Fatigue Durability Analysis for Suspenders of Arch Bridge Subjected to Moving Vehicles in Southwest China
Abstract
:1. Introduction
2. Establishment of a Standard Fatigue Car Model
2.1. Vehicle Statistics
- Closure of lanes in a reasonable manner. The Xijiang Bridge has four lanes, and there are two lanes in the same direction. Therefore, in the same direction, the roadside lane is closed first, and the other lane is opened to traffic.
- Draw lines and cut grooves in the closed driveway.
- Cleaning and blow-drying the cut groove.
- Install the sensor in the groove, see Figure 1. The circuit leads to the roadside cabinet.
- Fill the groove with caulking glue, and it takes 3–8 h for the caulking glue to cure according to the weather conditions.
- Grind the joint sealant and the road surface.
2.2. Establish a Standard Fatigue Car Model
3. Calculation Method of the Fatigue Life of Suspenders
Concrete Calculation Steps of the Fatigue Life of Suspenders
- Find or calculate the local standard fatigue car model.
- Traffic flow statistics on the bridge, which can be made by the health monitoring system.
- Establishment of the bridge MIDAS model.
- Simulation of random traffic flow based on the Monte Carlo method.
- 5.
- Calculation of suspenders’ stress spectrum.
- 6.
- Calculation of the fatigue life of suspenders.
- (a)
- The S–N curve of the material is modified by the mean stress [37].
- (b)
- Calculation of equivalent stress amplitude σae.
- (c)
- Calculation of the fatigue life according to the fatigue damage degree.
4. Engineering Verification and Application
4.1. Brief Introduction of the Project
4.2. Finite Element Verification
4.3. Engineering Application
4.3.1. Traffic Flow Statistics
4.3.2. Establishment of the Bridge MIDAS Model
4.3.3. Simulation of Random Traffic Flow Based on Monte Carlo Method
4.3.4. Simulated Traffic Load and Stress Spectrum Calculation of Suspenders
4.3.5. Fatigue Life Calculation of Suspenders
5. Conclusions
- According to the traffic flow statistics of typical road sections, a standard fatigue vehicle model in Southwest China is established. Comparing our model with the standard fatigue vehicle in the Chinese General Code for Design JGD60-2015, we established that the model’s weight is lower. It is proved that even near the port, the number of heavy vehicles and their weight are not necessarily too high. There are differences in different regions, so it is inevitable to establish standard fatigue vehicles in Southwest China. Subsequently, this model can be used for vehicle fatigue simulation of similar road sections in Southwest China and other areas. It is not essential to obtain a large number of vehicle statistics and calculations again, thus improving the efficiency of further vehicle fatigue simulation.
- A set of calculation methods for the fatigue life of suspenders under the vehicle load is put forward. Compared with finite element calculation, this method has an error rate of less than 5% and can be effectively applied to practical projects, which proves its accuracy and feasibility. In the future, this method can be applied to the bridge health monitoring software system. According to the established standard fatigue vehicle model and the road traffic volume counted, the fatigue damage of bridge suspenders in Southwest China can be monitored in real time. Therefore, the fatigue life of bridges in Southwest China can be evaluated, which provides a reference for replacing suspenders.
