Seismic Performance Research of Self-Centering Single-Column Bridges Using Equivalent Stiffness Theory
Abstract
1. Introduction
2. Theory of Equivalent Elastic Stiffness for SHR-SCSAB
2.1. Finite Strip Method
2.2. A Comprehensive Theoretical Framework for Sectional Collapse Analysis
2.2.1. Stage I: Full Cross-Section Compression Stage, Increase in Bending Moment from Zero to Dissipating Bending Moment
2.2.2. Stage II: The Bending Moment Continues to Increase Until the Energy-Consuming Reinforcement Enters the Yield State
2.2.3. Stage III: The Bending Moment Continues to Increase Until the Section Breaks
2.3. Equivalent Elastic Stiffness Derivation
3. Analytical Models for Hybrid Systems
3.1. Finite Element Modelling
3.2. Description of Bridge
4. Numerical Modelling
4.1. Pushover Analysis
4.2. Hysteretic Response Analysis
4.3. Concrete Material Deterioration Effects
5. Summary
6. Future Work
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Concrete | Posttensioned Tendon | Energy-Consuming Reinforcement | FRP Reinforcement | Stirrup | |||||
---|---|---|---|---|---|---|---|---|---|
Compressing strength | Elastic modulus | Yield strength | Ultimate strength | Elastic modulus | Yield strength | Elastic modulus | Ultimate strength | Elastic modulus | Yield strength |
40.0 | 32.5 | 1670 | 1860 | 195 | 400 | 200 | 2100 | 140 | 286 |
Bridge Pier Stiffness | Simulated Value (kN/m) | Analytical Solution (kN/m) | Discrepancy (%) |
---|---|---|---|
4054 | 4155 | 2.43 | |
2420 | 2321 | 4.09 |
Hybrid Ratio | Yield Displacement (cm) | Yield Force (kN) | Peak Displacement (cm) | Peak Force (kN) | Ultimate Displacement (cm) | Yield Stiffness (kN/m) | Equivalent Elastic Stiffness (kN/m) | Ductility Factor |
---|---|---|---|---|---|---|---|---|
0.3 | 2.4 | 132 | 6.8 | 156 | 13.6 | 5500 | 2294 | 5.67 |
0.5 | 3.2 | 149 | 7.8 | 180 | 16.0 | 4656 | 2307 | 5.00 |
0.7 | 4.0 | 170 | 9.0 | 210 | 19.6 | 4250 | 2333 | 4.90 |
Axial Pressure Ratio | Yield Displacement (cm) | Yield Force (kN) | Peak Displacement (cm) | Peak Force (kN) | Ultimate Displacement (cm) | Yield Stiffness (kN/m) | Equivalent Elastic Stiffness (kN/m) | Ductility Factor |
---|---|---|---|---|---|---|---|---|
0.08 | 3.5 | 160 | 8.6 | 197 | 20.0 | 4571 | 2295 | 5.70 |
0.16 | 3.0 | 169 | 8.4 | 201 | 16.6 | 5633 | 2401 | 5.53 |
0.24 | 2.5 | 173 | 5.6 | 202 | 13.2 | 6920 | 3606 | 5.28 |
Shear-to-Span Ratio | Yield Displacement (cm) | Yield Force (kN) | Peak Displacement (cm) | Peak Force (kN) | Ultimate Displacement (cm) | Yield Stiffness (kN/m) | Equivalent Elastic Stiffness (kN/m) | Ductility Factor |
---|---|---|---|---|---|---|---|---|
7 | 3.8 | 164 | 8.6 | 200 | 19.0 | 4316 | 2320 | 5.00 |
8 | 4.4 | 138 | 10.6 | 167 | 19.6 | 3136 | 1572 | 4.45 |
9 | 4.9 | 114 | 12.8 | 137 | 20.6 | 2327 | 1067 | 4.20 |
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Gao, H.; Xia, W.; Lu, H. Seismic Performance Research of Self-Centering Single-Column Bridges Using Equivalent Stiffness Theory. Buildings 2025, 15, 2000. https://doi.org/10.3390/buildings15122000
Gao H, Xia W, Lu H. Seismic Performance Research of Self-Centering Single-Column Bridges Using Equivalent Stiffness Theory. Buildings. 2025; 15(12):2000. https://doi.org/10.3390/buildings15122000
Chicago/Turabian StyleGao, Huixing, Wenjing Xia, and Hongxu Lu. 2025. "Seismic Performance Research of Self-Centering Single-Column Bridges Using Equivalent Stiffness Theory" Buildings 15, no. 12: 2000. https://doi.org/10.3390/buildings15122000
APA StyleGao, H., Xia, W., & Lu, H. (2025). Seismic Performance Research of Self-Centering Single-Column Bridges Using Equivalent Stiffness Theory. Buildings, 15(12), 2000. https://doi.org/10.3390/buildings15122000