# Fatigue Life Evaluation of Orthotropic Steel Deck of Steel Bridges Using Experimental and Numerical Methods

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## Abstract

**:**

## 1. Introduction

## 2. Fatigue Crack Expansion and Analysis of Calculation Results

#### 2.1. Calculation of the Stress Intensity Factor

^{1/2}, which shows that the initial crack expands relatively quickly at the ends of the long and short semi−axes; the stress intensity factors of Type II and Type III fluctuate around 0 MPa·m

^{1/2}, which is much smaller than the stress intensity factors for Type II and Type III, which fluctuate around 0 MPa.mm and are much smaller than those for Type I. It shows that the crack is a composite crack dominated by Type I cracks.

#### 2.2. Fatigue Life Assessment Method Based on Fracture Mechanics

#### 2.3. Simulation of Crack Extension

- (1)
- The local torsion angle can be calculated based on the stress at the leading edge of the local crack in the local co-ordinate system, shown in Figure 4, where the stress is determined by the local stress intensity factor.
- (2)
- Solve for the length of the local extension at each point.

#### 2.4. The Steps of Calculating Fracture Parameters by Finite Element Method

- (1)
- Building the finite element model

- (2)
- Introduction of initial cracking

- (3)
- Finite element calculation

- (4)
- Prediction of crack growth

- (5)
- Performing new finite element calculations

## 3. Model Design of Fatigue Test

#### 3.1. Model Design

#### 3.2. Layout of Measuring Points

## 4. Fatigue Test Results

#### 4.1. Static Load Test Results

#### 4.2. Fatigue Test Process

#### 4.3. Fatigue Cracking’s Location

## 5. Fatigue Crack Life Prediction

#### 5.1. Fatigue Cracking’s Location

**Figure 16.**Crack shape simulation in Step 1: (

**a**) Side view of the crack; (

**b**) Front view of the crack.

**Figure 17.**Crack shape simulation in Step 6: (

**a**) Side view of the crack; (

**b**) Front view of the crack.

**Figure 18.**Crack shape simulation in Step 12: (

**a**) Side view of the crack; (

**b**) Front view of the crack.

**Figure 19.**Crack shape simulation in Step 18: (

**a**) Side view of the crack; (

**b**) Front view of the crack.

**Figure 20.**Crack shape simulation in Step 24: (

**a**) Side view of the crack; (

**b**) Front view of the crack.

**Figure 21.**Crack shape simulation in Step 30: (

**a**) Side view of the crack; (

**b**) Front view of the crack.

**Figure 22.**Crack shape simulation in Step 36: (

**a**) Side view of the crack; (

**b**) Top view of the crack; (

**c**) Front view of the crack.

#### 5.2. Life Expectancy

## 6. Influences of Different Parameters on Residual Life of Structure

#### 6.1. Initial Crack Size

#### 6.2. Thickness of U-Rib

#### 6.3. U-Rib Height

#### 6.4. Thickness of Top Plate

#### 6.5. Thickness of the Horizontal Partition

## 7. Conclusions

- (1)
- A crack with a length of 15.1 cm appears near the boundary of the loading position for the first time after 3 million~3.25 million cycles of loading. After 3.25 million~3.5 million cycles of cyclic loading, the crack expanded to 18.6 cm in the model test;
- (2)
- The finite element calculation results and the test results are basically the same, so the test can reflect the real state of the model force, and the test data have real reliability;
- (3)
- The Mode I stress intensity factor of the initial crack is symmetrically distributed, and the value is large, reaching 77.67 MPa. The stress intensity factors of Type II and III fluctuate around 0 MPa·mm
^{1/2}, which belongs to the crack type dominated by the Mode I crack; - (4)
- With the expansion of the crack, the stress intensity factor at the middle point of the leading edge of the crack tends to increase and then decrease. When the size of the short semi-axis of the crack reaches 16 mm, the number of load cycles is nearly 3.9 million, while the number of fatigue cycle loads tested is 3.5 million, with a relative error of 11.4%, which is within an acceptable range.
- (5)
- The increases of U-rib thickness and roof thickness have the positive effect of prolonging the fatigue life of OSD. The influence of roof thickness is particularly significant. When the roof thickness increases from 10 mm to 18 mm, the amplitude of the stress intensity factor decreases by about 70%, which is more helpful in increasing the fatigue life.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 8.**Layout of measuring points: (

**a**) Layout of measuring points of the middle diaphragm; (

**b**) Layout of U-rib measuring points; (

**c**) Layout of roof measuring points.

**Figure 23.**Calculation of stress intensity factors for the leading edge of some extended−step cracks.

**Figure 24.**Crack growth changes of long and short half axes: (

**a**) Crack growth variation of long half-axis; (

**b**) Crack growth change of short half-axis.

**Figure 26.**The relationship between the propagation depth at the middle point of crack front and the amplitude of the stress intensity factor.

**Figure 27.**The relationship between the propagation depth at the middle point of the crack front and the number of cyclic loadings.

**Figure 28.**The relationship between the propagation depth at the middle point of the crack front and the amplitude of the stress intensity factor.