- In practical engineering, the life of Dafeng River Bridge suspenders is calculated. It is found that the life of nos. 1–7 suspenders is on the rise. The life of the no. 1 suspender is the shortest, even less than one-third of that of the no. 7 suspender, mainly because the no. 1 suspender is short in length and close to the arch foot. Its stress amplitude is large under the action of vehicle load, so its fatigue damage is large and its fatigue life is low. Therefore, more attention should be paid to the health status of short suspenders near the arch foot in practical engineering.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Vehicles | Quantity | D1 | d1 | D2 | d2 | D3 | d3 | D4 | d4 | D5 | d5 | W | w | Classification |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
2 axle-1 | 92 | 1.50 | 0.08 | 0.467 | 0.2 | V1 | ||||||||
2 axle-2 | 11,672 | 2.66 | 0.10 | 1.40 | 0.47 | |||||||||
2 axle-3 | 1754 | 3.20 | 0.16 | 2.60 | 2.17 | |||||||||
2 axle-4 | 134 | 4.20 | 0.25 | 7.9 | 3.08 | V2 | ||||||||
2 axle-5 | 251 | 5.20 | 0.26 | 11.4 | 2.86 | V3 | ||||||||
3 axle-1 | 36 | 1.85 | 0.12 | 3.9 | 1.15 | 13.9 | 7.1 | V4 | ||||||
3 axle-2 | 123 | 3.60 | 0.20 | 1.3 | 0.51 | 20.3 | 12.5 | V5 | ||||||
3 axle-3 | 138 | 4.20 | 0.45 | 1.4 | 0.31 | 23.0 | 13.3 | |||||||
4 axle-1 | 437 | 1.90 | 0.10 | 4.1 | 0.76 | 1.35 | 0.09 | 31.9 | 20.0 | V6 | ||||
4 axle-2 | 19 | 2.90 | 0.66 | 7.4 | 2.10 | 2.50 | 0.74 | 8.20 | 11.50 | V7 | ||||
4 axle-3 | 66 | 2.70 | 0.20 | 7.8 | 1.45 | 2.70 | 0.18 | 3.25 | 0.73 | |||||
5 axle-1 | 4 | 2.00 | 0.17 | 3.0 | 2.07 | 3.50 | 0.57 | 1.3 | 0.26 | 28.4 | 11.3 | V8 | ||
5 axle-2 | 10 | 1.90 | 0.12 | 2.7 | 0.86 | 4.00 | 0.66 | 1.3 | 0.12 | 29.1 | 10.8 | |||
5 axle-3 | 22 | 3.40 | 0.14 | 1.4 | 0.41 | 3.70 | 0.37 | 1.3 | 0.10 | 29.2 | 12.0 | |||
5 axle-4 | 6 | 3.50 | 0.79 | 1.36 | 0.18 | 5.65 | 2.14 | 1.4 | 0.41 | 26.56 | 12.8 | |||
5 axle-5 | 2 | 3.60 | 0.37 | 6.8 | 1.21 | 2.20 | 2.58 | 1.5 | 0.53 | 30.6 | 15.1 | |||
6 axle-1 | 16 | 1.80 | 0.25 | 3.0 | 1.36 | 3.10 | 0.87 | 1.8 | 2.10 | 1.4 | 0.38 | 26.15 | 10.1 | V9 |
6 axle-2 | 96 | 3.40 | 0.15 | 1.36 | 0.31 | 3.60 | 0.67 | 1.3 | 0.27 | 1.3 | 0.06 | 33.5 | 19.9 | |
6 axle-3 | 198 | 3.37 | 0.10 | 1.35 | 0.07 | 5.88 | 0.39 | 1.3 | 0.05 | 1.3 | 0.03 | 43.6 | 23.1 |
Parameter | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 |
---|---|---|---|---|---|---|---|---|
axles | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 6 |
D1 (m) | 4.2 | 5.2 | 1.85 | 3.90 | 1.90 | 2.70 | 2.95 | 3.3 |
D2 (m) | 3.90 | 1.35 | 4.10 | 7.70 | 2.00 | 1.4 | ||
D3 (m) | 1.35 | 2.65 | 3.95 | 5.0 | ||||
D4 (m) | 1.30 | 1.3 | ||||||
D5 (m) | 1.3 |
Parameter | V2 | V3 | V4 | V5 | V6 | V7 | V8 | V9 |
---|---|---|---|---|---|---|---|---|
axles | 2 | 2 | 3 | 3 | 4 | 4 | 5 | 6 |
A1 (μ1) | 27 (0.34) | 36 (0.32) | 36 (0.26) | 52 (0.24) | 57 (0.18) | 11 (0.21) | 45 (0.15) | 52 (0.13) |
A2 (μ2) | 52 (0.66) | 78 (0.68) | 30 (0.22) | 83 (0.38) | 57 (0.18) | 13 (0.25) | 47 (0.16) | 68 (0.17) |
A3 (μ3) | 73 (0.52) | 84 (0.38) | 101 (0.32) | 14 (0.27) | 48 (0.20) | 70 (0.17) | ||
A4 (μ4) | 104 (0.18) | 14 (0.27) | 71 (0.24) | 66 (0.16) | ||||
A5 (μ5) | 74 (0.25) | 69 (0.17) | ||||||
A6 (μ6) | 79 (0.20) | |||||||
G (kN) | 79 | 114 | 139 | 219 | 319 | 52 | 295 | 404 |
Classification | Axles | G(kN) | Model Legend | Quantity | Frequency (%) |
---|---|---|---|---|---|
V2 | 2 | 79 | 134 | 8.61 | |
V3 | 2 | 114 | 251 | 16.11 | |
V4 | 3 | 139 | 36 | 2.31 | |
V5 | 3 | 219 | 261 | 16.75 | |
V6 | 4 | 319 | 437 | 28.05 | |
V7 | 4 | 52 | 85 | 5.45 | |
V8 | 5 | 295 | 44 | 2.82 | |
V9 | 6 | 404 | 310 | 19.9 |
Suspender | Fatigue Life Calculated by ANSYS (Years) | Theoretical Fatigue Life (Years) | Error |
---|---|---|---|
No. 7 | 677.8 | 670 | 1.16% |
No. 6 | 583.4 | 575 | 1.46% |
No. 1 | 185.2 | 178 | 4.04% |
