# Experimental and Analytical Investigation on Flexural Retrofitting of RC T-Section Beams Using CFRP Sheets

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## Abstract

**:**

## 1. Introduction

## 2. Research Significance

## 3. Test Program

#### 3.1. Materials Properties and Test Specimens

#### 3.2. Test Setup and Procedures

_{1}–R

_{5}) were installed on the concrete surface with equal spacing along the depth of the cross-section at mid-span. Five linear strain gauges were also installed on the main flexural reinforcement with equal spacing to record strains developed in the reinforcing steel during the testing process. Three linear strain gauges were also attached to the strengthening CFRP at the bottom of the T-section beams.

## 4. Experimental Test Results

#### 4.1. General Behavior

_{cr}(Figure 3a). Subsequently, in the stage II, the applied load was redistributed. Both strains in the main flexural reinforcement and CFRP sheet increased rapidly. At the end of this stage, the RC T-section beam behaved elastically and reached it yield strength, P

_{y}(Figure 3a).

**P**was improved significantly when bonding layers increased. However, it showed obvious brittle failure (Figure 3a,b). Figure 4a,b illustrate the strain versus resistance curves of the main flexural reinforcement and CFRP sheet at mid-span, respectively. It can be observed that the flexural reinforcement reached its yielding strain. The stiffness of the beam in stage II was smaller than that in stage I due to flexural cracking of the T-section beam. Figure 5a–f display the observed cracks due to the flexural bending moment. In stage III, there were two distinct structural behaviors for the tested specimens. Beams B1~B3 exhibited ductile behavior, whilst the T-section beams strengthened with CFRP sheets exhibited sudden drop in P-δ curves as shown in Figure 3. This implies that different types of failure modes occurred in the test specimens with and without CFRP-strengthening.

_{cr}#### 4.2. Load Resistance and Failure Modes

_{cr}, resistance corresponding to steel yielding P

_{y}, and ultimate resistance P

_{u}of the tested T-section beams could be determined from P-δ curves of beams as shown in Figure 3. Table 1 lists the P

_{cr}, P

_{y}, and P

_{u}values and the corresponding failure mode for each of the tested 8 T-section beam specimens. Based on the P-δ curves and load-strain curves of the main steel reinforcement and CFRP, two distinct failure modes were observed. The first is a flexural mode that occurred in beams B1~B3, which was characterized by: (1) strength hardening plateau of the P-δ curves; (2) yielding of the bottom steel reinforcement at final failure (Figure 4a); and (3) flexural cracks at the pure bending region in the T-section beam (Figure 5). The combined flexural failure and CFRP-concrete debonding failure occurred in beams C1~C5 at final failure stage. This was accompanied by: (1) much smaller strains of about 6000μ in the CFRP than failure strain of 13090μ, which implies that the CFRP did not fail in tension; (2) yielding of the bottom steel reinforcement at final failure (Figure 4a); and (3) step drops in the P-δ curves of specimens C1~C5.

**P**and P

_{cr}_{y}increased significantly when bonding layers increased (C4) or the reinforcement ratio increased (C3). However, peeling failure often occurred when there was excessive bonding of FRP.The peeling of the CFRP from the bottom of the T-section beam specimens was evident in C4 (Figure 5).

#### 4.3. Effect of Different Parameters

_{fl}from 0.95% to 1.29%, decreasing U-wrap spacing from 150 mm to 100 mm, and increasing the compressive strength of concrete from 20 MPa to 40 MPa increased the Pcr value by 16%, 19%, and 23%, respectively. Using higher strength concrete leads to higher cracking tensile strength of the beam as expected. Also, increasing the flexural reinforcing ratio offers larger equivalent cross-section area; and decreasing the spacing of the CFRP U-rap increases the stiffness of the beam, which delays the cracking of the concrete. As the number of CFRP sheets increased from 0 to 1 and 2, the Py (or Pu) values increased by 42% (or 6%) and 62% (or 48%), respectively. This is because introducing CFRP sheets to RC T-section beams increases the equivalent reinforcing ratio of the beam, which contributes to their Py and Pu resistance. However, the CFRP-concrete bonding failure limits the full utilization of the CFRP, which is reflected in the much lower than the strain at failure of the T-section beams. Hence, peeling of the CFRP from the strengthened RC T-section beams needs further study. Increasing the flexural reinforcing ratio of the T-section beam, ρ

