

B-U2-C-14 | 46.2 | 150 | 240 | 3.0 | 0.48 | 534 | 210 | 0.33 | 90 | 0.44 | 3450 | 230 | R, U | 0.35 | |

B-U1-C-17 | 46.2 | 150 | 240 | 3.0 | 0.39 | 534 | 210 | 0.17 | 90 | 0.22 | 3450 | 230 | R, U | 0.32 | |

B-U2-C-17 | 46.2 | 150 | 240 | 3.0 | 0.39 | 534 | 210 | 0.33 | 90 | 0.44 | 3450 | 230 | R, U | 0.33 | |

Grande et al. (2009) [33] | RS4Wa | 21.0 | 250 | 411 | 3.4 | 0.10 | 476 | 210 | 0.19 | 90 | 0.15 | 2600 | 392 | R, C | 0.26 |

RS3Wa | 21.0 | 250 | 411 | 3.4 | 0.13 | 476 | 210 | 0.19 | 90 | 0.15 | 2600 | 392 | R, C | 0.34 | |

RS2Wa | 21.0 | 250 | 411 | 3.4 | 0.20 | 476 | 210 | 0.19 | 90 | 0.15 | 2600 | 392 | R, C | 0.31 | |

RS4Ub | 21.0 | 250 | 411 | 3.4 | 0.10 | 476 | 210 | 0.19 | 90 | 0.15 | 2600 | 392 | R, U* | 0.23 | |

RS3Ua | 21.0 | 250 | 411 | 3.4 | 0.13 | 476 | 210 | 0.19 | 90 | 0.15 | 2600 | 392 | R, U* | 0.28 | |

RS2Ua | 21.0 | 250 | 411 | 3.4 | 0.20 | 476 | 210 | 0.19 | 90 | 0.15 | 2600 | 392 | R, U* | 0.29 | |

Belarbi et al. (2012) [16] | RC-8-S90-NA | 20.7 | 457 | 831 | 3.3 | 0.15 | 276 | 200 | 0.22 | 90 | 0.06 | 3792 | 228 | T, U | 0.24 |

RC-8-S90-DMA | 23.8 | 457 | 831 | 3.3 | 0.15 | 276 | 200 | 0.22 | 90 | 0.06 | 3792 | 228 | T, U* | 0.23 | |

RC-12-S90-NA | 28.9 | 457 | 831 | 3.3 | 0.10 | 276 | 200 | 0.22 | 90 | 0.06 | 3792 | 228 | T, U | 0.15 | |

RC-12-S90-DMA | 30.5 | 457 | 831 | 3.3 | 0.10 | 276 | 200 | 0.22 | 90 | 0.06 | 3792 | 228 | T, U* | 0.18 | |

RC-12-S90-PC | 19.2 | 457 | 831 | 3.3 | 0.10 | 276 | 200 | 0.22 | 90 | 0.06 | 3792 | 228 | T, U* | 0.29 | |

RC-12-S90-HS-PC | 18.3 | 457 | 831 | 3.3 | 0.10 | 276 | 200 | 0.22 | 90 | 0.06 | 3792 | 228 | T, U* | 0.27 | |

Panda et al.(2013) [42] | S300-1L-SZ-U-90 | 40.4 | 100 | 230 | 3.2 | 0.19 | 252 | 200 | 0.36 | 90 | 0.72 | 160 | 13 | T, U | 0.22 |

S300-1L-SZ-UA-90 | 40.4 | 100 | 230 | 3.2 | 0.19 | 252 | 200 | 0.36 | 90 | 0.72 | 160 | 13 | T, U | 0.23 | |

S200-1L-SZ-U-90 | 42.1 | 100 | 230 | 3.2 | 0.28 | 252 | 200 | 0.36 | 90 | 0.72 | 160 | 13 | T, U | 0.22 | |

S200-1L-SZ-UA-90 | 42.1 | 100 | 230 | 3.2 | 0.28 | 252 | 200 | 0.36 | 90 | 0.72 | 160 | 13 | T, U | 0.23 | |

Baggio et al. (2014) [43] | 6-G-N | 50.1 | 150 | 310 | 2.9 | 0.21 | 384 | 200 | 0.51 | 90 | 0.34 | 575 | 26 | R, U | 0.16 |