Lane | Periods | The Daily Traffic Flow | The Hourly Traffic Flow |
---|---|---|---|
No. 3 | daytime (6:00–20:00) | 831 | 60 |
night (20:00–6:00) | 208 | 21 | |
No. 2 | daytime (6:00–20:00) | 415 | 30 |
night (20:00–6:00) | 104 | 11 |
Periods | Lane | Average Vehicle Distance (m) |
---|---|---|
daytime | No. 2 | 2758.6 |
No. 3 | 1355.9 | |
night | No. 2 | 8000 |
No. 3 | 4000 |
Data Set | Capacity | U (m) | u (m) | D (m) | d (m) | Error |
---|---|---|---|---|---|---|
daytime lane no. 2 | 29 | 2758.6 | 2759 | 40 | 40.62 | 1.55% |
daytime lane no. 3 | 59 | 1355.9 | 1356 | 20 | 20.11 | 0.55% |
night lane no. 2 | 10 | 8000 | 8000 | 120 | 119.41 | 0.494% |
night lane no. 3 | 20 | 4000 | 4000.1 | 60 | 60.83 | 1.33% |
Lane | Number of Cars | Distance from the Front Car (m) | Position (m) |
---|---|---|---|
No. 2 | 1 | 0 | |
2 | 2770.55 | 2770.55 | |
3 | 2752.07 | 5522.62 | |
4 | 2782.89 | 8305.51 | |
29 | 2784.16 | 77,226.51 | |
30 | 2773.49 | 80,000 | |
No. 3 | 1 | 0 | |
2 | 1337.79 | 1337.79 | |
3 | 1358.82 | 2696.61 | |
4 | 1383.86 | 4080.47 | |
59 | 1409.4 | 78,644.22 | |
60 | 1355.78 | 80,000 |
Lane | Number of Cars | Distance from the Front Car (m) | Position (m) |
---|---|---|---|
No. 2 | 1 | 0 | |
2 | 7977.34 | 7977.34 | |
3 | 8017.79 | 15,995.13 | |
4 | 7785.93 | 23,781.06 | |
10 | 8194.95 | 71,896.35 | |
11 | 8103.65 | 80,000 | |
No. 3 | 1 | 0 | |
2 | 3974.09 | 3974.09 | |
3 | 3949.9 | 7923.99 | |
4 | 4010.78 | 11,934.77 | |
20 | 3988.2 | 76,053.54 | |
21 | 3946.46 | 80,000 |
Suspenders | Dead Load (kN) | Dead Load Stress (MPa) |
---|---|---|
No. 1 | 996.8 | 79.942 |
No. 2 | 1250.6 | 100.297 |
No. 3 | 1233.3 | 98.909 |
No. 4 | 1154.6 | 92.598 |
No. 5 | 1186.0 | 95.116 |
No. 6 | 1172.4 | 94.025 |
No. 7 | 1209.5 | 97.001 |
Stress Amplitude σa (MPa) | Number of Cycles | Stress Amplitude σa (MPa) | Number of Cycles |
---|---|---|---|
0–1 | 167 | 50–70 | 49 |
1–25 | 3 | 70–95 | 59 |
25–50 | 2 |
Suspender Number | Periods | Equivalent Stress Amplitude σae (MPa) | Fatigue Loading Cycles | Daily Cycles | Daily Damage Degree (10−6) | Fatigue Life (Years) |
---|---|---|---|---|---|---|
No. 7 | daytime | 50.22 | 1,158,594,655 | 3920 | 3.38 | 670 |
night | 49.103 | 1,256,558,780 | 890 | 0.71 | ||
No. 6 | daytime | 52.48 | 999,296,804 | 3892 | 3.90 | 575 |
night | 51.95 | 1,037,712,186 | 890 | 0.86 | ||
No. 5 | daytime | 53.15 | 953,834,246 | 3864 | 4.05 | 561 |
night | 51.967 | 1,034,303,102 | 860 | 0.83 | ||
No. 4 | daytime | 54.21 | 894,520,612 | 3920 | 4.38 | 513 |
night | 53.699 | 926,746,173 | 880 | 0.95 | ||
No. 3 | daytime | 55.55 | 810,817,727 | 3612 | 4.46 | 469 |
night | 59.66 | 633,102,176 | 870 | 1.30 | ||
No. 2 | daytime | 59.419 | 638,575,289 | 3976 | 6.23 | 359 |
night | 59.35 | 642,890,010 | 900 | 1.40 | ||
No. 1 | daytime | 82.72 | 209,448,213 | 2702 | 13.00 | 178 |
night | 79.47 | 241,175,283 | 580 | 2.40 |
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Zhang, Z.; Wang, H.; Yang, T.; Wang, L.; Wang, X. Fatigue Durability Analysis for Suspenders of Arch Bridge Subjected to Moving Vehicles in Southwest China. Sustainability 2022, 14, 10008. https://doi.org/10.3390/su141610008
Zhang Z, Wang H, Yang T, Wang L, Wang X. Fatigue Durability Analysis for Suspenders of Arch Bridge Subjected to Moving Vehicles in Southwest China. Sustainability. 2022; 14(16):10008. https://doi.org/10.3390/su141610008
Chicago/Turabian StyleZhang, Zimo, Hua Wang, Tao Yang, Longlin Wang, and Xirui Wang. 2022. "Fatigue Durability Analysis for Suspenders of Arch Bridge Subjected to Moving Vehicles in Southwest China" Sustainability 14, no. 16: 10008. https://doi.org/10.3390/su141610008