# Flexural Behavior of Precast UHPC Segmental Beams with Unbonded Tendons and Epoxy Resin Joints

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Specimen Design

#### 2.2. Raw Materials

#### 2.2.1. UHPC

_{2}mass content of over 98% was used as the filler; the fine aggregate was quartz sand, with a grain size of less than 0.6 mm. 847 kg of Portland cement per cubic meter of UHPC was required. Straight steel fibers with an average length (L

_{f}) of 12 mm, a diameter (d

_{f}) of 0.16 mm, and accordingly, an aspect ratio (L

_{f}/d

_{f}) of 75, were added with a fiber volume ratio of 2% to enhance the tensile ductility of the UHPC. The steel fibers were characterized by a density of 7.8 kg/m

^{3}, a tensile strength of 2500 MPa, and an elastic modulus of 200,000 MPa. Meanwhile, a high-performance water-reducing polycarboxylic acid agent (i.e., superplasticizer) was added to ensure good fluidity of the UHPC. The production of UHPC followed a well-established procedure suggested by Yoo et al. [8,38].

^{4}MPa, respectively.

#### 2.2.2. Steel Strand

^{2}, and a unit weight of 1.1 kg per meter, as per ASTM A416 [40]. As reported by the supplier, the strands had a tensile yield load of 222 kN, a tensile breaking load of 261 kN, a modulus of elasticity ranging from 1.85 × 10

^{5}MPa to 2.05 × 10

^{5}MPa, a minimum elongation of 3.5%, and a maximum relaxation of 2.5%. Table 4 shows the material properties of the steel strands.

#### 2.2.3. Joint Glue

#### 2.3. Test Setup and Instrumentation

- (1)
- Load and deflection test. Linear variable differential transformers (LVDTs) were arranged at the mid-span, loading point, and support, in order to record the displacement changes of each point during the loading process. A 50 t pressure sensor was arranged above the hydraulic jack. It was used to measure the applied load value and finally obtain the load–deflection curve. The device layout is shown in Figure 2.
- (2)
- Stress increment test of steel strand. A 30 t pressure sensor was arranged on each steel bundle to test its stress increment. Table 6 shows the stress increments of steel strand in different beams. The stress increment of steel strand is an important basis for determining the ultimate stress of steel strand. At the ultimate stage, the stresses of all tendons in the tension zone were greater than 1500 MPa, but no rupture of tendons was observed.
- (3)
- Strain test of pure bending concrete. The strain of concrete was measured by LVDTs, and 5 horizontal LVDTs were uniformly arranged along the section height. Two joint sections were tested by splicing beam, and the mid-span section was tested by casting beam. The arrangement of the measuring points is shown in Figure 3. The mechanical strain gauge placed on the monolithic beam is M1–M5 from top to bottom. The left side of the mechanical strain gauge placed on the segmental beam is L1–L5. The left side of the mechanical strain gauge placed on the segmental beam is R1–R5.
- (4)
- Crack observation. The crack formation law was noted when the load was applied, and the typical crack width was measured using the crack width meter.

## 3. Results and Discussion

#### 3.1. Deformation Characteristics

#### 3.2. Failure Mode

#### 3.3. Pure Bending Section Median Strain

## 4. Finite Element Analysis

#### 4.1. Finite Element Modeling

#### 4.2. Constitutive Material Models

#### 4.2.1. Concrete Model

#### 4.2.2. Steel Model

#### 4.3. Finite Element Mesh

#### 4.4. Contact and Boundary Conditions

#### 4.5. Unbonded Tendons and Loading

## 5. Verification of the FE Model

#### 5.1. Load–Deflection Curve

#### 5.2. Comparison of Simulated Data and Experimental Data

## 6. Conclusions

- (1)
- The failure mode of the four specimens was typical flexural failure, which originated from concrete crushing of the top flange adjacent to the load point.
- (2)
- The flexural strengths of the prefabricated components were 9~15% lower than those of the monolithic beams with unbonded tendons.
- (3)
- The shape of the joints also influenced the flexural bearing capacity. The bearing capacity of the dual-tooth joint beam was 4.5% lower than that of the single-tooth one, and the bearing capacity of the flat butt joint member was 5.7% lower than that of the dual-tooth joint beam.
- (4)
- The commercial finite element software ABAQUS was utilized to perform finite element analysis on the precast UHPC segmental bridges with unbonded tendons, and compare this with the field model test results; the simulated load–mid-span deflection curve and ultimate bearing capacity were in good agreement with the test data.
- (5)
- Testing for larger-sized UHPC prefabricated fabricated beams and numerical simulation analysis of more parameters are necessary to understand the flexural load bearing capacity of unbonded prestressed concrete flexural members. In addition, it is necessary to summarize the calculation methods of UHPC prefabricated/fabricated beams with unbonded tendons and epoxy joints.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Geometries of the test beams (units: mm): (

