Numerical Simulation of Engineering Cementitious Composite Beams Strengthened with Fiber-Reinforced Polymer and Steel Bars
Abstract
:1. Introduction
2. Materials and Methods
2.1. Material Properties
2.1.1. Concrete
2.1.2. ECC Material
2.1.3. Steel Reinforcement and Steel Plates
2.1.4. FRP Reinforcement
2.2. Nonlinear Finite Element Model (NLFEM)
2.3. Model Verification
3. Results and Discussion
3.1. Parametric Study Parameters
3.2. Effect of FRP Type and Concrete Compressive Strength
3.3. Effect of Hybrid Tensile Reinforcement Ratio and tECC
4. Conclusions
- The numerical simulation models accurately predict the load-deflection response with an error of less than 10% of the ultimate load, ultimate deflection, and stiffness. This provides researchers with a valuable tool for studying the behavior of ECC-concrete hybrid reinforced beams, particularly considering the higher costs associated with ECC material and FRP bars.
- In hybrid composite beams (using 50 mm ECC), when the BFRP reinforcement ratio is kept constant, utilizing a higher steel reinforcement ratio results in a reduction in ultimate load capacity, toughness, and ultimate deflection, along with insufficient ductility (less than 3), leading to early failure immediately after yielding of steel rebars due to high stress concentration in the ECC layer.
- In hybrid composite beams (using 100 mm ECC), when the BFRP reinforcement ratio is kept constant, using a higher steel reinforcement ratio leads to improvements in ultimate load, toughness, and flexural stiffness, but reduces beam ductility and shows a slight decrease in maximum deflection.
- With the remaining steel reinforcement ratio constant in the hybrid reinforcement system, an increase in the ratio of BFRP enhances ultimate load capacity, toughness, and flexural stiffness, but causes a decline in maximum deflection and ductility.
- The BFRP/steel tensile reinforcement ratio should be carefully designed to achieve the required strength, acceptable ductile performance, and improved load-carrying capacity of the composite beam.
- Strengthening composite hybrid beams with CFRP bars instead of BFRP results in better mechanical behavior in terms of ultimate load, toughness, flexural stiffness, and plastic stiffness, albeit with a reduction in ductility index. Conversely, replacing BFRP with GFRP bars exhibits a higher enhancement in ductility performance but a reduction in other mechanical properties. Additionally, the use of AFRP bars provides moderate mechanical behavior, performing better than BFRP but still inferior to CFRP bars.
- Using a higher grade of concrete strength in composite hybrid beams contributes minimally to improving mechanical behavior, with no noticeable effect on enhancement or reduction when using different types of FRP bars.
- In composite hybrid reinforced beams, using a 100 mm ECC layer in the tension zone significantly impacts the load-deflection response and greatly improves mechanical performance with increasing effective beam depth.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Flow potential eccentricity (ϵ) | 0.1 |
Dilation angle (ψ) | 30 |
Compressive meridian at in initial yield (k) | 2/3 |
Viscosity (μ) | 0.0005 |
Initial biaxial compressive yield stress to initial uniaxial compressive yield stress (fb0/fc0) | 1.16 |
Bars Type | Diameter (mm) | Elastic Modulus (GPa) | fy (MPa) | fu (MPa) | Ultimate Strain |
---|---|---|---|---|---|
Top steel bar | 10 | 198 | 403 | 495 | 0.051 |
Bottom steel bar | 12 | 199 | 408 | 503 | 0.0675 |
Stirrups | 8 | 198 | 406 | 485 | 0.075 |
Bars Type | Ultimate Tensile Stress (MPa) | Elastic Modulus (GPa) |
---|---|---|
CFRP | 2070 | 156 |
AFRP | 1172 | 83 |
BFRP | 1250 | 50 |
GFRP | 1080 | 40 |
Group | Beam Notation | As (Steel) | Afrp (BFRP) | ECC Layer Thickness (mm) |
---|---|---|---|---|
I | B1 | 2ϕ12 (226.2 mm2) | _ | 0 |
B2 | 2ϕ12 (226.2 mm2) | _ | 50 | |
B3 | 2ϕ12 (226.2 mm2) | _ | 100 | |