7-PD-G-N | 50.1 | 150 | 310 | 2.9 | 0.21 | 384 | 200 | 0.51 | 90 | 0.34 | 575 | 26 | R, U | 0.15 | |

8-PD-G-CA | 50.1 | 150 | 310 | 2.9 | 0.21 | 384 | 200 | 0.51 | 90 | 0.34 | 575 | 26 | R, U* | 0.15 | |

9-PD-G-GA | 50.1 | 150 | 310 | 2.9 | 0.21 | 384 | 200 | 0.51 | 90 | 0.34 | 575 | 26 | R, U* | 0.16 | |

Colalillo & Sheikh (2014) [44] | S5-US | 47.6 | 400 | 545 | 3.1 | 0.07 | 501 | 195 | 1.00 | 90 | 0.25 | 961 | 95 | R, U* | 0.11 |

S5-UA | 47.6 | 400 | 545 | 3.1 | 0.07 | 501 | 195 | 1.00 | 90 | 0.50 | 961 | 95 | R, U | 0.13 | |

S5-CS | 47.6 | 400 | 545 | 3.1 | 0.07 | 501 | 195 | 1.00 | 90 | 0.25 | 961 | 95 | R, C | 0.16 | |

S2-US | 47.5 | 400 | 545 | 3.1 | 0.14 | 501 | 195 | 1.00 | 90 | 0.25 | 961 | 95 | R, U* | 0.13 | |

S2-UA | 47.5 | 400 | 545 | 3.1 | 0.14 | 501 | 195 | 1.00 | 90 | 0.50 | 961 | 95 | R, U | 0.15 | |

Ozden et al. (2014) [45] | FBwoA-CFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.13 | 90 | 0.05 | 4300 | 238 | T, U | 0.27 |

FBwA-CFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.13 | 90 | 0.05 | 4300 | 238 | T, U/C | 0.36 | |

PBwA-CFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.13 | 90 | 0.05 | 4300 | 238 | U, U/C | 0.29 | |

FBwoA-GFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.16 | 90 | 0.06 | 3400 | 73 | T, U | 0.27 | |

FBwA-GFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.16 | 90 | 0.06 | 3400 | 73 | T, U/C | 0.34 | |

PBwA-GFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.16 | 90 | 0.06 | 3400 | 73 | T, U/C | 0.34 | |

FBwoA-Hi-CFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.14 | 90 | 0.05 | 2600 | 640 | T, U | 0.24 | |

FBwA-Hi-CFRP | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.14 | 90 | 0.05 | 2600 | 640 | T, U/C | 0.27 | |

PBw-Hi-C | 12.4 | 120 | 339 | 3.8 | 0.14 | 249 | 200 | 0.14 | 90 | 0.05 | 2600 | 640 | T, U/C | 0.31 | |

Mofidi & Chaallal (2014) [36] | WT-ST-50 | 31.0 | 152 | 350 | 3.0 | 0.38 | 540 | 206 | 0.11 | 90 | 0.07 | 3450 | 230 | T, U | 0.33 |

WT-ST-70 | 31.0 | 152 | 350 | 3.0 | 0.38 | 540 | 206 | 0.11 | 90 | 0.10 | 3450 | 230 | T, U | 0.34 | |

WT-SH-100 | 31.0 | 152 | 350 | 3.0 | 0.38 | 540 | 206 | 0.11 | 90 | 0.14 | 3450 | 230 | T, U | 0.34 | |

Mofidi et al. (2014) [46] | S1-LS-NE | 33.7 | 152 | 350 | 3.0 | 0.38 | 650 | 205 | 2.00 | 90 | 0.60 | 1350 | 90 | T, U | 0.34 |

S1-LS-PE | 33.7 | 152 | 350 | 3.0 | 0.38 | 650 | 205 | 2.00 | 90 | 0.60 | 1350 | 90 | T, U* | 0.37 | |

S1-EB-NA | 33.7 | 152 | 350 | 3.0 | 0.38 | 650 | 205 | 0.11 | 90 | 0.14 | 3450 | 230 | T, U | 0.36 | |

El-Saikaly et al. (2015) [47] | S1-EB | 28.0 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 0.38 | 90 | 0.50 | 894 | 65 | T, U | 0.32 |

S1-LS | 28.0 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 1.40 | 90 | 0.21 | 2250 | 120 | T, U | 0.30 | |

