Testing and Evaluation of Anchor Channels under Fatigue Loading
Abstract
:1. Introduction
2. Fatigue Behavior of Anchor Channels
2.1. Steel Failure of the Channel Bolt
2.2. Steel Failure of the Anchor
2.3. Steel Failure of the Connection Anchor Channel
2.4. Steel Failure of the Channel Lips or Flanges
2.5. Steel Failure by Flexure of the Channel
3. Evaluation of the Fatigue Resistance
3.1. General Procedure
3.2. Linear Regression Analysis
3.3. Characteristic Fatigue Resistance of Finite Life
3.4. Verification of Endurance Limit
- Carbon steel: 5 × 106 ≤ nlim ≤ 8 × 106
- Stainless steel: 7 × 106 ≤ nlim ≤ 1 × 107
4. Experimental Example
5. Comparison of Test Methods
6. Discussion and Conclusions
- For the generation of the S/N curve, a minimum of six pre-tests for each load position (anchor/ middle of two anchors) and 16–20 fatigue tests for the decisive position are recommended.
- The fatigue resistance of finite life may be determined by the linear regression of test data in logarithmic scale using the least square method, taking the number of cycles as a dependent variable. Tests that had been stopped without failure cannot be included in the evaluation.
- For the verification of the endurance limit at least four run-out tests with sufficient load level reaching a predefined limit number of cycles must be identified.
- The evaluation procedure is described in detail and illustrated by a worked example, which facilitates the reproducibility of the calculations to assure reliable and consistent results from different testing institutes.
- Based on the results, a comparison with the existing methods shows good agreement, although the proposed method focuses on fatigue relevant loading with more than 104 cycles. This indicates that the evaluation principles of Eurocode 3 are also applicable to adequately capture the steel fatigue resistance of anchor channels.
- The provided bilinear function has the advantage that the fatigue resistance can be defined by two parameters, the value at a certain number of cycles, e.g., nlim, and the slope of the S/N curve.
- The characteristic fatigue resistance in the finite life area (1 × 104 ≤ n ≤ 5 × 106) may be represented by the linear 5%-quantile line determined under the assumption of a constant standard deviation.
- Using the characteristic resistance values obtained with this method, a constant partial factor for steel failure can be recommended for design as the scatter of fatigue data is regarded as almost constant for n ≥ 1 × 104 load cycles. Therefore, the use of a variable factor to consider the transition from the static resistance is not required.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A. Experimental Example
Test i | Load Range ∆Fi [kN] | Load Cycles n [-] | log ∆Fi [-] | log n [-] | log ∆Fi∙log n [-] | log ∆Fi 2 [-] |
---|---|---|---|---|---|---|
1 | 30 | 3.462 | 1.477 | 3.539 | 5.227 | 2.182 |
2 | 24 | 7.063 | 1.380 | 3.849 | 5.312 | 1.904 |
3 | 24 | 11.632 | 1.380 | 4.066 | 5.611 | 1.904 |
4 | 22 | 20.029 | 1.342 | 4.302 | 5.773 | 1.801 |
5 | 22 | 10.307 | 1.342 | 4.013 | 5.385 | 1.801 |
6 | 21 | 6.239 | 1.322 | 3.795 | 5.017 | 1.748 |
7 | 20 | 10.189 | 1.301 | 4.008 | 5.214 | 1.693 |
8 | 20 | 16.748 | 1.301 | 4.224 | 5.495 | 1.693 |
9 | 18 | 44.292 | 1.255 | 4.646 | 5.831 | 1.575 |
10 | 18 | 12.593 | 1.255 | 4.100 | 5.146 | 1.575 |
11 | 16 | 25.584 | 1.204 | 4.408 | 5.307 | 1.450 |
12 | 16 | 66.416 | 1.204 | 4.822 | 5.806 | 1.450 |
13 | 16 | 27.244 | 1.204 | 4.435 | 5.340 | 1.450 |
14 | 15 | 73.128 | 1.176 | 4.864 | 5.720 | 1.383 |
15 | 14 | 45.298 | 1.146 | 4.656 | 5.336 | 1.313 |
16 | 14 | 119.701 | 1.146 | 5.078 | 5.819 | 1.313 |
17 | 13 | 45.596 | 1.114 | 4.659 | 5.190 | 1.241 |
18 | 12 | 95.377 | 1.079 | 4.979 | 5.372 | 1.164 |
19 | 12 | 241.237 | 1.079 | 5.382 | 5.807 | 1.164 |
20 | 11 | 528.773 | 1.041 | 5.723 | 5.958 | 1.084 |
21 | 11 | 118.807 | 1.041 | 5.075 | 5.283 | 1.084 |
22 | 10 | 90.829 | 1.000 | 4.958 | 4.958 | 1.000 |
23 | 10 | 345.629 | 1.000 | 5.539 | 5.539 | 1.000 |
24 | 9.5 | 336.363 | 0.978 | 5.527 | 5.405 | 0.956 |
25 | 9 | 886.566 | 0.954 | 5.948 | 5.674 | 0.910 |
26 | 9 | 192.857 | 0.954 | 5.285 | 5.042 | 0.910 |
27 | 8 | 353.193 | 0.903 | 5.548 | 5.010 | 0.815 |
28 | 8 | 948.260 | 0.903 | 5.977 | 5.397 | 0.815 |
29 | 8 | 1.413.670 | 0.903 | 6.150 | 5.553 | 0.815 |
30 | 7 | 2.081.140 | 0.845 | 6.318 | 5.339 | 0.714 |
31 | 7 | 1.767.506 | 0.845 | 6.247 | 5.279 | 0.714 |
32 | 6 | 2.530.311 | 0.778 | 6.403 | 4.982 | 0.605 |
33 | 6 | 2.692.952 | 0.778 | 6.430 | 5.003 | 0.605 |
34 | 6 | 1.021.174 | 0.778 | 6.009 | 4.675 | 0.605 |
35 | 5.8 | 2.561.643 | 0.763 | 6.409 | 4.890 | 0.582 |
m | ∑ log ∆Fi | ∑ log n | ∑ log ∆Fi ∙log n | ∑ log ∆Fi 2 | ||
35 | 38.171 | 177.371 | 187.695 | 43.018 |
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Method A1 | Method A2 | Method B | |
---|---|---|---|
Function for S/N curve | continuous | trilinear | no |
Area of application | N = 1 to n = ∞ | N = 1 to n = ∞ | n = ∞ |
Number of tests 1 | 20 | 20 | 3 |
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Fröhlich, T.; Lotze, D. Testing and Evaluation of Anchor Channels under Fatigue Loading. CivilEng 2021, 2, 1-13. https://0-doi-org.brum.beds.ac.uk/10.3390/civileng2010001
Fröhlich T, Lotze D. Testing and Evaluation of Anchor Channels under Fatigue Loading. CivilEng. 2021; 2(1):1-13. https://0-doi-org.brum.beds.ac.uk/10.3390/civileng2010001
Chicago/Turabian StyleFröhlich, Thilo, and Dieter Lotze. 2021. "Testing and Evaluation of Anchor Channels under Fatigue Loading" CivilEng 2, no. 1: 1-13. https://0-doi-org.brum.beds.ac.uk/10.3390/civileng2010001