**Figure 29.**The relationship between the propagation depth at the middle point of the crack front and the number of cyclic loadings.

**Figure 30.**The relationship between the propagation depth at the middle point of the crack front and the amplitude of the stress intensity factor.

**Figure 31.**The relationship between the propagation depth at the middle point of the crack front and the number of cyclic loadings.

**Figure 32.**The relationship between the propagation depth at the middle point of the crack front and the amplitude of the stress intensity factor.

**Figure 33.**The relationship between the propagation depth at the middle point of the crack front and the number of cyclic loadings.

**Figure 34.**The relationship between the propagation depth at the middle point of the crack front and the amplitude of the stress intensity factor.

**Figure 35.**The relationship between the propagation depth at the middle point of the crack front and the number of cyclic loadings.

**Table 1.**Comparison of measured and calculated values at selected measurement points under static load.

Location | Measurement Points | Measured Values/MPa | Calculated Values/MPa |
---|---|---|---|

Roof plates | P2 | 56.6 | 55.5 |

P3 | 156.6 | 160.1 | |

P4 | 112.7 | 113.3 | |

U-ribs | U2 | 53.4 | 55.0 |

U3 | 64.7 | 63.9 | |

U4 | 36.6 | 35.2 | |

Side dividers 1 | BHGB1-6 | 9.3 | 9.6 |

BHGB1-8 | 12.4 | 11.9 | |

BHGB1-10 | 14.2 | 14.5 | |

BHGB1-12 | 11.5 | 12.6 | |

BHGB1-14 | 6.3 | 6.8 | |

Mid-transom bulkhead | ZHGB1-7 | 29.0 | 29.3 |

ZHGB1-9 | 39.8 | 40.2 | |

ZHGB 1-10 | 89.3 | 90.0 | |

ZHGB 1-19 | 21.6 | 21.9 | |

ZHGB 1-22 | 50.9 | 51.2 | |

ZHGB 1-31 | 19.3 | 18.7 | |

ZHGB 1-33 | 29.1 | 30.3 | |

ZHGB1-35 | 11.1 | 10.9 |

Extension Steps | Current Size/mm | Extended Step Size/mm | Extension Steps | Current Size/mm | Extended Step Size/mm |
---|---|---|---|---|---|

0 | 0.100 | 0.015 | 19 | 1.424 | 0.213 |

1 | 0.115 | 0.017 | 20 | 1.637 | 0.245 |

2 | 0.132 | 0.020 | 21 | 1.882 | 0.282 |

3 | 0.152 | 0.023 | 22 | 2.164 | 0.325 |

4 | 0.175 | 0.026 | 23 | 2.489 | 0.373 |

5 | 0.201 | 0.030 | 24 | 2.863 | 0.429 |

6 | 0.231 | 0.035 | 25 | 3.292 | 0.494 |

7 | 0.266 | 0.040 | 26 | 3.786 | 0.568 |

8 | 0.306 | 0.046 | 27 | 4.354 | 0.653 |

9 | 0.352 | 0.053 | 28 | 5.007 | 0.751 |

10 | 0.405 | 0.061 | 29 | 5.758 | 0.864 |

11 | 0.465 | 0.070 | 30 | 6.621 | 0.993 |

12 | 0.535 | 0.080 | 31 | 7.614 | 1.142 |

13 | 0.615 | 0.092 | 32 | 8.757 | 1.313 |

14 | 0.708 | 0.106 | 33 | 10.070 | 1.510 |

15 | 0.814 | 0.122 | 34 | 11.580 | 1.737 |

16 | 0.936 | 0.140 | 35 | 13.318 | 1.341 |

17 | 1.076 | 0.161 | 36 | 14.659 | 1.341 |

18 | 1.238 | 0.186 | 37 | 16.000 | / |

$\mathit{K}\mathrm{unit}$ | $\mathit{C}$ | $\mathit{m}$ |
---|---|---|

N·mm^{−3/2} | 5.21 × 10^{−13} | 3 |

MPa·m^{1/2} | 1.65 × 10^{−11} | 3 |

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## Share and Cite

**MDPI and ACS Style**

Zeng, Y.; Wang, S.; Xue, X.; Tan, H.; Zhou, J.
Fatigue Life Evaluation of Orthotropic Steel Deck of Steel Bridges Using Experimental and Numerical Methods. *Sustainability* **2023**, *15*, 5945.
https://doi.org/10.3390/su15075945

**AMA Style**

Zeng Y, Wang S, Xue X, Tan H, Zhou J.
Fatigue Life Evaluation of Orthotropic Steel Deck of Steel Bridges Using Experimental and Numerical Methods. *Sustainability*. 2023; 15(7):5945.
https://doi.org/10.3390/su15075945

**Chicago/Turabian Style**

Zeng, Yong, Shenxu Wang, Xiaofang Xue, Hongmei Tan, and Jianting Zhou.
2023. "Fatigue Life Evaluation of Orthotropic Steel Deck of Steel Bridges Using Experimental and Numerical Methods" *Sustainability* 15, no. 7: 5945.
https://doi.org/10.3390/su15075945