S1-LS-Rope | 28.0 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 1.40 | 90 | 0.21 | 2250 | 120 | T, U/C | 0.38 | |

S3-EB | 28.0 | 152 | 350 | 3.0 | 0.38 | 580 | 200 | 0.38 | 90 | 0.50 | 894 | 65 | T, U | 0.38 | |

S3-LS | 28.0 | 152 | 350 | 3.0 | 0.38 | 580 | 200 | 1.40 | 90 | 0.21 | 2250 | 120 | T, U | 0.36 | |

S3-LS-Rope | 28.0 | 152 | 350 | 3.0 | 0.38 | 580 | 200 | 1.40 | 90 | 0.21 | 2250 | 120 | T, U/C | 0.42 | |

Qin et al. (2015) [48] | S00 | 29.6 | 125 | 295 | 3.1 | 0.29 | 542 | 210 | 1.00 | 90 | 1.60 | 986 | 96 | T, U | 0.37 |

Chen et al. (2016) [49] | S8-U | 46.1 | 200 | 320 | 3.0 | 0.25 | 416 | 200 | 0.17 | 90 | 0.08 | 4361 | 226 | T, U | 0.23 |

S8-UFA1 | 46.1 | 200 | 320 | 3.0 | 0.25 | 416 | 200 | 0.17 | 90 | 0.08 | 4361 | 226 | T, U* | 0.24 | |

S8-UFA2 | 46.1 | 200 | 320 | 3.0 | 0.25 | 416 | 200 | 0.17 | 90 | 0.08 | 4361 | 226 | T, U* | 0.28 | |

Frederick et al. (2017) [50] | TB2 | 27.2 | 130 | 235 | 3.2 | 0.17 | 415 | 200 | 0.15 | 90 | 0.23 | 1400 | 119 | T, U | 0.37 |

TB4 | 27.2 | 130 | 235 | 3.2 | 0.17 | 415 | 200 | 0.15 | 90 | 0.23 | 1400 | 119 | T, U* | 0.42 | |

El-Saikaly et al. (2017) [51] | EBS-BL | 28.0 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 0.38 | 90 | 0.50 | 894 | 65 | T, U* | 0.37 |

EBS-ER | 28.0 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 0.38 | 90 | 0.50 | 894 | 65 | T, U* | 0.40 | |

EBL-RF | 28.0 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 2.00 | 90 | 0.30 | 1350 | 90 | T, U/C | 0.4 | |

EBS-NA | 28 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 0.38 | 90 | 0.5 | 894 | 65 | T, U | 0.32 | |

EBL-NA | 28 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 2.00 | 90 | 0.3 | 1350 | 90 | T, U | 0.30 | |

EBL-RW | 28 | 152 | 350 | 3.0 | 0.25 | 580 | 200 | 2.00 | 90 | 0.3 | 1350 | 90 | T, U/C | 0.38 | |

Nguyen-Minh et al. (2018) [52] | P-A1-2.3-C | 30.6 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.00 | 90 | 0.83 | 986 | 96 | T, U | 0.41 |

P-A1-2.3-G | 30.6 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.30 | 90 | 1.08 | 575 | 26 | T, U | 0.40 | |

P-A1-2.3-G-Cont. | 30.6 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.30 | 90 | 2.17 | 575 | 26 | T, U | 0.43 | |

P-A1-2.3-C-Cont. | 30.6 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.00 | 90 | 1.67 | 986 | 96 | T, U | 0.45 | |

P-A2-2.3-C | 30.6 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 2.00 | 90 | 1.67 | 986 | 96 | T, U | 0.43 | |

P-B1-2.3-C | 44.4 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.00 | 90 | 0.83 | 986 | 96 | T, U | 0.32 | |

P-B1-2.3-G | 44.4 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.30 | 90 | 1.08 | 575 | 26 | T, U | 0.32 | |

P-B1-2.3-G-Cont. | 44.4 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.30 | 90 | 2.17 | 575 | 26 | T, U | 0.34 | |

P-B1-2.3-C-Cont. | 44.4 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.00 | 90 | 1.67 | 986 | 96 | T, U | 0.36 | |

P-B2-2.3-C | 44.4 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 2.00 | 90 | 1.67 | 986 | 96 | T, U | 0.34 | |

P-C1-2.3-C | 58.7 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.00 | 90 | 0.83 | 986 | 96 | T, U | 0.29 | |

