# Research on Fatigue Strength for Weld Structure Details of Deck with U-rib and Diaphragm in Orthotropic Steel Bridge Deck

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fatigue Test for Weld Structure of U-Rib and Deck Plate

#### 2.1. Microstructure Analysis of Welded Joint

#### 2.2. Fatigue Test and Result Analysis

^{6}, Δσ

_{1}was equal to 171.92 MPa.

_{1}, then compared N

_{1}with the number of cycles N when the specimen was fractured, and the proportion of initiation life could be obtained, as shown in Table 6.

_{1}curve equation at 50% probability of survival of the details of the structure was fitted as shown in Equation (2):

^{6}, Δσ

_{2}was equal to 170.47 MPa.

_{1}curve equation at 97.7% probability of survival of the details of the structure was fitted as shown in Equation (3):

^{6}, Δσ

_{2}was equal to 111.53 MPa.

#### 2.3. The Effect of Surface Roughness on Fatigue Life

## 3. Stress Spectrum Calculation

#### 3.1. Loading Method

#### 3.2. FE Model and Stress Calculation of Steel Bridge Structure

#### 3.2.1. Simplified Finite Element Model of Steel Bridge Structure

#### 3.2.2. Determination of the Concerned Point

#### 3.2.3. The Calculation of Stress Frequency Spectrum

## 4. Fatigue Life Assessment of the Concerned Point

^{2}) of the fatigue strength at two million cycles, the constant amplitude fatigue limit corresponded to the fatigue strength for five million cycles, and the cut-off limit corresponded to the fatigue strength for 100 million cycles. According to the test result, when the probability of survival was 50%, the constant amplitude fatigue limit (N = 5 × 10

^{6}) of the detail of the weld joint was Δσ

_{L}

_{50%}= 135.71 MPa, and the cut-off limit (N = 10

^{8}) was Δσ

_{cut50%}= 81.50 MPa. The maximum stress amplitude of the detail was 38.29 MPa, less than the cut-off limit. When the probability of survival was 97.7%, the constant amplitude fatigue limit (N = 5 × 10

^{6}) of the detail was Δσ

_{L}

_{97.7%}= 88.43 MPa, and the cut-off limit (N = 10

^{8}) was Δσ

_{cut97.7%}= 53.11 MPa.

_{i}is the i-th stress amplitude, N

_{i}is the total number of cycles of the i-th stress amplitude, n

_{i}is the number of cycles of the i-th stress amplitude, and i = 1, 2, 3, 4, 5,….

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Microstructures of a steel weld joint: (

**a**) Steel specimen; (

**b**) weld metal; and (

**c**) the heat affected zone.

**Figure 3.**The crack of the specimen SY-2-1-8: (

**a**) Fatigue test; (

**b**) crack of the specimen; and (

**c**) the position of the crack.

**Figure 5.**The crack of the specimen SY-2-1-6: (

**a**) Crack of the specimen; and (

**b**) position of the crack.

**Figure 9.**The position of the concerned point: (

**a**) Position of the concerned point; and (

**b**) the concerned point in the model.

**Figure 12.**The stress-time curve of concerned point by various vehicles load: (

**a**) Vehicle model V1; (

**b**) Vehicle model V2; (

**c**) Vehicle model V3; (

**d**) Vehicle model V4; (

**e**) Vehicle model V5; (

**f**) Vehicle model V6; and (

**g**) Vehicle model V7.

Designation | Element (%) | |||||
---|---|---|---|---|---|---|

C | Si | Mn | P | S | Als | |

Q345qD | ≤0.18 | ≤0.60 | 1.1–1.6 | ≤0.025 | ≤0.025 | ≥0.015 |

E501T-1 | ≤0.18 | ≤0.90 | ≤1.75 | ≤0.03 | ≤0.03 | - |

Designation | Specimen Number | Yield Strength/MPa | Tensile Strength/MPa |
---|---|---|---|

Q345qD | 1 | 331.3 | 507.5 |

2 | 342.6 | 517.3 | |

3 | 344.5 | 509.9 | |

Mean value | 339.5 | 511.6 | |

E501T-1 | 1 | 495 | 575 |

Electrode Diameter (mm) | Welding Current (A) | Arc Voltage (V) | Welding Speed (cm/min) |
---|---|---|---|

Φ1.2 | 180 | 24 | 20 |

Specimens Number | Stress Amplitudes Δσ/MPa | Number of Cycles N | lgΔσ | lgN |
---|---|---|---|---|

SY-2-1-1 | 332.4 | 152,168 | 2.522 | 5.182 |

SY-2-1-2 | 272.4 | 820,188 | 2.435 | 5.914 |

SY-2-1-3 | 212.5 | 1,031,746 | 2.327 | 6.014 |

SY-2-1-4 | 164.5 | 1,513,565 | 2.216 | 6.180 |

SY-2-1-5 | 272.4 | 365,118 | 2.435 | 5.562 |

SY-2-1-6 | 272.4 | 1,354,662 | 2.435 | 6.132 |

SY-2-1-7 | 272.4 | 290,476 | 2.435 | 5.463 |

SY-2-1-8 | 272.4 | 376,123 | 2.435 | 5.575 |

SY-2-1-9 | 272.4 | 217,132 | 2.435 | 5.337 |

SY-2-1-10 | 272.4 | 677,876 | 2.435 | 5.831 |

SY-2-1-11 | 176.5 | 1,419,414 | 2.247 | 6.152 |

Probabilities of Survival (%) | Δσ-N Curve Equations | Stress Amplitude Δσ/MPa (N = 2 × 10^{6}) |
---|---|---|

