Nonlinear Analysis of Prestressed Steel-Reinforced Concrete Beams Based on Bond–Slip Theory
Abstract
:1. Introduction
2. Experimental Program
2.1. Specimen Design
2.2. Loading Equipment and Measuring Instrumentations
3. Numerical Analysis of Prestressed Steel-Reinforced Concrete Beams
3.1. Determination of the Bond–Slip Constitutive Relationship
3.2. Establishment of a Spring Element
- (1)
- Normal direction: Considering that when the section steel and concrete slips greatly, the normal displacement is much less than the longitudinal displacement, the bonding action in this direction can be simplified as a spring with a high stiffness coefficient, according to the suggestions given in the literature [31]. As shown in Figure 10, the F-D curve is a broken line passing through the origin: in the third quadrant, it is a line with a steep slope, which indicates a significant stiffness coefficient, and in the first quadrant, it is a line coincident with the D axis.
- (2)
- Transverse tangential: It can be assumed that the bond–slip effects of the transverse tangential and longitudinal tangential effects are identical for the profile steel flange; hence, the same F-D relationship curve can be used. Because of the anchoring impact of the flange on the section steel web, the lateral slip will be greatly reduced. Therefore, the same treatment method for the normal direction can be adopted; the F-D curve is defined as a line with a steep slope passing through the origin, as shown in Figure 11.
- (3)
- Longitudinal tangential: The bond–slip effect between the section steel and the concrete in this direction is the main component of the bond slip. The longitudinal tangential bond–slip constitutive relationship was discussed in the previous section. According to the relationship curve, the F-D curve of the nonlinear spring element can be derived, and its mathematical expression is as follows:
3.3. Model Establishment
4. Comparison between the Simulation and Test Results
4.1. Finite Element Calculation Results
- (1)
- Calculation results of longitudinal reinforcement stresses
- (2)
- Calculation results of axial stress of steel sections
- (3)
- Calculation results of the total axial strain of concrete in the mid-span section
4.2. Bearing Capacity
4.3. Load–Deflection Curve
4.4. Failure Propagation and Crack Development
5. Application Analysis of a Finite Element Model of a Prestressed Steel-Reinforced Concrete Beam
5.1. Slip Distribution at Different Sections of the Test Beam
5.2. Load–Slip Curve
5.3. Analysis of the Influencing Factors of the Bond–Slip Effect on Prestressed Steel-Reinforced Concrete Beams
5.3.1. Influence of Different Prestresses on the Load–Slip Curves
5.3.2. Effect of Different Concrete Strengths on the Load–Slip Curve
5.3.3. Influence of Different Stirrup Ratios on the Load–Slip Curve
5.3.4. Influence of Different Steel Contents on the Load–Slip Strength Curve
6. Limitations
- (1)
- The results of the bearing capacity calculated according to the finite element model analysis are greater than the test results; this difference may be caused by the non-uniformity of the material properties of the three test beams, in which the measured material strengths of the reinforcement and section steel are slightly greater than the actual material strengths. Subsequently, a lot of experiments are still needed to identify the problems and measures in the subsequent work.
- (2)
- For the bond–slip constitutive relationship, this study only applies it, and in future work, we intend to revise and improve it through experiments and simulations.
- (3)
- In the study of the effect of a different prestress, concrete strength, stirrup ratio, and steel content of section steel on the ultimate bearing capacity of section steel and concrete, the specific effect of simultaneous changes in a variety of parameters was not taken into account, which can be investigated by simulation and experiments in the subsequent work.
7. Conclusions
- (1)
- The test results are compared with the numerical simulation results to verify the accuracy of the finite element model. The calculation results of the finite element model considering the bond–slip constitutive relationship proposed by Yang Yong, among other constitutive relationships tested, are more consistent with the test results, indicating that this bond–slip constitutive relationship is more suitable for the numerical simulation of prestressed steel-reinforced concrete beams.
- (2)
- To establish a finite element model for calculation, it is appropriate to place bolt nails in the bending and shearing sections to restrict slip between the steel and concrete. The load–slip curve of the steel–concrete beam is also obtained, which reflects the bond slip of the steel–concrete after bearing the load.
- (3)
- Different finite element models are built to investigate the effects of various prestressing forces, concrete strengths, stirrup ratios, and steel contents of section steel on the ultimate bearing capacity of section steel-reinforced concrete beams and the bond–slip motion between them. The resulting load–slip curves are subsequently applied to the corresponding design curves.