P-C1-2.3-G | 58.7 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.30 | 90 | 1.08 | 575 | 26 | T, U | 0.27 | |

P-C1-2.3-G-Cont. | 58.7 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.30 | 90 | 2.17 | 575 | 26 | T, U | 0.31 | |

P-C1-2.3-C-Cont. | 58.7 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 1.00 | 90 | 1.67 | 986 | 96 | T, U | 0.32 | |

P-C2-2.3-C | 58.7 | 120 | 406 | 2.3 | 0.16 | 342 | 205 | 2.00 | 90 | 1.67 | 986 | 96 | T, U | 0.30 | |

Oller et al. (2019) [20] | M1-a | 42.8 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.04 | 3400 | 230 | T, U | 0.15 |

M1-b | 42.8 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.04 | 3400 | 230 | T, U | 0.15 | |

M1A | 39.0 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.04 | 3400 | 230 | T, U* | 0.16 | |

M1B | 38.5 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.04 | 3400 | 230 | T, U* | 0.17 | |

M2A | 39.0 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.07 | 3400 | 230 | T, U* | 0.21 | |

M2B | 38.5 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.07 | 3400 | 230 | T, U* | 0.21 | |

H1-a | 44.4 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.04 | 3400 | 230 | T, U | 0.15 | |

H2-a | 44.4 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.07 | 3400 | 230 | T, U | 0.19 | |

H2-b | 49.7 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.07 | 3400 | 230 | T, U | 0.17 | |

H2A | 44.7 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.07 | 3400 | 230 | T, U* | 0.19 | |

H2B | 49.6 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.07 | 3400 | 230 | T, U* | 0.17 | |

H3A | 44.7 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.17 | 3400 | 230 | T, U* | 0.23 | |

H3B | 49.6 | 200 | 493 | 3.0 | 0.12 | 646 | 200 | 0.17 | 90 | 0.17 | 3400 | 230 | T, U* | 0.21 | |

Alzate et al. (2013) [53] | U90S5-a(L) | 37.0 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.14 | 4000 | 240 | R, U | 0.16 |

U90S5-a(S) | 37.0 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.14 | 4000 | 240 | R, U | 0.14 | |

U90S5-b(L) | 28.0 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.14 | 4000 | 240 | R, U | 0.21 | |

U90S5-b(S) | 28.0 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.14 | 4000 | 240 | R, U | 0.20 | |

U90C5-a(L) | 24.5 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.23 | 4000 | 240 | R, U | 0.22 | |

U90C5-a(S) | 24.5 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.23 | 4000 | 240 | R, U | 0.20 | |

U90C5-b(L) | 22.6 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.23 | 4000 | 240 | R, U | 0.26 | |

U90C5-b(S) | 22.6 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 90 | 0.23 | 4000 | 240 | R, U | 0.24 | |

U90S3-a(L) | 20.5 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.08 | 3800 | 240 | R, U | 0.25 | |

U90S3-a(S) | 20.5 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.08 | 3800 | 240 | R, U | 0.23 | |

U90S3-b(L) | 22.6 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.08 | 3800 | 240 | R, U | 0.22 | |

U90S3-b(S) | 22.6 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.08 | 3800 | 240 | R, U | 0.24 | |

U90S3-c(L) | 28.0 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.08 | 3800 | 240 | R, U | 0.20 | |

U90S3-c(S) | 28.0 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.08 | 3800 | 240 | R, U | 0.16 | |

U90C3-a(L) | 30.2 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.13 | 3800 | 240 | R, U | 0.17 | |

U90C3-a(S) | 30.2 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.13 | 3800 | 240 | R, U | 0.18 | |

U90C3-b(L) | 30.2 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.13 | 3800 | 240 | R, U | 0.16 | |

U90C3-b(S) | 30.2 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.17 | 90 | 0.13 | 3800 | 240 | R, U | 0.17 | |

U45S5(L) | 30.7 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 45 | 0.14 | 4000 | 240 | R, U | 0.17 | |

U45S5(S) | 30.7 | 250 | 420 | 3.5 | 0.11 | 500 | 200 | 0.29 | 45 | 0.14 | 4000 | 240 | R, U | 0.18 |

## Appendix B. Calculation Examples of the Colajanni et al. Model

_{5}and R

_{6}, equal to 0.65 and 0.18, respectively). Then, starting from the R-factor value, the r factor is computed based on the procedure described in Section 3, equal to 0.92. After that, the inclination of the concrete strut is calculated via Equation (14), which provides a value of cot θ > 2.5; thus, due to the limitations of cot θ values, cot θ = 2.5 is assumed. Consequently, assuming $\tilde{\sigma}$

_{f}= $\tilde{\sigma}$

_{s}= 1, the shear capacity can be calculated using Equation (9), which provides a value of 310 kN.