_{fl}from 0.95% to 1.29% led to 13% and 48% increments in Py and Pu, respectively. Increasing the flexural reinforcing ratio of the T-section beams increases the bending moment resistance of the cross-section. Due to premature failure of the CFRP-concrete bonding, the contribution of the CFRP to the bending resistance is minimized.

## 5. Discussion

_{yT}and P

_{u}denote the yielding and ultimate resistance of the T-section beam; P

_{T}denotes tensile resistance of the strengthening materials; f

_{yr}and A

_{r}denote the yield strength and cross-sectional area of the strengthening CFRP sheet, respectively. In Equation (1) higher ${\overline{\mathit{P}}}_{\mathit{u}}$ values denote improved resistance of the beam by unit strength of strengthening sheets. Figure 7 shows the ${\overline{\mathit{P}}}_{\mathit{u}}$ values for the strengthened specimens. The effect of premature failure of the bonding glue that connects the CFRP to the T-section beams can be noted. As can be observed in Figure 4, all strengthened CFRP materials did not reach maximum strain at the failure stage of strengthened beam specimens.

_{max}of the tested T-section beam specimens at their ultimate resistance, P

_{u}. Central deflections were increased on average by 20% from 50 mm to 60 mm compared with that of the un-strengthened T-section beams. However, the ductility of the T-section beams strengthened by CFRP was decreased due to premature failure of the bonding materials. The average central deflection of beams strengthened by CFRP sheets was about 20 mm, which is only 40% of that for the un-strengthened beams.

## 6. Ultimate Load Carrying Capacity of strengthened T-Section Beams

#### 6.1. Resistance of T-Section Beams Corresponding to Crack Initiation P_{cr}

_{ct}, ε

_{R}, ε

_{ts}, ε

_{cs}, and ε

_{c}denote the strain at the bottom fiber of the T-section beam, strengthening plate, tensile reinforcement, compressive reinforcement, and top fiber of the T-section beam, respectively (see Figure 9); b and Bf denote the width of web and flange of the T-section beam, respectively; h

_{t}, h

_{0}, and h denote the depth of flange, effective depth, and overall depth of the cross-section, respectively.

_{ct}= ε

_{t}

_{0}into Equations (3)–(9), the neutral axis position, x, could be found. With x solved, the bending resistance of the cross-section could be determined through taking the moment to the neutral axis as follows;

_{t}denotes the ultimate tensile strength of the concrete A

_{sc}, A

_{st}and A

_{R}denote the area of the compressive reinforcement, tensile reinforcement, and strengthening materials attached to the T-section beam. With the developed equations, the bending resistance of the cross-section can be determined. Thus, the resistance of the T-section beam corresponding to the crack initiation can be determined as follows:

_{a}denotes the shear span of the beam.

#### 6.2. Yielding Resistance and Ultimate Resistance of Strengthened T-Section Beams

_{cc}, N

_{sc}, N

_{st}, N

_{R}, denote the internal resultant forces acting on the concrete under compression, compressive reinforcement, tensile reinforcement, and strengthening materials, respectively (see Figure 7); λ = 0.8 for fck ≤ 50 MPa, λ = 0.8 − (fck − 50)/400 for 50 < fck ≤ 90 MPa; η = 1.0 for fck ≤ 50 MPa; η = 1.0 − (fck − 50)/200 for 50 < fck ≤ 90 MPa [16]; B

_{f}, b, h

_{t}denote the width of the flange, width of the web, and height of the flange of the T-section beam, respectively; f

_{yc}, f

_{yt}denote the yield strength of the compressive and tensile steel reinforcement, respectively; A

_{sc}, A

_{st}and A

_{R}denote the area of compressive reinforcement, tensile reinforcement, and strengthening CFRP attached to the T-section beam; h

_{t}, h

_{0}denote the depth of flange, effective depth, and overall depth of the cross-section, respectively; ${\u03f5}_{cu}$ denotes the ultimate strain of the concrete under compression. Corresponding values for different strength of concrete could be determined as per the Eurocode 2 [16]. Thus, with the solved x, the plastic bending moment of the cross-section corresponding to yielding of the tensile reinforcement could be determined as follows;

_{c}denotes the compressive strength of the concrete.

