# Performance Evaluation of a Long-Span Cable-Stayed Bridge Using Non-Destructive Field Loading Tests

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## Abstract

**:**

## 1. Introduction

## 2. Non-Destructive Field Loading Test for Pingnan Xiangsizhou Bridge

#### 2.1. Objective of Non-Destructive Field Loading Tests

- (1)
- Defining the real load of the bridge under static load conditions;
- (2)
- Verifying the rationality of the design, and providing reference for similar bridge design;
- (3)
- Verifying the validity of the finite element model, which provides the basis for the model’s improvement and optimization;
- (4)
- Providing data for bridge monitoring and maintenance.

#### 2.2. Structural Features of Pingnan Xiangsizhou Bridge

- The stay cables of the bridge are fan-shaped, with two cable planes in space; 20 pairs of cables are arranged on both sides of the main tower, with a total of 80 pairs of cables on the whole bridge. The stay cables are anchored by steel anchor beams on the towers, and by anchor plates on the beams. All stay cables are tensioned on the tower;
- The bridge tower is diamond shaped. An upper beam is set on the top of the tower connecting the two tower columns. In order to strengthen the lateral stability of the cable tower, a middle beam is set. The elevation of the top of the bearing platform is 21.20 m, the elevation of the tower base is 23.20 m, and the elevation of the top of the tower is 170.50 m. The total height of the cable tower above the tower base is 147.30 m. The heights of the lower, middle, and upper tower columns are 26.186 m, 51.375 m, and 69.739 m, respectively;
- The bridge deck is paved with asphalt concrete with a thickness of 10 cm. Column-type crash barriers are set on both sides of the carriageway. Sidewalks and maintenance railings are set on both sides of the bridge deck.

#### 2.3. Non-Destructive Field Loading Test for Pingnan Xiangsizhou Bridge

#### 2.3.1. Non-Destructive Field Loading Test Instrumentations

#### 2.3.2. Cable Force Test and Principle in Non-Destructive Field Loading Test

_{nr}is the r-th natural frequency (rad/s), T is the tension of the cable (N), l is the length of the cable (m), ρ is the density of the cable (kg/m), E is Young’s modulus (Pa), and I is the moment of inertia (kg·m

^{2}).

#### 2.4. Structural Theoretical Calculation for Pingnan Xiangsizhou Bridge

#### 2.4.1. Geometric and Physical Parameters of Pingnan Xiangsizhou Bridge

_{c}= 3.55 × 10

^{4}MPa, bulk density: γ = 26 kN/m

^{3}) and the main body of the steel beam is composed of Q345C steel (E

_{s}= 2.06 × 10

^{5}MPa, γ = 78.5 kN/m

^{3}). The center height of the composite beam is 3.50 m, the top plate is provided with 2% cross slope, the bottom plate is horizontal, and the full width of the main beam is 33.50 m. The stay cable adopts a parallel steel strand cable system. The cable body is composed of multiple unbonded high-strength galvanized steel strands with a tensile strength of 1860 MPa, and the outer layer is equipped with a high-density polyethylene (HDPE) cable sleeve. The cable tower uses a diamond-type cable tower structure and C50 concrete (E

_{c}= 3.45 × 10

^{4}MPa, γ = 26 kN/m

^{3}). The total height of the cable tower above the tower base is 147.30 m. C30 concrete (E

_{c}= 3.0 × 10

^{4}MPa, γ = 26 kN/m

^{3}) is used for the capping beam, transition pier body, auxiliary pier body, and bearing platform.

#### 2.4.2. Establishment of a Finite Element Model for Pingnan Xiangsizhou Bridge

- Concrete and steel are ideal elastic materials, and the elastic moduli of the concrete and steel of the new bridge are constant, being essentially consistent with the design values;
- The section deformation of the beam element conforms to the plane section assumption;
- Deformation coordination between the bridge’s concrete deck and the main beam’s steel plate, and there is no relative slip between the deck and the main beam.