_{5}and R

_{6}, equal to 0.50 and 0.23, respectively). Then, starting from the R-factor value, the r factor is computed based on the procedure described in Section 3, equal to 1. After that, the inclination of the concrete strut is calculated via Equation (14), which provides a value of cot θ = 2.09. Therefore, assuming $\tilde{\sigma}$

_{c}= $\tilde{\sigma}$

_{f}= $\tilde{\sigma}$

_{s}= 1, the shear capacity can be calculated using one of Equations (9)–(11), which provide a value of 272 kN.

_{5}because the section is considered fully wrapped thanks to the presence of the anchorages, and it is equal to 0.66). Then, starting from the R-factor value, the r factor is computed based on the procedure described in Section 3. After that, the inclination of the concrete strut is calculated via Equation (14), which provides a value of cot θ = 1.28. Therefore, the spacing of the CFRP is reduced to 110 mm, with which, again using Equation (14), a cot θ = 0.97 is obtained. Thus, cot θ = 1 is assumed, so Equation (10) is used considering $\tilde{\sigma}$

_{f}= 1 and Equation (11) is used with $\tilde{\sigma}$

_{s}= −1. The shear strength of the beam is the minimum one obtained through the above two equations, and it is equal to 335 kN.

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**Figure 1.**Variables used in the ACI 440.2R model for shear-strengthening calculations (

**a**) cross-sectional parameters (

**b**) spacing and width of FRP (

**c**) inclination angle between FRP strip and beam axis.

**Figure 2.**Beam segments identified via three sections parallel to stress field directions of (

**a**) concrete strut; (

**b**) steel stirrups; (

**c**) FRP reinforcement. M* and V* represent the moment and shear acting on the considered section.

**Figure 4.**Experimental vs. theoretical shear strength for the Colajanni et al. model with six different R factors. (Data Set 1, α = β). RU* and TU* represents Rectangular and T beam having U-jacketing with partially efficient anchorages.

**Figure 5.**Shear strength calculation (experimental vs. theoretical) for the Colajanni et al. model with six different R factors. (For Data Set 2, α ≠ β). RU* represents Rectangular while TU* represents T beam having U-jacketing with partially efficient anchorages.

**Table 1.**Evaluation of combined results of Data Set 1 and Data Set 2 using the Colajanni et al. model with different R factors.

R (K&N, P&M) | R (ACI) | R (CNR) | R fib | R M&C | R C&T | |
---|---|---|---|---|---|---|

τ_{avg} | 0.94 | 0.97 | 0.97 | 0.82 | 1.12 | 0.95 |

CoV | 0.27 | 0.32 | 0.25 | 0.25 | 0.29 | 0.20 |

**Table 2.**Results of calculation on the basis of the 1st and 2nd approaches from Database 1 and Database 2.

For α = β | Colajanni et al. Model | R Factors | RU | RU* | RF | For α = β | Colajanni et al. Model | R Factors | TU | TU* | TU/F | ||||||

τ_{avg} | CoV | τ_{avg} | CoV | τ_{avg} | CoV | τ_{avg} | CoV | τ_{avg} | CoV | τ_{avg} | CoV | ||||||

