# Experimental Investigation of the Fatigue Life of a Bridge Crane Girder Using S-N Method

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Analyzed Bridge Crane’s Description

#### 2.2. Strain Gauge Measurement

#### 2.3. Description of Operating Modes

## 3. Results

#### 3.1. Normal and Shear Stresses Calculated at Individual Operating Modes

#### 3.2. Calculation of Maximum Stresses Taking into Account the Validity of STN 270103

- load factor from self-weight
| ${\gamma}_{g}=1.1;$ |

- load factor from the rated load for D2
| ${\gamma}_{\ell 0}=1.3;$ |

- dynamic lift coefficient for H3
| ${\delta}_{h}=1.37.$ |

^{−1}.

- for the upper fibers
| ${W}_{z}^{-}=\mathrm{14,71,606}{\mathrm{mm}}^{3};$ |

- for the lower fibers
| ${W}_{z}^{+}=\mathrm{13,831,936}{\mathrm{mm}}^{3}.$ |

#### 3.3. Assessment of the Dynamic Lift Coefficient

- Lifting speed controlled by the crane operator;
- Speed stage 2;
- Speed stage 3;
- Speed stage 4 (maximum lifting speed 10.79 m/min).

#### 3.4. Assessment of Fatigue Life and Strength According to STN 270103

#### 3.5. Experimental-Computational Verification of the Possible Accumulation of Fatigue Damage of the Bridge Crane

#### 3.6. Analysis of the Cycles Operated

- 50% from 17 t to 21 t (steel coil + C-hook);
- 25% from 14 t to 17 t (steel coil + C-hook);
- 25% from 11 t to 14 t (steel coil + C-hook).

#### 3.7. Comparasion of Fatique Life

## 4. Discussion

- Inspection of parts of the steel support structure revealed that the welded joints (accessible from the footbridge) did not show any flags of damage and were without significant corrosion. The auxiliary steel elements on the bridge and the crab, footbridge and protective railing were intact. It could be concluded that the visual inspection did not reveal any corrosion.
- Strain gauge measurements showed that the stress increments and the stresses from self-weight and other effects did not exceed the allowable stress values. The experimentally determined dynamic lift coefficient was less than that specified in STN 270103 standard. Based on the strain gauge measurements analysis, it could be concluded that the girders of the bridge crane were satisfactory in terms of strength.
- The assessment of the fatigue damage accumulation showed that under the operating modes considered, the current technical state of the crane’s steel structure had a sufficient fatigue life reserve.
- The differences in the values of the normal stresses determined from the strain gauge measurements at the center of the girders A (location A1) and B (location B3) of the bridge crane were, in some cases, greater than 50%. This phenomenon occurs regularly when the crab passes through the center of the girder. It is due to the attachment of the rails to the girders. Although on girder B, the rail near locations B3 and B4 was welded to the top flange, even at these stress levels, girder B was satisfactory in terms of both strength and fatigue life. Since there was a significantly higher level of damage in the areas around the welded rail, the authors recommended that the rail attachment to the girders be carefully checked when the rails were replaced.
- The effect of welding the rail to the top flange of the girder was evident from a comparison of the measured normal stresses on girders A and B (Figure 13). This welding significantly increased the damage level in the corresponding cross-section, i.e., reduced the fatigue life of girder B.
- The stress values at locations A1 and A2 on girder A and at locations B3 and B4 on girder B were different during all operational measurements, although their nature was the same. This fact confirmed the deformation (twisting) of the girders’ cross-section and the crab’s associated slope, i.e., the height difference of the girders. For this reason, it was also recommended to check the wear of the crab wheels.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Time courses of stresses, Mode 1; movement of the crab without load: (

**a**) full record, (

**b**) detail record for the crab passing through the center of the girders.

**Figure 4.**Time courses of stresses, Mode 2; manipulation of coils 1, 2 and 3: (

**a**) full record, (

**b**) detail record for the crab passing through the center of the girders.

**Figure 5.**Time courses of stresses, Mode 3; coil 6: (

**a**) full record, (

**b**) detail record for the crab passing through the center of the girders.

**Figure 6.**The cross-section of girder: (

**a**) at the center of the bridge crane (location of the maximum bending moment), (

**b**) at 300 mm distance from the center of the bridge crane.

**Figure 7.**Experimental determination of the dynamic lift coefficient—time courses of calculated normal stresses and visualization of their mean values.

