Simplified Criterion for Low Gravity Center Cable-Stayed Bridge Based on Response Spectrum Analyses
Abstract
:1. Introduction
2. Simplified Calculation of the Fundamental Period of Cable-Stayed Bridge
2.1. The Floating Cable-Stayed Bridge
2.2. The Longitudinal Hinged Cable-Stayed Bridge
3. Criterion of Low Gravity Center Cable-Stayed Bridge
3.1. Simplified Calculation of Tower Bottom Moment
3.2. Criterion of Low Gravity Center Cable-Stayed Bridge
3.3. Comparison with Numerical Results
- (1)
- For the 10 floating cable-stayed bridges, according to the comparison of the bottom bending moment calculated by Equation (9) and that from the finite element method (FEM) with the 10 floating cable-stayed bridges, the maximum relative error was −12.56%, the minimum relative error was only −0.83%, and the average relative error was 1.36%. This indicates that the simplified calculation formula of Equation (9) could very well predict the bottom bending moment of the floating cable-stayed bridge.
- (2)
- For the 10 longitudinal hinged cable-stayed bridges, the maximum relative error between the bottom bending moment calculated by Equation (11) and that of the FEM was 11.55%, the minimum relative error was only −2.17%, and the average relative error was 4.65%. This showed that the simplified calculation formula of the bottom bending moment of the longitudinal hinged cable-stayed bridge was reasonable.
- (3)
- The standard deviations of relative error of the bending moment calculated by the simplified formulae and FEM of the floating cable-stayed bridge and the longitudinal hinged cable-stayed bridge were 9.2% and 4.5%, respectively, which showed that the simplified formulae had good stability.
- (4)
- The conclusion given by the criterion formula of Equation (12) of a low gravity center cable-stayed bridge was in good agreement with that from the FEM, which showed that the criterion formula of a low gravity center cable-stayed bridge was reliable and was helpful for the reasonable structural system selection in the preliminary design of the cable-stayed bridge.
4. Conclusions
- (1)
- Based on the simplified formula of the longitudinal fundamental period of cable-stayed bridges and combined with the response spectrum analysis method, the criterion formula of a low gravity center cable-stayed bridge was developed.
- (2)
- The conclusion given by the criterion formula of a low gravity center cable-stayed bridge was in good agreement with that from the FEM and tests, which revealed that the criterion formula of a low gravity center cable-stayed bridge is reasonable and can provide references for the preliminary design and the scheme selection of the cable-stayed bridge.
- (3)
- The seismic response characteristics of cable-stayed bridges are related to the structural system and the seismic characteristics. Therefore, whether a cable-stayed bridge is a low center of gravity cable-stayed bridge is also related to the structural characteristics of the cable-stayed bridge itself and the ground motion characteristics of its site.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Site Type | Single-Tower Cable-Stayed Bridge (Ji’nan No.3 Bridge) | Dual-Tower Cable-Stayed Bridge (Qidu Bridge) | |||||