**a**) elevation of specimen UB-K2; (

**b**) top view of specimens; (

**c**) sectional view; and (

**d**) geometric details of key tooth.

**Figure 7.**Cross−sectional strain distributions at pure bending regions of (

**a**) UB-KN; (

**b**) UB-K0; (

**c**) UB-K1; and (

**d**) UB-K2.

**Figure 8.**Constitutive models of concrete based on damaged plasticity under (

**a**) uniaxial compression; and (

**b**) uniaxial tension.

**Figure 10.**Finite element models of (

**a**) segment prefabricated splicing and (

**b**) segmental prefabricated integral beams.

**Figure 11.**Comparisons of FEA and experimental load–displacement curves of (

**a**) UB-KN; (

**b**) UB-K0; (

**c**) UB-K1; and (

**d**) UB-K2.

Name of Beam | Number of Joints | Type of Joint | Effective Stress of Tendons (MPa) | Mean Compressive Stress at Mid-Span (MPa) | |
---|---|---|---|---|---|

Upper | Bottom | ||||

UB-K0 | 2 | flat-key | 1049.3 | 1030.3 | 16.17 |

UB-K1 | 2 | single-key | 1050.9 | 1026.8 | 16.16 |

UB-K2 | 2 | dual-key | 1031.0 | 1018.2 | 15.94 |

UB-KN | 0 | monolithic beam | 1102.6 | 1019.5 | 16.50 |

W/B ^{1} | Relative Weight Ratios to Cement | Steel Fiber ^{2} | |||||
---|---|---|---|---|---|---|---|

Water | Cement | Silica Fume | Silica Flour | Quartz Sand | Super Plasticizer | ||

0.16 | 0.224 | 1.0 | 0.25 | 0.3 | 1.11 | 0.02 | 2% |

^{1}W/B water-to-binder ratio.

^{2}Volume percent of steel fiber in a 1 m

^{3}UHPC material mix.

Cube Compressive Strength (MPa) | Split Strength (MPa) | Modulus of Elasticity (MPa) |
---|---|---|

142.6 | 12.9 | 4.25 × 10^{4} |

Diameter (mm) | Area (mm ^{2}) | Ultimate Strength (MPa) | Modulus of Elasticity (MPa) | Elongation (%) | Relaxation (%) |
---|---|---|---|---|---|

15.2 | 140.0 | 1860 | 1.95 × 10^{5} | 3.5 | 0.3 |

Test Parameters | 12-h Compressive Strength | 7-Day Compressive Strength | Oblique Shear Strength | Positive Tensile Bond Strength of Glue to Concrete |
---|---|---|---|---|

Test result | 58 | 94 | 30 | 4.3 |

Name of Specimen | Cracking Loads (kN) | Ultimate Flexural Moment (kN·m) | Ultimate Load (kN) | Maximum Deflection at Mid-Span (mm) | The Maximum Compressive Strain of UHPC (10 ^{−6}) | Stress Increment (MPa) | |
---|---|---|---|---|---|---|---|

Tensile Zone | Compressive Zone | ||||||

UB-KN | 138.8 | 119.93 | 225.0 | 7.9 | 9538 | −58.5 | 327.2 |

UB-K0 | 97.3 | 102.55 | 192.4 | 8.8 | 8679 | 109.4 | 576.4 |

UB-K1 | 135.4 | 113.74 | 213.4 | 6.4 | 7268 | 101.0 | 363.2 |

UB-K2 | 129.6 | 108.57 | 203.7 | 8.4 | 7522 | 106.1 | 514.7 |

Number | Ultimate Load, kN | Mid-Span Deflection, mm | |||
---|---|---|---|---|---|

Test Data | Simulation Data | T/S | Test Data | Simulation Data | |

UB-KN | 225.00 | 237.18 | 0.95 | 7.90 | 10.00 |

UB-K0 | 192.40 | 210.42 | 0.91 | 8.80 | 9.61 |

UB-K1 | 213.40 | 213.50 | 1.00 | 8.30 | 10.00 |

UB-K2 | 203.70 | 209.22 | 0.97 | 8.40 | 8.20 |

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## Share and Cite

**MDPI and ACS Style**

Zheng, H.; Chen, D.; Ou, M.; Liang, X.; Luo, Y.
Flexural Behavior of Precast UHPC Segmental Beams with Unbonded Tendons and Epoxy Resin Joints. *Buildings* **2023**, *13*, 1643.
https://doi.org/10.3390/buildings13071643

**AMA Style**

Zheng H, Chen D, Ou M, Liang X, Luo Y.
Flexural Behavior of Precast UHPC Segmental Beams with Unbonded Tendons and Epoxy Resin Joints. *Buildings*. 2023; 13(7):1643.
https://doi.org/10.3390/buildings13071643

**Chicago/Turabian Style**

Zheng, Hui, Daixing Chen, Mingfu Ou, Xuejiao Liang, and Yuan Luo.
2023. "Flexural Behavior of Precast UHPC Segmental Beams with Unbonded Tendons and Epoxy Resin Joints" *Buildings* 13, no. 7: 1643.
https://doi.org/10.3390/buildings13071643