K&N, P&M ^{1} | 0.78 | 0.25 | 0.87 | 0.25 | 1.01 | 0.10 | K&N, P&M | 1.06 | 0.27 | 1.04 | 0.16 | 1.01 | 0.22 | ||||

ACI | 0.79 | 0.24 | 0.92 | 0.33 | 1.01 | 0.24 | ACI | 1.10 | 0.31 | 1.16 | 0.22 | 1.09 | 0.29 | ||||

CNR | 0.82 | 0.18 | 0.89 | 0.23 | 1.13 | 0.24 | CNR | 1.05 | 0.21 | 1.17 | 0.21 | 1.13 | 0.18 | ||||

FIB | 0.70 | 0.21 | 0.71 | 0.17 | 0.89 | 0.14 | FIB | 0.97 | 0.20 | 0.91 | 0.15 | 0.85 | 0.13 | ||||

M&C ^{2} | 0.95 | 0.13 | 1.00 | 0.15 | 1.25 | 0.20 | M&C | 1.30 | 0.29 | 1.27 | 0.17 | 1.12 | 0.18 | ||||

C&T ^{3} | 0.82 | 0.13 | 0.84 | 0.15 | 0.88 | 0.17 | C&T | 1.04 | 0.19 | 1.10 | 0.15 | 0.81 | 0.11 | ||||

Average | 0.81 | 0.19 | 0.87 | 0.21 | 1.03 | 0.18 | Average | 1.09 | 0.24 | 1.11 | 0.18 | 1.00 | 0.19 | ||||

ACI Model | K&N, P&M | 0.99 | 0.21 | 0.90 | 0.11 | 1.10 | 0.08 | ACI Model | K&N, P&M | 0.95 | 0.19 | 1.03 | 0.20 | 0.91 | 0.30 | ||

ACI | 0.95 | 0.15 | 0.86 | 0.09 | 1.06 | 0.26 | ACI | 0.96 | 0.19 | 1.07 | 0.24 | 0.96 | 0.35 | ||||

CNR | 0.99 | 0.15 | 0.86 | 0.08 | 1.16 | 0.17 | CNR | 0.96 | 0.18 | 1.07 | 0.23 | 1.00 | 0.32 | ||||

FIB | 0.91 | 0.17 | 0.79 | 0.07 | 0.94 | 0.10 | FIB | 0.94 | 0.19 | 1.00 | 0.23 | 0.83 | 0.34 | ||||

M&C | 1.10 | 0.18 | 0.95 | 0.07 | 1.26 | 0.11 | M&C | 1.04 | 0.20 | 1.11 | 0.23 | 1.02 | 0.38 | ||||

C&T | 1.01 | 0.14 | 0.88 | 0.06 | 0.91 | 0.15 | C&T | 0.98 | 0.19 | 1.07 | 0.22 | 0.77 | 0.29 | ||||

Average | 0.99 | 0.17 | 0.87 | 0.08 | 1.07 | 0.15 | Average | 0.97 | 0.19 | 1.06 | 0.23 | 0.91 | 0.33 | ||||

CNR Model | K&N, P&M | 0.78 | 0.25 | 0.87 | 0.25 | 1.01 | 0.10 | CNR Model | K&N, P&M | 1.06 | 0.27 | 1.04 | 0.16 | 1.01 | 0.22 | ||

ACI | 0.79 | 0.24 | 0.92 | 0.33 | 1.01 | 0.24 | ACI | 1.10 | 0.31 | 1.16 | 0.22 | 1.09 | 0.29 | ||||

CNR | 0.82 | 0.18 | 0.89 | 0.23 | 1.13 | 0.24 | CNR | 1.05 | 0.21 | 1.17 | 0.21 | 1.13 | 0.18 | ||||

FIB | 0.70 | 0.21 | 0.71 | 0.17 | 0.89 | 0.14 | FIB | 0.97 | 0.20 | 0.91 | 0.15 | 0.85 | 0.13 | ||||

M&C | 0.95 | 0.13 | 1.00 | 0.15 | 1.25 | 0.20 | M&C | 1.30 | 0.29 | 1.27 | 0.17 | 1.12 | 0.18 | ||||

C&T | 0.82 | 0.13 | 0.84 | 0.15 | 0.88 | 0.17 | C&T | 1.04 | 0.19 | 1.10 | 0.15 | 0.81 | 0.11 | ||||

Average | 0.81 | 0.19 | 0.87 | 0.21 | 1.03 | 0.18 | Average | 1.09 | 0.24 | 1.11 | 0.18 | 1.00 | 0.19 | ||||

For α ≠ β | Colajanni et al. Model | K&N, P&M | 0.79 | 0.20 | 0.79 | 0.11 | 0.62 | xxxxx | For α ≠ β | Colajanni et al. Model | K&N, P&M | 0.91 | 0.09 | xxxxx | xxxxx | xxxxx | xxxxx |

ACI | 0.75 | 0.14 | 0.71 | 0.09 | 0.58 | xxxxx | ACI | 1.01 | 0.01 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