_{pu}the ultimate strength of the tensile steel reinforcement f

_{u}can be used for the calculation. Thus, the value of Equation (20) used in Equation (17) needs to be modified as follows:

_{pu}can be determined as follows:

_{py}and M

_{pu}can be determined. The load carrying capacity of the T-section beam corresponding to yield and ultimate strength of the flexural tensile reinforcement can be determined as follows:

_{cr}, P

_{y}, and P

_{u}values for the tested T-section beams are compared with the experimental values in Table 1. It can be observed that the developed analytical models predictions with reasonable accuracy for the resistance of the T-section beams strengthened by CFRP. The developed analytical models also provide reasonable prediction of the cracking resistance, yielding and ultimate resistance of the RC T-section beams strengthened with CFRP sheets. The average test-to-prediction ratio (or COVs) for P

_{cr}, P

_{y}, and P

_{u}are 1.01 (0.12), 1.10 (0.12), and 1.08 (0.10), respectively.

## 7. Conclusions

_{cr}, yielding resistance P

_{y}, and ultimate resistance P

_{u}of the T-section beams strengthened by CFRP. Model accuracy was verified though validation against the experimental data. Based on the experimental and analytical study, the following conclusions can be drawn;

- (1)
- The RC T-section beam specimens strengthened with CFRP sheets failed in a flexural failure. Increasing the thickness of the strengthening CFRP did not enhance the cracking resistance of the beam, but significantly improved the yielding and ultimate resistance.
- (2)
- Increasing the flexural reinforcing ratio of the beam by 36% from 0.95% to 1.29% increased the P
_{cr}, P_{y}, and P_{u}by 17%, 13%, and 48%, respectively. - (3)
- Increasing the CFRP U-wrap spacing had little effect on the resistance of the RC T-section beams. Moreover, increasing the compressive strength of concrete only had marginal influence on the yielding and ultimate resistance of the CFRP strengthened RC T-section beams.
- (4)
- The T-section beams strengthened by CFRP sheets exhibited lower ductility at the final failure stage due to brittle failure of the bond between the CFRP sheet and concrete.
- (5)
- The developed analytical models offered reasonable predictions of the cracking resistance, yielding and ultimate resistance of the RC T-section beams strengthened with CFRP sheets. The average test-to-prediction ratios (or COVs) for
**P**,_{cr}**P**, and_{y}**P**were 1.01 (0.12), 1.10 (0.12), and 1.08 (0.10), respectively._{u}

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Details of tested T-section beams. (

**a**) Layout of reinforcement in the T-beam. (

**b**) Layout of CFRP type of U-wrap. (

**c**) A-A section for T-beam.

**Figure 3.**Load-central deflection curves of RC T-section beams retrofitted by CFRP. (

**a**) P-δ curves for B1, C1, C4-5; (

**b**) P-δ curves for B2-3, C2-3.

**Figure 4.**Load-strain curves of RC T-section beams retrofitted by CFRP. (

**a**) Strain in steel reinforcement at mid-span; (

**b**) Strain in CFRP at mid-span.

**Figure 5.**Cracks developed in RC T-section beams strengthened by CFRP. (

**a**) B1 (

**b**) B2. (

**c**) B3 (

**d**) C1. (

**e**) C2 (

**f**) C3. (

**g**) C4 (

**h**) C5.

**Figure 9.**Strain and stress distribution on cross-section of T-section beam before concrete cracking.

**Figure 10.**Strain and stress distribution on cross-section of T-section beams corresponding to yielding and ultimate resistance.