B4 | 2ϕ12 (226.2 mm2) | _ | 200 | |
II | B5 | 1 ϕ12 (113.1 mm2) | 2ϕ8 (100.53 mm2) | 0 |
B6 | 1 ϕ12 (113.1 mm2) | 2ϕ8 (100.53 mm2) | 50 | |
B7 | 1 ϕ12 (113.1 mm2) | 2ϕ8 (100.53 mm2) | 100 | |
B8 | 1 ϕ12 (113.1 mm2) | 2ϕ8 (100.53 mm2) | 200 | |
III | B9 | _ | 3ϕ8 (150.80 mm2) | 0 |
B10 | _ | 3ϕ8 (150.80 mm2) | 50 | |
B11 | _ | 3ϕ8 (150.80 mm2) | 100 | |
B12 | _ | 3ϕ8 (150.80 mm2) | 200 |
Group | Beam Notation | Ultimate Deflection (mm) | Ultimate Load (kN) | ||||
---|---|---|---|---|---|---|---|
Experiment [22] | NLFEA | %Error | Experiment [22] | NLFEA | %Error | ||
I | B1 | 29.5 | 32.05 | 8.64 | 38.6 | 36.98 | 4.2 |
B2 | 22.0 | 23.09 | 4.95 | 39 | 39.83 | 2.13 | |
B3 | 19.1 | 19.99 | 4.66 | 39.6 | 41.28 | 4.24 | |
B4 | 33.3 | 35.15 | 5.56 | 45 | 45.68 | 1.51 | |
II | B5 | 31.1 | 33.29 | 7.04 | 42.4 | 42.61 | 0.5 |
B6 | 41.5 | 41.47 | 0.07 | 53.6 | 54.79 | 2.22 | |
B7 | 29.5 | 30.89 | 4.51 | 47.2 | 45.59 | 3.41 | |
B8 | 47.9 | 50.14 | 4.68 | 54.2 | 58.73 | 8.36 | |
III | B9 | 31.5 | 33.41 | 6.06 | 35.6 | 38.79 | 8.96 |
B10 | 29.7 | 31.36 | 5.59 | 40.8 | 41.39 | 1.45 | |
B11 | 28.1 | 29.67 | 5.59 | 44.6 | 43.88 | 1.61 | |
B12 | 35.0 | 36.92 | 5.49 | 45 | 49.0 | 8.89 | |
Overall | 5.25 | 3.96 |
Model | fʹc (MPa) | Beam Height (mm) | ρs(%) | FRP Type | ρfrp (%) | tECC (mm) |
---|---|---|---|---|---|---|
M1 | 24 | 200 | 0.43 | BFRP | 0.38 | 100 |
M2 | 24 | 200 | 0.43 | CFRP | 0.38 | 100 |
M3 | 24 | 200 | 0.43 | AFRP | 0.38 | 100 |
M4 | 24 | 200 | 0.43 | GFRP | 0.38 | 100 |
M5 | 30 | 200 | 0.43 | BFRP | 0.38 | 100 |
M6 | 30 | 200 | 0.43 | CFRP | 0.38 | 100 |
M7 | 30 | 200 | 0.43 | AFRP | 0.38 | 100 |
M8 | 30 | 200 | 0.43 | GFRP | 0.38 | 100 |
M9 | 40 | 200 | 0.43 | BFRP | 0.38 | 100 |
M10 | 40 | 200 | 0.43 | CFRP | 0.38 | 100 |
M11 | 40 | 200 | 0.43 | AFRP | 0.38 | 100 |
M12 | 40 | 200 | 0.43 | GFRP | 0.38 | 100 |
M13 | 24 | 250 | 0.43 | BFRP | 0.38 | 100 |
M14 | 24 | 300 | 0.43 | BFRP | 0.38 | 100 |
M15 | 24 | 200 | 0.19 | BFRP | 0.38 | 50 |
M16 | 24 | 200 | 0.19 | BFRP | 0.86 | 50 |
M17 | 24 | 200 | 0.19 | BFRP | 1.53 | 50 |
M18 | 24 | 200 | 0.43 | BFRP | 0.38 | 50 |
M19 | 24 | 200 | 0.43 | BFRP | 0.86 | 50 |
M20 | 24 | 200 | 0.43 | BFRP | 1.53 | 50 |
M21 | 24 | 200 | 0.77 | BFRP | 0.38 | 50 |
M22 | 24 | 200 | 0.77 | BFRP | 0.86 | 50 |
M23 | 24 | 200 | 0.77 | BFRP | 1.53 | 50 |
M24 | 24 | 200 | 1.22 | BFRP | 0.38 | 50 |
M25 | 24 | 200 | 1.22 | BFRP | 0.86 | 50 |
M26 | 24 | 200 | 1.22 | BFRP | 1.53 | 50 |
M27 | 24 | 200 | 0.19 | BFRP | 0.38 | 100 |
M28 | 24 | 200 | 0.19 | BFRP | 0.86 | 100 |
M29 | 24 | 200 | 0.19 | BFRP | 1.53 | 100 |
M30 | 24 | 200 | 0.43 | BFRP | 0.86 | 100 |
M31 | 24 | 200 | 0.43 | BFRP | 1.53 | 100 |
M32 | 24 | 200 | 0.77 | BFRP | 0.38 | 100 |
M33 | 24 | 200 | 0.77 | BFPR | 0.86 | 100 |
M34 | 24 | 200 | 0.77 | BFPR | 1.53 | 100 |
M35 | 24 | 200 | 1.22 | BFPR | 0.38 | 100 |
M36 | 24 | 200 | 1.22 | BFPR | 0.86 | 100 |
M37 | 24 | 200 | 1.22 | BFPR | 1.53 | 100 |
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Shbeeb, N.I.; Barham, W.S.; Alyahya, W. Numerical Simulation of Engineering Cementitious Composite Beams Strengthened with Fiber-Reinforced Polymer and Steel Bars. Fibers 2024, 12, 49. https://doi.org/10.3390/fib12060049
Shbeeb NI, Barham WS, Alyahya W. Numerical Simulation of Engineering Cementitious Composite Beams Strengthened with Fiber-Reinforced Polymer and Steel Bars. Fibers. 2024; 12(6):49. https://doi.org/10.3390/fib12060049
Chicago/Turabian StyleShbeeb, Nadim I., Wasim S. Barham, and Wala’a Alyahya. 2024. "Numerical Simulation of Engineering Cementitious Composite Beams Strengthened with Fiber-Reinforced Polymer and Steel Bars" Fibers 12, no. 6: 49. https://doi.org/10.3390/fib12060049
APA StyleShbeeb, N. I., Barham, W. S., & Alyahya, W. (2024). Numerical Simulation of Engineering Cementitious Composite Beams Strengthened with Fiber-Reinforced Polymer and Steel Bars. Fibers, 12(6), 49. https://doi.org/10.3390/fib12060049