Effects of Size and Flexural Reinforcement Ratio on Ambient-Cured Geopolymer Slag Concrete Beams under Four-Point Bending
Abstract
:1. Introduction
2. Mix Design
2.1. Raw Materials
2.1.1. Binder
2.1.2. Aggregate
2.1.3. Activator
2.2. Mix Proportion
2.2.1. Conventional Concrete Mix
2.2.2. Geopolymer Concrete Mix
2.3. Mechanical Properties
2.3.1. Concrete
2.3.2. Reinforcing Steel
3. Experimental Plan
3.1. Details of the Test Specimens
3.2. Test Setup and Procedure
4. Results and Discussion
4.1. Cracks Distribution
- is the coefficient relating to average crack width and = 1.7,
- is the mean steel strain,
- is the mean crack spacing in mm.
4.2. Load–Deflection Relationship
4.3. Strains in the Concrete and Steel Bars
4.4. Stiffness, Ductility and Toughness
- K1 is the pre–yield “initial” stiffness in kN/mm,
- Py is the yielding load in kN,
- is the deflection at the yielding load in mm,
- K2 is the post–yield “effective” stiffness in kN/mm,
- Pu is the ultimate load in kN,
- is the deflection at the ultimate load in mm.
4.5. Cracking and Ultimate Moments
- Mcr is the theoretical cracking moment in kNm,
- fctr is the modulus of rupture of concrete in kN/m2,
- Ig is the gross moment of inertia of beam section in m4,
- yt is the distance from the tension side of beam to the neutral axis in m.
- Mu is the theoretical ultimate moment in kNm,
- fy is the steel yielding stress in MPa,
- As is the main steel area in mm2,
- d is the effective depth of beam in mm,
- a is the concrete compression zone depth in mm,
- b is the beam width in mm.
- Mn is the unfactored theoretical nominal moment in kNm,
- is the cylinder compressive strength of concrete in MPa,
- is the ratio of the depth of the equivalent stress block to the actual neutral axis depth.
5. Conclusions
- The load-carrying capacity of the GPC beams increased with increasing both the beam depth and rebar ratio. Compared to the CC beams, the flexural moment capacity of the reinforced GPC beams was 7.4% higher, and the cracking moment was 17.5% lower due to the lower modulus of rupture.
- The initial and effective stiffnesses of the GPC beams increased with increasing both the beam depth and rebar ratio. Compared to the CC beams, the initial and effective stiffnesses of the GPC beams were lower by 60%. Furthermore, the deflection of the GPC beams was 48.7% higher due to their lower modulus of elasticity.
- Increasing the beam depth significantly increases the beam ductility but using a higher rebar ratio decreases the beam ductility. However, the toughness of the GPC beams increased by increasing either beam depth or rebar ratio. Compared to the CC beams, the ductility of GPC beams was 28% lower, and the toughness was 18.3% higher.
- The crack distributions of the GPC beams occurred earlier, in more numbers and longer than those appearing in the CC beams. As the rebar ratio increased, the appearance of the cracks was retarded, and the average spacing of the developed cracks on the GPC beams decreased and the number of cracks increased. Increasing the GPC beam depth led to the delay in the occurrence of the cracks and the increase in the average spacing of the developed cracks.
- The Egyptian code of practice ECP203 and ACI318 should be applicable in predicting the flexural moment capacity of under-reinforced GPC beams.
