Variability Analysis of the Hysteretic Behavior of Fiber-Reinforced Polymer (FRP)-Confined Concrete Columns Based on a Secondary Development Model
Abstract
:1. Introduction
2. Secondary Development of a Modified FRP-Confined Concrete Model
2.1. Uniaxial and Cyclic Constitutions of Lam and Teng
2.2. A New Modified Model of FRP-Confined Concrete
- (1)
- The envelope curve under cyclic compression
- (2)
- Unloading and reloading paths under cyclic compression
- (3)
- Partial unloading and partial reloading under cyclic compression
- (4)
- The envelope curve under cyclic tension
- (5)
- Unloading and reloading paths under cyclic tension
2.3. OpenSees Program Realization of the Modified Model
3. Validation of the Modified FRP-Confined Concrete Model
3.1. Basic Information of the FRP-C RC Column
3.2. Comparison with Test Data
4. Hysteretic Behavior Variability of FRP-C RC Columns Considering Concrete Strength Variations
4.1. Major Random Variable for Concrete Material
4.2. Random Sampling Methods
4.3. Variability Analysis for Hysteretic Behavior of FRP-C RC Columns
4.3.1. Variability Analysis of the Maximum Horizontal Force of FRP-C RC Columns
4.3.2. Variability Analysis of the Equivalent Viscous Damping Ratio of FRP-C RC Columns
5. Conclusions
- Based on the Lam–Teng 2003 model, the mechanical tension properties and the stress drop section after the peak stress point of the compressive skeleton curve are considered in FRP-confined concrete materials. The proposed model has been verified by comparing with test data from the literature.
- In this paper, the OpenSees secondary development function and the quasi-Monte Carlo random sampling method are first applied to study the influence of concrete material variations on the hysteretic behavior of FRP-C RC columns.
- By analyzing the variability in hysteretic behavior of FRP-C RC columns, some interesting rules are found, which will be helpful in the optimization of seismic structure designs. For instance, the average value of the maximum horizontal force is positively correlated with the influencing parameters (i.e., the concrete strength grade, reinforcement ratio and axial compression ratio). However, the variation rule of the maximum force is different, and is positively correlated with the axial compression ratio and negatively correlated with the strength grade and reinforcement ratio of concrete. Additionally, for example, the variation coefficient of the equivalent damping ratio is almost constant with the increase in the lateral displacement rate of the specimen under cyclic loading.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Specimen | FRP Type | Sectional Type | S-D/mm | H/mm | γ |
---|---|---|---|---|---|
CVH3 (Li et al., 2002 [53]) | CFRP | Square | 300 × 300 | 480 | 0.52 |
CF30-4-48 (Ye et al., 2001 [54]) | CFRP | Square | 200 × 200 | 600 | 0.48 |
C1H1C3N2 (Wang, 2012 [52]) | GFRP | Cylinder | 400 | 1200 | 0.45 |
CL1 (Gu et al., 2006 [55]) | CFRP | Cylinder | 360 | 600 | 0.35 |
CL2 (Gu et al., 2006 [55]) | CFRP | Cylinder | 360 | 600 | 0.35 |
Specimen | fc/MPa | fy/MPa | Φ/mm | fy,FRP/MPa | εcu,FRP | tFRP/mm | nFRP |
---|---|---|---|---|---|---|---|
CVH3 (Li et al., 2002 [53]) | 32.1 | 359.64 | 20 | 3200 | 0.0144 | 0.086 | 1 |
CF30-4-48 (Ye et al., 2001 [54]) | 34 | 360 | 16 | 3500 | 0.0149 | 0.111 | 1 |
C1H1C3N2 (Wang, 2012 [52]) | 34 | 335 | 20 | 4340 | 0.0178 | 0.167 | 3 |
CL1 (Gu et al., 2006 [55]) | 44.3 | 382.4 | 25 | 3950 | 0.0158 | 0.167 | 1 |
CL2 (Gu et al., 2006 [55]) | 44.3 | 382.4 | 25 | 3950 | 0.0158 | 0.167 | 2.5 |
Specimen | Fmax+/kN | Fmax−/kN | Error Mean | ||||
---|---|---|---|---|---|---|---|
Test | Simulation | Re+ | Test | Simulation | Re− | ||
CVH3 [53] | 451.45 | 465.92 | 3.20% | −485.19 | −463.83 | 4.40% | 3.8% |
CF30-4-48 [54] | 97.34 | 106.54 | 9.46% | −98.98 | −100.45 | 1.48% | 5.47% |
C1H1C3N2 [52] | 223.77 | 221.64 | 0.95% | −224.36 | −220.90 | 1.54% | 1.25% |
CL1 [55] | 556.68 | 564.97 | 1.49% | −597.14 | −563.39 | 5.65% | 3.57% |
CL2 [55] | 618.35 | 654.26 | 5.81% | −649.09 | −645.38 | 0.57% | 3.19% |
Specimen | fcu,m/MPa | fy/MPa | Φ/mm | ρ/% | H/mm | D/mm | n | fy,FRP/MPa | εcu,FRP | tFRP/mm | nFRP |
---|---|---|---|---|---|---|---|---|---|---|---|
C30-series | 38.98 | 360 | 18 | 2.2/2.7/3.2 | 1000 | 300 | 0.1/0.2/0.3 | 3500 | 0.0149 | 0.111 | 3 |
C40-series | 49.84 | 360 | 18 | 2.2/2.7/3.2 | 1000 | 300 | 0.1/0.2/0.3 | 3500 | 0.0149 | 0.111 | 3 |
C50-series | 61.05 | 360 | 18 | 2.2/2.7/3.2 | 1000 | 300 | 0.1/0.2/0.3 | 3500 | 0.0149 | 0.111 | 3 |
ρ | Average Values (kN) | Variation Coefficient | |||||
---|---|---|---|---|---|---|---|
n | 2.2% | 2.7% | 3.2% | 2.2% | 2.7% | 3.2% | |
0.1 | 76.77 | 88.17 | 100.44 | 0.0488 | 0.0445 | 0.0412 | |
0.2 | 90.40 | 101.30 | 113.24 | 0.0665 | 0.0582 | 0.0532 | |
0.3 | 104.38 | 114.40 | 125.55 | 0.0770 | 0.0705 | 0.0632 |
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Wang, Y.; Pan, L.; Niu, W.; Li, K.; Guo, K. Variability Analysis of the Hysteretic Behavior of Fiber-Reinforced Polymer (FRP)-Confined Concrete Columns Based on a Secondary Development Model. Buildings 2023, 13, 2396. https://doi.org/10.3390/buildings13092396
Wang Y, Pan L, Niu W, Li K, Guo K. Variability Analysis of the Hysteretic Behavior of Fiber-Reinforced Polymer (FRP)-Confined Concrete Columns Based on a Secondary Development Model. Buildings. 2023; 13(9):2396. https://doi.org/10.3390/buildings13092396
Chicago/Turabian StyleWang, Yuanfeng, Lei Pan, Weitao Niu, Kai Li, and Kun Guo. 2023. "Variability Analysis of the Hysteretic Behavior of Fiber-Reinforced Polymer (FRP)-Confined Concrete Columns Based on a Secondary Development Model" Buildings 13, no. 9: 2396. https://doi.org/10.3390/buildings13092396