**Figure 8.**Dependence between the calculated fatigue strengths R

_{fat}(−1) and R

_{fat}(χ). Note: σ

_{U}—ultimate strength, σ

_{Y}—yield strength, σ

_{max}—maximum stress, σ

_{min}—minimum stress, σ

_{fat, t}—fatigue strength by tensile loading, σ

_{fat, c}—fatigue strength by compression.

**Figure 13.**Comparison of the normal stress courses obtained at the same instant of time when the crab passed through the center of the girders: (

**a**) girder A (locations 1, 2, 8), (

**b**) girder B (locations 3, 4, 7).

Parameter | Value |
---|---|

capacity | 22,000/5000 kg |

lifting height | 10 m |

span | 28.5 m |

control | from the cab |

drive type | Electric |

main lift | 10.79 m/min |

auxiliary lift | 25 m/min |

crab travel | 0.833 m/s, (50 m/min) |

crane travel | 1.667 m/s, (100 m/min)–4 speed levels |

length | 168 m |

height level | 11 m |

Parameter | Group |
---|---|

lifting class | H3 |

type of operation | D2 |

stress spectrum | S2 |

operational group | J5 |

Coil Group/Sector | Coil Number | Total Weight of Load (kg) ^{1} |
---|---|---|

I/Sector 2A | 1 | 13,400 |

2 | 19,120 | |

3 | 20,950 | |

II/Sector 2B | 1 | 13,610 |

2 | 19,300 | |

3 | 20,930 |

^{1}The total weight of the load consists of the steel coil unladen and the crane hook used.

Stress | Measured Location | Normal/Shear Stress at Load 20,930 kg (MPa) | Absolute Difference (MPa) |
---|---|---|---|

Normal | A1 | −54.3 | 0.1 |

A1 | −54.2 | ||

B3 | −70.8 | 4.6 | |

B4 | −66.2 | ||

B7 | −46.4 | 7.3 | |

A8 | −53.7 | ||

Shear | B5 | - | |

A6 | 16.0 |

Mode | Number of Cycles to Failure H_{PM} at Strain Gauge Locations | |||||
---|---|---|---|---|---|---|

A1 | A2 | B3 | B4 | B7 | A8 | |

2 | 1,042,204 | 926,605 | 527,273 | 594,307 | 877,733 | 912,436 |

3 | 905,820 | 886,978 | 417,921 | 482,169 | 857,737 | 888,170 |

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**MDPI and ACS Style**

Pástor, M.; Lengvarský, P.; Hagara, M.; Kuľka, J.
Experimental Investigation of the Fatigue Life of a Bridge Crane Girder Using S-N Method. *Appl. Sci.* **2022**, *12*, 10319.
https://doi.org/10.3390/app122010319

**AMA Style**

Pástor M, Lengvarský P, Hagara M, Kuľka J.
Experimental Investigation of the Fatigue Life of a Bridge Crane Girder Using S-N Method. *Applied Sciences*. 2022; 12(20):10319.
https://doi.org/10.3390/app122010319

**Chicago/Turabian Style**

Pástor, Miroslav, Pavol Lengvarský, Martin Hagara, and Jozef Kuľka.
2022. "Experimental Investigation of the Fatigue Life of a Bridge Crane Girder Using S-N Method" *Applied Sciences* 12, no. 20: 10319.
https://doi.org/10.3390/app122010319