60 | $\mathrm{lg}N=14.875-3.876\mathrm{lg}\Delta \sigma $ | 162.95 |

70 | $\mathrm{lg}N=14.778-3.876\mathrm{lg}\Delta \sigma $ | 153.81 |

80 | $\mathrm{lg}N=14.663-3.876\mathrm{lg}\Delta \sigma $ | 143.64 |

90 | $\mathrm{lg}N=14.504-3.876\mathrm{lg}\Delta \sigma $ | 130.74 |

97.7 | $\mathrm{lg}N=14.244-3.876\mathrm{lg}\Delta \sigma $ | 112.08 |

99 | $\mathrm{lg}N=14.126-3.876\mathrm{lg}\Delta \sigma $ | 104.44 |

Specimen Number | Stress Amplitude Δσ/MPa | Number of Cycles when Crack Occurred N_{1} | Number of Cycles N | Proportion of Initiation Life |
---|---|---|---|---|

SY-2-1-1 | 332.37 | 113,210 | 152,168 | 74.40% |

SY-2-1-3 | 212.47 | 964,524 | 1,031,746 | 93.48% |

SY-2-1-4 | 164.51 | 1,440,870 | 1,513,565 | 95.20% |

SY-2-1-5 | 272.42 | 323,484 | 365,118 | 88.60% |

SY-2-1-7 | 272.42 | 230,748 | 290,476 | 79.44% |

SY-2-1-8 | 272.42 | 351,444 | 376,123 | 93.44% |

SY-2-1-9 | 272.42 | 171,784 | 217,132 | 79.12% |

SY-2-1-10 | 272.42 | 592,622 | 677,876 | 87.42% |

SY-2-1-11 | 176.50 | 1,207,128 | 1,419,414 | 85.04% |

Specimen Number | Theoretical Number of Cycles | Test Number of Cycles | Growth Rate/% |
---|---|---|---|

SY-2-1-2 | 344,372 | 820,188 | 138.2% |

SY-2-1-6 | 344,372 | 1,354,662 | 293.4% |

Vehicle Model | Number of Axles | Illustrations Axle Load/kN, Wheelbase/mm | Total Weight/kN | Number of Vehicles | Ratio of Total Traffic |
---|---|---|---|---|---|

V1 | 2 | 137 | 19,078 | 14.74% | |

V2 | 3 | 222 | 2778 | 2.15% | |

V3 | 3 | 318 | 916 | 0.71% | |

V4 | 4 | 317 | 5342 | 4.13% | |

V5 | 5 | 375 | 163 | 0.13% | |

V6 | 5 | 384 | 1682 | 1.30% | |

V7 | 6 | 467 | 18,009 | 13.91% | |

Total | 47,968 | 37.06% |

Vehicle Weight | Vehicle Model | Inside Lane | Center Lane | Outside Lane |
---|---|---|---|---|

0–2 t | Cars, light buses | 0.699 | 0.248 | 0.054 |

2–8 t | Bus Two axle truck I | 0.244 | 0.372 | 0.384 |

>8 t | Two-axle bus Two axle truck II | 0.042 | 0.650 | 0.309 |

Number of Axles | Daily Average Number of Vehicles | Inside Lane | Center Lane | Outside Lane |
---|---|---|---|---|

3 | 1171 | 0.076 | 0.435 | 0.489 |

4 | 3384 | 0.043 | 0.310 | 0.648 |

5 | 1284 | 0.067 | 0.401 | 0.533 |

6 | 543 | 0.091 | 0.420 | 0.488 |

Stress Level | Stress Amplitude/MPa | Number of Cycles |
---|---|---|

1 | 0–5 | 498,915 |

2 | 5–10 | 0 |

3 | 10–15 | 838,642 |

4 | 15–20 | 183,148 |

5 | 20–25 | 1,139,528 |

6 | 25–30 | 997,920 |

7 | 30–35 | 339,727 |

8 | 35–40 | 78,374 |

Total | 4,076,254 |

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## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Lv, P.; Li, D.
Research on Fatigue Strength for Weld Structure Details of Deck with U-rib and Diaphragm in Orthotropic Steel Bridge Deck. *Metals* **2019**, *9*, 484.
https://doi.org/10.3390/met9050484

**AMA Style**

Chen Y, Lv P, Li D.
Research on Fatigue Strength for Weld Structure Details of Deck with U-rib and Diaphragm in Orthotropic Steel Bridge Deck. *Metals*. 2019; 9(5):484.
https://doi.org/10.3390/met9050484

**Chicago/Turabian Style**

Chen, Yixin, Pengmin Lv, and Datao Li.
2019. "Research on Fatigue Strength for Weld Structure Details of Deck with U-rib and Diaphragm in Orthotropic Steel Bridge Deck" *Metals* 9, no. 5: 484.
https://doi.org/10.3390/met9050484