---|---|---|---|---|---|---|---|
I | 1/10 | 8.86 | 9.80 | 1.23 | 5.45 | 6.34 | 1.19 |
2/10 | 9.04 | 10.1 | 1.37 | 8.28 | 8.65 | 1.09 | |
3/10 | 11.52 | 12.93 | 1.47 | 13.66 | 13.29 | 1.06 | |
4/10 | 13.35 | 14.28 | 1.49 | 19.33 | 18.57 | 1.01 | |
5/10 | 15.65 | 17.33 | 1.52 | 26.42 | 25.02 | 1.05 | |
II | 1/10 | 13.12 | 14.52 | 1.25 | 8.07 | 9.26 | 1.18 |
2/10 | 13.39 | 14.97 | 1.37 | 12.27 | 12.74 | 1.09 | |
3/10 | 17.06 | 19.15 | 1.47 | 20.24 | 19.7 | 1.06 | |
4/10 | 19.78 | 21.16 | 1.49 | 28.64 | 27.52 | 1.06 | |
5/10 | 23.18 | 25.67 | 1.52 | 39.14 | 37.07 | 1.09 | |
III | 1/10 | 18.04 | 19.96 | 1.23 | 11.09 | 12.76 | 1.18 |
2/10 | 18.41 | 20.58 | 1.39 | 16.87 | 17.39 | 1.09 | |
3/10 | 23.46 | 26.34 | 1.47 | 27.84 | 27.1 | 1.06 | |
4/10 | 27.2 | 29.10 | 1.49 | 39.38 | 37.86 | 1.10 | |
5/10 | 31.87 | 35.30 | 1.52 | 53.81 | 50.96 | 1.11 | |
IV | 1/10 | 22.14 | 24.50 | 1.25 | 13.62 | 15.57 | 1.18 |
2/10 | 22.6 | 25.27 | 1.39 | 8.28 | 8.65 | 1.08 | |
3/10 | 28.79 | 32.35 | 1.47 | 34.16 | 33.24 | 1.05 | |
4/10 | 33.38 | 35.72 | 1.49 | 48.33 | 46.48 | 1.11 | |
5/10 | 39.11 | 43.32 | 1.52 | 66.04 | 62.56 | 1.12 | |
average | - | - | 1.42 | - | - | 1.10 |
Bridge | The Floating Cable-Stayed Bridge | The Longitudinal Hinged Cable-Stayed Bridge | Criterion | |||||
---|---|---|---|---|---|---|---|---|
Jinan No.3 | 18.41 | 20.58 | 10.55 | 16.87 | 17.39 | 3.03 | 0.92 | 0.84 |
Songhuajiang | 15.36 | 14.31 | −7.33 | 10.49 | 10.27 | −2.17 | 0.68 | 0.72 |
Songyuan | 14.58 | 13.20 | −10.45 | 24.14 | 26.43 | 8.66 | 1.66 | 2.00 |
Nanye Road | 12.88 | 12.23 | −5.30 | 16.59 | 16.06 | −3.29 | 1.29 | 1.31 |
Haihe | 16.01 | 17.08 | 6.26 | 18.73 | 19.81 | 5.44 | 1.17 | 1.16 |
Feiyunjiang | 7.51 | 8.44 | 11.02 | 9.53 | 10.03 | 4.99 | 1.27 | 1.19 |
Jintang | 15.07 | 13.39 | −12.56 | 20.43 | 22.56 | 9.47 | 1.36 | 1.68 |
Qidu | 8.02 | 9.01 | 10.98 | 10.47 | 10.74 | 2.51 | 1.31 | 1.19 |
Taizhouwan | 10.06 | 9.98 | −0.83 | 10.18 | 10.86 | 6.28 | 1.01 | 1.09 |
Sutong | 48.15 | 54.25 | 11.24 | 48.51 | 54.85 | 11.55 | 1.01 | 1.01 |
Standard Deviation | / | / | 9.2% | / | / | 4.5% | / | / |
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Chen, Y.; Wang, Y.; Zhang, W.; Liang, K.; Du, X. Simplified Criterion for Low Gravity Center Cable-Stayed Bridge Based on Response Spectrum Analyses. Sustainability 2022, 14, 10570. https://doi.org/10.3390/su141710570
Chen Y, Wang Y, Zhang W, Liang K, Du X. Simplified Criterion for Low Gravity Center Cable-Stayed Bridge Based on Response Spectrum Analyses. Sustainability. 2022; 14(17):10570. https://doi.org/10.3390/su141710570
Chicago/Turabian StyleChen, Ying, Yonghuan Wang, Wenxue Zhang, Kun Liang, and Xiuli Du. 2022. "Simplified Criterion for Low Gravity Center Cable-Stayed Bridge Based on Response Spectrum Analyses" Sustainability 14, no. 17: 10570. https://doi.org/10.3390/su141710570