Item | Conc Grade | ρ_{fl} (%) | Bonding Layers | S (mm) | u_{y} (mm) | u_{max} (mm) | P_{cr,T} (kN) | P_{y,T} (kN) | P_{u,T} (kN) | Failure Mode | P_{cr} (kN) | P_{cr,T}/P_{c}_{r} ratio | P_{y} (kN) | P_{y,T}/P_{y} Ratio | P_{u} (kN) | P_{u,T}/P_{u} Ratio |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

B1 | C20 | 0.95 | - | - | 6.6 | 49.2 | 8.7 | 29.9 | 44.9 | FB | 7.7 | 1.13 | 24.7 | 1.21 | 37.7 | 1.19 |

B2 | C40 | 0.95 | - | - | 7.1 | 60.0 | 9.3 | 29.5 | 45.4 | FB | 10.7 | 0.87 | 26.5 | 1.11 | 38.0 | 1.20 |

B3 | C20 | 1.29 | - | - | 8.0 | 44.2 | 7.5 | 46.2 | 61.4 | FB | 7.9 | 0.95 | 34.6 | 1.33 | 52.7 | 1.17 |

C1 | C20 | 0.95 | 1 | 100 | 6.6 | 51.2 | 9.2 | 42.6 | 47.5 | FB&DB | 7.8 | 1.07 | 38.7 | 1.10 | 50.1 | 0.95 |

C2 | C40 | 0.95 | 1 | 100 | 7.3 | 20.0 | 9.0 | 41.9 | 50.5 | FB&DB | 10.8 | 0.94 | 39.2 | 1.07 | 51.1 | 0.99 |

C3 | C20 | 1.29 | 1 | 100 | 7.8 | 19.0 | 8.2 | 48.2 | 70.5 | FB&DB | 8.0 | 1.20 | 46.9 | 1.03 | 62.2 | 1.13 |

C4 | C20 | 0.95 | 2 | 100 | 7.3 | 15.5 | 11.4 | 48.5 | 66.6 | FB&DB | 7.8 | 1.09 | 54.4 | 0.89 | 67.6 | 0.99 |

C5 | C20 | 0.95 | 1 | 150 | 6.5 | 20.5 | 9.7 | 42.0 | 51.0 | FB&DB | 7.8 | 0.90 | 38.7 | 1.08 | 50.1 | 1.02 |

Mea | 1.01 | 1.10 | 1.08 | |||||||||||||

Cov | 0.12 | 0.12 | 0.10 |

Type | E_{s} (GPa) | f_{y} (MPa) | F_{u} (MPa) | δ_{u} (%) |
---|---|---|---|---|

Ø8 HPB235 | 200 | 308 | 538 | 30.5 |

Ø12 HRB335 | 200 | 365 | 550 | 28.5 |

Ø14 HRB335 | 200 | 388 | 605 | 27.5 |

Type | f_{y} (MPa) | E_{F} (GPa) | δ_{u} (%) | τ_{c} (MPa) |
---|---|---|---|---|

CFRP | 3168 | 242 | 1.71 | 3.5 |

JGJ-20 | 43 | 2.59 | - | 3.6 |

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**MDPI and ACS Style**

Zhang, Y.; Nehdi, M.L.
Experimental and Analytical Investigation on Flexural Retrofitting of RC T-Section Beams Using CFRP Sheets. *Appl. Sci.* **2020**, *10*, 1233.
https://doi.org/10.3390/app10041233

**AMA Style**

Zhang Y, Nehdi ML.
Experimental and Analytical Investigation on Flexural Retrofitting of RC T-Section Beams Using CFRP Sheets. *Applied Sciences*. 2020; 10(4):1233.
https://doi.org/10.3390/app10041233

**Chicago/Turabian Style**

Zhang, Yannian, and Moncef L. Nehdi.
2020. "Experimental and Analytical Investigation on Flexural Retrofitting of RC T-Section Beams Using CFRP Sheets" *Applied Sciences* 10, no. 4: 1233.
https://doi.org/10.3390/app10041233