CNR | 0.74 | 0.16 | 0.67 | 0.10 | 0.78 | xxxxx | CNR | 0.97 | 0.08 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

FIB | 0.57 | 0.11 | 0.58 | 0.07 | 0.66 | xxxxx | FIB | 0.89 | 0.02 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

M&C | 0.77 | 0.20 | 0.73 | 0.08 | 0.75 | xxxxx | M&C | 1.14 | 0.04 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

C&T | 0.88 | 0.17 | 0.85 | 0.07 | 0.65 | xxxxx | C&T | 1.00 | 0.03 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

Average | 0.75 | 0.16 | 0.72 | 0.09 | 0.67 | xxxxx | Average | 0.99 | 0.04 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

ACI Model | K&N, P&M | 0.84 | 0.12 | 0.90 | 0.06 | 0.60 | xxxxx | ACI Model | K&N, P&M | 1.04 | 0.01 | xxxxx | xxxxx | xxxxx | xxxxx | ||

ACI | 0.83 | 0.13 | 0.83 | 0.07 | 0.56 | xxxxx | ACI | 1.09 | 0.05 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

CNR | 0.82 | 0.14 | 0.79 | 0.08 | 0.78 | xxxxx | CNR | 1.07 | 0.02 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

FIB | 0.71 | 0.13 | 0.71 | 0.07 | 0.65 | xxxxx | FIB | 1.04 | 0.06 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

M&C | 0.82 | 0.16 | 0.85 | 0.08 | 0.75 | xxxxx | M&C | 1.13 | 0.06 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

C&T | 0.88 | 0.13 | 0.95 | 0.09 | 0.64 | xxxxx | C&T | 1.09 | 0.04 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

Average | 0.82 | 0.14 | 0.84 | 0.07 | 0.66 | xxxxx | Average | 1.08 | 0.04 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

CNR Model | K&N, P&M | 0.79 | 0.20 | 0.78 | 0.13 | 0.57 | xxxxx | CNR Model | K&N, P&M | 0.89 | 0.12 | xxxxx | xxxxx | xxxxx | xxxxx | ||

ACI | 0.75 | 0.15 | 0.68 | 0.11 | 0.54 | xxxxx | ACI | 1.01 | 0.01 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

CNR | 0.74 | 0.17 | 0.63 | 0.10 | 0.76 | xxxxx | CNR | 0.97 | 0.08 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

FIB | 0.56 | 0.13 | 0.54 | 0.07 | 0.61 | xxxxx | FIB | 0.89 | 0.01 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

M&C | 0.76 | 0.21 | 0.68 | 0.06 | 0.72 | xxxxx | M&C | 1.14 | 0.04 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

C&T | 0.87 | 0.17 | 0.85 | 0.07 | 0.61 | xxxxx | C&T | 1.00 | 0.03 | xxxxx | xxxxx | xxxxx | xxxxx | ||||

Average | 0.75 | 0.17 | 0.69 | 0.09 | 0.64 | xxxxx | Average | 0.98 | 0.05 | xxxxx | xxxxx | xxxxx | xxxxx |

^{1}represents Khalifa and Nanni, Pellegrino and Modena, MC

^{2}represents Modifi and Challal. C&T

^{3}represents Chen and Teng. U* represents beam having U-jacketing with partially efficient anchorages.

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## Share and Cite

**MDPI and ACS Style**

Ahmed, M.; Colajanni, P.; Pagnotta, S.
Influence of Cross-Section Shape and FRP Reinforcement Layout on Shear Capacity of Strengthened RC Beams. *Materials* **2022**, *15*, 4545.
https://doi.org/10.3390/ma15134545

**AMA Style**

Ahmed M, Colajanni P, Pagnotta S.
Influence of Cross-Section Shape and FRP Reinforcement Layout on Shear Capacity of Strengthened RC Beams. *Materials*. 2022; 15(13):4545.
https://doi.org/10.3390/ma15134545

**Chicago/Turabian Style**

Ahmed, Muhammad, Piero Colajanni, and Salvatore Pagnotta.
2022. "Influence of Cross-Section Shape and FRP Reinforcement Layout on Shear Capacity of Strengthened RC Beams" *Materials* 15, no. 13: 4545.
https://doi.org/10.3390/ma15134545