#### 2.5. Field Loading Test Conditions and Loading Arrangement

_{q}) of the static load test can be calculated according to Equation (7):

_{S}is the calculated effect value of the test load.

_{S}is the calculated effect value of the test load, and η

_{q}is the load efficiency.

## 3. Experimental Results and Analysis

#### 3.1. Vibration Mode and Frequency Analysis for the Field Loading Test of Pingnan Xiangsizhou Bridge

#### 3.2. Displacement Analysis for the Field Loading Test of Pingnan Xiangsizhou Bridge

_{C}/V

_{D},

_{C}is the tested result and V

_{D}is the designed value.

#### 3.3. Strain Analysis for the Field Loading Test of Pingnan Xiangsizhou Bridge

#### 3.4. Cable Tension Increment Test Analysis for the Field Loading Test of Pingnan Xiangsizhou Bridge

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Non-destructive field loading test instrumentation: (

**a**) strain; (

**b**) deflection; (

**c**) frequency; (

**d**) cable force.

**Figure 4.**Finite element models of Pingnan Xiangsizhou Bridge: (

**a**) single-beam model and (

**b**) plate element model.

**Figure 5.**Strain measuring point arrangement of Pingnan Xiangsizhou Bridge: (

**a**) layout elevation and (

**b**) layout of a standard cross-section of the main beam (unit: cm).

**Figure 7.**Vibration modes of Pingnan Xiangsizhou Bridge: (

**a**) 1st vertical bending; (

**b**) 1st transverse bending; (

**c**) 2nd vertical bending; (

**d**) 3rd vertical bending; (

**e**) 4th vertical bending.

**Figure 8.**Measured and calculated strain values of the main girder at section A, considering loading cases 1 and 2: (

**a**) 1–6 at the bottom of the bottom plate; (

**b**) 7–15 at the bottom of the top plate.

**Figure 9.**Measured and calculated strain values of the main girder at section B, considering loading cases 3 and 4: (

**a**) 1–6 at the bottom of the bottom plate; (

**b**) 7–15 at the bottom of the top plate.

**Figure 10.**Measured and calculated strain values of the main girder at section C, considering loading cases 5 and 6: (

**a**) 1–6 at the bottom of the bottom plate; (

**b**) 7–15 at the bottom of the top plate.

**Figure 11.**Measured and calculated strain values of the main girder at section D, considering loading cases 7 and 8: (

**a**) 1–6 at the bottom of the bottom plate; (

**b**) 7–15 at the bottom of the top plate.

**Figure 12.**Measured and calculated strain values of the main girder at section E, considering loading cases 9 and 10: (

**a**) 1–6 at the bottom of the bottom plate; (

**b**) 7–15 at the bottom of the top plate.

**Figure 13.**Measured and calculated cable tension increment values of inner and outer stay cables, considering various loading cases: (

**a**) loading case No. 2; (

**b**) loading case No. 4; (

**c**) loading case No. 7; (

**d**) loading case No. 8.

Case No. | Loading Test Arrangement | S(1 + μ) | S_{S} | η_{q} |
---|---|---|---|---|

1 | Symmetrical loading of the maximum positive moment (section A) of No. 1 span | 22,944.0 | 20,725.7 | 0.903 |

2 | Eccentric loading of the maximum negative moment (section A) of No. 1 span | −21,392.8 | −19,305.6 | 0.902 |

3 | Eccentric loading of the maximum positive moment (section B) of No. 2 span | 38,815.6 | 35,583.7 | 0.917 |

4 | Symmetrical loading of the maximum positive moment (section B) of No. 2 span | 38,782.7 | 35,533.5 | 0.916 |

5 | Symmetrical loading of the maximum negative bending moment (section C) of the main girder at No. 3 pier | −31,122.2 | −27,352.1 | 0.879 |

6 | Eccentric loading of the maximum negative bending moment (section C) of the main girder at No. 3 pier | −31,122.0 | −27,395.3 | 0.880 |