6. Future Recommendations
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Component | SiO2 | Al2O3 | Fe2O3 | Na2O | CaO | MgO | K2O | SO3 | TiO2 | Mn2O3 |
---|---|---|---|---|---|---|---|---|---|---|
GGBFS | 35.41 | 17.42 | 1.39 | 0.49 | 36.87 | 6.83 | 0.97 | - | 0.11 | 0.35 |
OPC | 21.07 | 5.01 | 3.47 | 0.29 | 63.25 | 2.52 | 0.19 | 3.05 | - | - |
GGBFS | OPC | C. Agg. * | F. Agg. ** | NaOH | Na2SiO3 | Water | Superplastizer *** | |
---|---|---|---|---|---|---|---|---|
Conventional | - | 450 | 1058 | 710 | - | - | 176 | 12.2 |
Slag Concrete by Amer et al. [5] | 450 | - | 1093 | 547 | 41 | 131 | 112 | - |
Property | GPC | CC |
---|---|---|
Compressive strength fcu (MPa) | 51.62 | 45.36 |
Modulus of rupture fctr (MPa) | 4.38 | 5.46 |
Modulus of elasticity Ec (GPa) | 25.10 | 32.30 |
10 mm Diameter (T10) | 12 mm Diameter (T12) | 16 mm Diameter (T16) | |
---|---|---|---|
Yield stress (MPa) | 542.30 | 519.60 | 558.40 |
Ultimate stress (MPa) | 705.10 | 680.60 | 779.20 |
Young's modulus (GPa) | 231.20 | 246.20 | 248.60 |
Beam Label * | Bottom Reinforcement | Reinforcement Ratio, ρ | Total Depth (mm), t |
---|---|---|---|
CC-2T10-300 | 2T10 | 0.37% | 300 |
GPC-2T10-300 | 2T10 | 0.37% | 300 |
GPC-2T12-300 | 2T12 | 0.53% | 300 |
GPC-2T16-300 | 2T16 | 0.95% | 300 |
GPC-2T10-250 | 2T10 | 0.45% | 250 |
GPC-2T10-350 | 2T10 | 0.31% | 350 |
Specimens | Flexural Cracks | Shear Cracks | Crack Width (mm) |
---|---|---|---|
CC-2T10-300 | 5 | 1 | 0.23 |
GPC-2T10-300 | 7 | 1 | 0.26 |
GPC-2T12-300 | 9 | 2 | 0.24 |
GPC-2T16-300 | 12 | 5 | 0.22 |
GPC-2T10-250 | 6 | - | 0.27 |
GPC-2T10-350 | 9 | 1 | 0.21 |
Specimens | Py (kN) | Pu (kN) | K1 (kN/mm) | K2 (kN/mm) | Toughness (Joule) | |||
---|---|---|---|---|---|---|---|---|
CC-2T10-300 | 66.5 | 85.3 | 3.8 | 16.2 | 17.50 | 1.52 | 4.26 | 3368 |
GPC-2T10-300 | 76.6 | 91.6 | 7.23 | 24.1 | 10.59 | 0.89 | 3.33 | 3985 |
GPC-2T12-300 | 86.6 | 114.0 | 7.08 | 22.7 | 12.23 | 1.75 | 3.21 | 4605 |
GPC-2T16-300 | 172.0 | 211.0 | 6.58 | 19.9 | 26.14 | 2.93 | 3.02 | 6320 |
GPC-2T10-250 | 58.9 | 69.02 | 10.12 | 28.2 | 5.83 | 0.56 | 2.79 | 3055 |
GPC-2T10-350 | 80.3 | 96.7 | 4.8 | 19.03 | 16.73 | 1.15 | 3.96 | 4865 |
Specimens | Mcr (kNm) | Mu (kNm) by ECP203 | Mn (kNm) by ACI318 | |||||
---|---|---|---|---|---|---|---|---|
Mexp | Mtheo | Mexp/Mtheo | Mexp | Mtheo | Mexp/Mtheo | Mtheo | Mexp/Mtheo | |
CC-2T10-300 | 12.0 | 14.2 | 0.85 | 25.59 | 23.47 | 1.09 | 23.48 | 1.09 |
GPC-2T10-300 | 9.9 | 11.4 | 0.87 | 27.48 | 23.56 | 1.17 | 23.58 | 1.17 |
GPC-2T12-300 | 10.8 | 11.8 | 0.92 | 34.2 | 32.01 | 1.07 | 32.16 | 1.06 |
GPC-2T16-300 | 12.3 | 12.9 | 0.95 | 63.3 | 58.42 | 1.08 | 59.19 | 1.07 |
GPC-2T10-250 | 7.5 | 8.0 | 0.93 | 20.7 | 19.31 | 1.07 | 19.32 | 1.07 |
GPC-2T10-350 | 12.6 | 15.2 | 0.83 | 29.01 | 27.82 | 1.04 | 27.83 | 1.04 |
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Mamdouh, H.; Ali, A.M.; Osman, M.A.; Deifalla, A.F.; Ayash, N.M. Effects of Size and Flexural Reinforcement Ratio on Ambient-Cured Geopolymer Slag Concrete Beams under Four-Point Bending. Buildings 2022, 12, 1554. https://doi.org/10.3390/buildings12101554
Mamdouh H, Ali AM, Osman MA, Deifalla AF, Ayash NM. Effects of Size and Flexural Reinforcement Ratio on Ambient-Cured Geopolymer Slag Concrete Beams under Four-Point Bending. Buildings. 2022; 12(10):1554. https://doi.org/10.3390/buildings12101554
Chicago/Turabian StyleMamdouh, Hala, Ashraf M. Ali, Mostafa A. Osman, Ahmed F. Deifalla, and Nehal M. Ayash. 2022. "Effects of Size and Flexural Reinforcement Ratio on Ambient-Cured Geopolymer Slag Concrete Beams under Four-Point Bending" Buildings 12, no. 10: 1554. https://doi.org/10.3390/buildings12101554