- (4)
- These findings can serve as a starting point for future research and engineering applications of the bond–slip impact between the steel and concrete in prestressed steel-reinforced concrete beams.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Strength Grade of Concrete | fcu/MPa | fc/MPa | ft/MPa | Ec/MPa |
---|---|---|---|---|
C40 | 42.21 | 27.31 | 2.85 | 3.44 × 104 |
Steel Type | Nominal Diameter/mm | Yield Strength/MPa | Ultimate Strength/MPa |
---|---|---|---|
Steel strand | 15.2 | 1574 | 1889 |
HPB300 | 8 | 337 | 461 |
HRB400 | 12 | 403 | 564 |
HRB400 | 14 | 409 | 578 |
Q345 | — | 347 | 504 |
Cracking Load/kN | |||||||
---|---|---|---|---|---|---|---|
Specimen Type | Test Value | Calculated Value (Without Bond Slip) | Calculated Value (Bond–Slip Constitutive Relation A) | Calculated Value (Bond–Slip Constitutive Relation B) | Test Value/Calculated Value (Without Bond Slip) | Test value/Calculated Value (Bond–Slip Constitutive Relation A) | Test Value/Calculated Value (Bond–Slip Constitutive Relation B) |
PSRCB | 72.4 | 85.91 | 78.33 | 74.65 | 0.843 | 0.924 | 0.970 |
SRCB-A | 21.3 | 27.17 | 23.68 | 22.15 | 0.783 | 0.899 | 0.962 |
SRCB-B | 23.6 | 31.37 | 27.45 | 25.26 | 0.752 | 0.860 | 0.934 |
Ultimate Load/kN | |||||||
---|---|---|---|---|---|---|---|
Specimen Type | Test Value | Calculated Value (Without Bond Slip) | Calculated Value (Bond–Slip Constitutive Relation A) | Calculated Value (Bond–Slip Constitutive Relation B) | Test Value/Calculated Value (Without Bond Slip) | Test Value/Calculated Value (Bond–Slip Constitutive Relation A) | Test Value/Calculated Value (Bond–Slip Constitutive Relation B) |
PSRCB | 193.6 | 207.86 | 200.78 | 194.74 | 0.931 | 0.964 | 0.994 |
SRCB-A | 182.6 | 201.93 | 193.24 | 187.42 | 0.904 | 0.945 | 0.974 |
SRCB-B | 184.7 | 205.57 | 197.40 | 190.73 | 0.898 | 0.936 | 0.968 |
(a) | ||||
Model number | PSRCB-I-1 | PSRCB-I-2 | PSRCB-I-3 | PSRCB-I-4 |
Effective preload | 279.61 kN | 260.47 kN | 241.34 kN | 222.15 kN |
(b) | ||||
Model number | PSRCB-II-1 | PSRCB-II-2 | PSRCB-II-3 | PSRCB-II-4 |
Concrete strength | 37.21 MPa | 40.99 MPa | 44.51 MPa | 47.97 MPa |
(c) | ||||
Model number | PSRCB-III-1 | PSRCB-III-2 | PSRCB-III-3 | PSRCB-III-4 |
Hoop ratio | 0.25% | 0.34% | 0.42% | 0.50% |
(d) | ||||
Model number | PSRCB-IV-1 | PSRCB-IV-2 | PSRCB-IV-3 | PSRCB-IV-4 |
Steel content | 3.37% | 3.94% | 4.70% | 5.41% |
Model Number | Bond Slip Is Not Considered | Bond Slip Is Considered | Deviation |
---|---|---|---|
PSRCB-I-1 | 227.84 | 210.96 | 7.41% |
PSRCB-I-2 | 223.12 | 204.84 | 8.19% |
PSRCB-I-3 | 215.94 | 195.10 | 9.65% |
PSRCB-I-4 | 207.76 | 183.69 | 11.59% |
Model Number | Bond Slip Is Not Considered | Bond Slip Is Considered | Deviation |
---|---|---|---|
PSRCB-II-1 | 227.84 | 210.96 | 7.41% |
PSRCB-II-2 | 234.98 | 220.91 | 5.97% |
PSRCB-II-3 | 242.38 | 230.84 | 4.76% |
PSRCB-II-4 | 252.78 | 243.06 | 3.85% |
Model Number | Bond Slip Is Not Considered | Bond Slip Is Considered | Deviation |
---|---|---|---|
PSRCB-III-1 | 222.48 | 195.64 | 12.06% |
PSRCB-III-2 | 226.70 | 205.27 | 9.45% |
PSRCB-III-3 | 227.18 | 207.95 | 8.46% |
PSRCB-III-4 | 227.84 | 210.96 | 7.41% |
Model Number | Bond Slip Is Not Considered | Bond Slip Is Considered | Deviation |
---|---|---|---|
PSRCB-IV-1 | 215.42 | 204.23 | 5.19% |
PSRCB-IV-2 | 227.84 | 210.96 | 7.41% |
PSRCB-IV-3 | 238.21 | 217.55 | 8.67% |
PSRCB-IV-4 | 245.02 | 222.89 | 9.03% |
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Deng, N.; Li, W.; Du, L.; Deng, Y. Nonlinear Analysis of Prestressed Steel-Reinforced Concrete Beams Based on Bond–Slip Theory. Buildings 2024, 14, 2648. https://doi.org/10.3390/buildings14092648
Deng N, Li W, Du L, Deng Y. Nonlinear Analysis of Prestressed Steel-Reinforced Concrete Beams Based on Bond–Slip Theory. Buildings. 2024; 14(9):2648. https://doi.org/10.3390/buildings14092648
Chicago/Turabian StyleDeng, Nianchun, Wujun Li, Linyue Du, and Yanfeng Deng. 2024. "Nonlinear Analysis of Prestressed Steel-Reinforced Concrete Beams Based on Bond–Slip Theory" Buildings 14, no. 9: 2648. https://doi.org/10.3390/buildings14092648