7 | Symmetrical loading at L/4 (section D) of No. 3 span | 28,259.2 | 29,494.4 | 1.044 |

8 | Eccentric loading at L/4 (section D) of No. 3 span | 28,260.9 | 29,324.4 | 1.038 |

9 | Symmetrical loading of the maximum positive moment (section E) of No. 3 span | 40,677.5 | 40,040.8 | 0.984 |

10 | Eccentric loading of the maximum negative moment (section E) of No. 3 span | 40,677.5 | 40,040.8 | 0.984 |

Vehicle No. | Wheelbase 1 (m) | Wheelbase 2 (m) | Mass of Front Axle (kN) | Mass of Rear Axle (kN) | Total Weight of Vehicle (kN) |
---|---|---|---|---|---|

1#~24# | 3.80 | 1.35 | 70 | 300 | 370 |

Mode No. | Vibration Mode | Vibration Frequency (Hz) | ||
---|---|---|---|---|

Numerical | Experimental | Error (%) | ||

1 | 1st vertical bending | 0.303 | 0.313 | 3.30 |

2 | 1st transverse bending | 0.384 | 0.469 | 22.14 |

3 | 2nd vertical bending | 0.392 | 0.41 | 4.59 |

4 | 3rd vertical bending | 0.581 | 0.625 | 7.57 |

5 | 4th vertical bending | 0.683 | 0.85 | 24.45 |

**Table 4.**Comparison between measured and calculated displacement values and calibration coefficients.

Case No. | Left | Right | ||||
---|---|---|---|---|---|---|

Measured (mm) | Calculated (mm) | Calibration Coefficient | Measured (mm) | Calculated (mm) | Calibration Coefficient | |

1 | 4.5 | 6.73 | 0.67 | 4.28 | 6.73 | 0.64 |

2 | 4.18 | 7.24 | 0.58 | 2.91 | 5.03 | 0.58 |

3 | 80.5 | 116.79 | 0.69 | 54.6 | 91.13 | 0.60 |

4 | 68.22 | 103.18 | 0.66 | 67.92 | 103.18 | 0.66 |

9 | 287.13 | 328.25 | 0.87 | 270.68 | 328.25 | 0.82 |

10 | 340.23 | 379.06 | 0.90 | 250.63 | 277.94 | 0.90 |

Cable No. | Number per Bundle | Anchor Spacing (m) | Total Length (m) | Cable Elevation (°) | Cable Density (kg/m ^{3}) |
---|---|---|---|---|---|

A8 | 55 | 116.180 | 118.191 | 40.659 | 71.0 |

A9 | 55 | 126.236 | 128.225 | 38.424 | 71.0 |

A10 | 55 | 136.460 | 138.418 | 36.549 | 71.0 |

B8 | 43 | 116.312 | 118.256 | 39.821 | 56.3 |

B9 | 55 | 126.404 | 128.392 | 37.470 | 71.0 |

B10 | 55 | 136.661 | 138.623 | 35.568 | 71.0 |

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**MDPI and ACS Style**

Wang, X.; Wang, L.; Wang, H.; Ning, Y.; Huang, K.; Wang, W.
Performance Evaluation of a Long-Span Cable-Stayed Bridge Using Non-Destructive Field Loading Tests. *Appl. Sci.* **2022**, *12*, 2367.
https://doi.org/10.3390/app12052367

**AMA Style**

Wang X, Wang L, Wang H, Ning Y, Huang K, Wang W.
Performance Evaluation of a Long-Span Cable-Stayed Bridge Using Non-Destructive Field Loading Tests. *Applied Sciences*. 2022; 12(5):2367.
https://doi.org/10.3390/app12052367

**Chicago/Turabian Style**

Wang, Xirui, Longlin Wang, Hua Wang, Yihao Ning, Kainan Huang, and Wensheng Wang.
2022. "Performance Evaluation of a Long-Span Cable-Stayed Bridge Using Non-Destructive Field Loading Tests" *Applied Sciences* 12, no. 5: 2367.
https://doi.org/10.3390/app12052367