Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Depth
Abstract
:1. Introduction
1.1. Background
1.2. Research Goal and Objectives
2. Experimental Process/Program
2.1. Development of UHPC
2.1.1. Materials
2.1.2. Experimental Program
2.2. Mechanical Properties of the UHPC
2.3. Testing of UHPC Beams
2.3.1. Details of Specimens
2.3.2. Details of the Testing System
3. Results and Discussion
3.1. Modes of Failure and Crack Pattern
3.2. Load-Deflection Response
3.3. Ductility Analysis
3.4. Load–Strain Response
3.5. Load-Crack Width Response
3.6. Moment–Curvature Relations
3.7. Prediction of the Ultimate Moment Capacity of UHPC Beams
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Oxides (%) | PC | FA | SF |
---|---|---|---|
SiO2 | 20.41 | 55.23 | 86.20 |
Al2O3 | 5.32 | 25.95 | 0.49 |
Fe2O3 | 4.10 | 10.17 | 3.79 |
CaO | 64.14 | 1.32 | 2.19 |
MgO | 0.71 | 0.31 | 1.31 |
SO3 | 2.44 | 0.18 | 0.74 |
TiO2 | 0.30 | - | - |
Na2Oeq | 0.10 | 0.86 | 2.80 |
L.O.I. | 2.18 | 5.00 | 2.48 |
Relative density | 3.15 | 2.70 | 2.20 |
Property | RS | WS |
---|---|---|
Bulk Specific Gravity (OD Basis) | 2.64 | 2.73 |
Specific Gravity (SSD Basis) | 2.65 | 2.74 |
Apparent Specific Gravity | 2.67 | 2.76 |
Absorption, % | 0.30 | 0.37 |
Fineness Modulus (range of 2.3–3.1) | 1.11 | 1.46 |
Type | Length (mm) | Diameter (µm) | Unit Weight (kg/m3) | Tensile Strength (MPa) |
---|---|---|---|---|
F1 | 13 | 200 | 7850 | 2600 |
F2 | 20 | |||
F3 | 30 |
PC | SF | FA | WS | RS | Water | SP | Fiber | ||
---|---|---|---|---|---|---|---|---|---|
A | B | C | |||||||
1123.1 | 239.1 | 66.1 | 481.2 | 160.9 | 212.7 | 39.7 | 151.8 | 43.0 | 7.6 |
Property (MPa) | UHPC Batch | μ | σ | |||||
---|---|---|---|---|---|---|---|---|
B-1 | B-2 | B-3 | B-4 | B-5 | B-6 | |||
186.7 | 172.6 | 185.8 | 179.3 | 186.7 | 187.5 | 183.1 | 6.0 | |
34.6 | 35.9 | 48.6 | 39.0 | 53.8 | 48.9 | 43.5 | 8.0 | |
50,296 | 48,996 | 50,215 | 49,622 | 50,296 | 50,367 | 49,965 | 548 | |
17.7 | 18.4 | 24.9 | 20.0 | 27.6 | 25.1 | 22.3 | 4.1 |
Set | UHPC Batch | Beam | Dimensions | ρ (%) | ||||
---|---|---|---|---|---|---|---|---|
A | B-1 | A1 | 150 | 150 | 225 | - | - | - |
A2 | 150 | 150 | 225 | - | - | - | ||
B | B-2 | B1 | 150 | 150 | 225 | 125 | 1.206 | 4.00 |
B2 | 150 | 150 | 225 | 125 | 1.206 | 4.00 | ||
C | B-3 | C1 | 150 | 150 | 207 | 115 | 1.311 | 4.35 |
C2 | 150 | 150 | 207 | 115 | 1.311 | 4.35 | ||
D | B-4 | D1 | 150 | 150 | 171 | 95 | 1.587 | 5.26 |
D2 | 150 | 150 | 171 | 95 | 1.587 | 5.26 | ||
E | B-5 | E1 | 150 | 150 | 153 | 85 | 1.774 | 5.88 |
E2 | 150 | 150 | 153 | 85 | 1.774 | 5.88 | ||
F | B-6 | F1 | 150 | 150 | 135 | 75 | 2.011 | 6.67 |
F2 | 150 | 150 | 135 | 75 | 2.011 | 6.67 |
Beam | Elastic Phase | Yield Phase | Ultimate Phase | Ductility Indices | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(kN) | (mm) | (kN) | (mm) | (kN) | Mean (kN) | (mm) | (mm) | (kNm) | (mm) | Mean (mm) | Mean | Mean | |||
A1 | 103.6 | 0.46 | - | - | 195.2 | 172.8 | 2.37 | 8.62 | 21.96 | 7.4 | 7.7 | - | - | - | - |
A2 | 85.0 | 0.51 | - | - | 150.4 | 1.93 | 8.62 | 16.92 | 8.0 | - | - | ||||
B1 | 93.8 | 0.50 | 207.3 | 1.60 | 265.2 | 269.7 | 2.92 | 13.17 | 29.84 | 10.4 | 10.8 | 1.83 | 2.04 | 8.26 | 9.93 |
B2 | 104.4 | 0.52 | 179.6 | 1.20 | 274.1 | 2.70 | 13.92 | 30.83 | 11.2 | 2.25 | 11.61 | ||||
C1 | 130.2 | 1.06 | 245.0 | 2.40 | 253.9 | 268.4 | 2.76 | 17.66 | 26.28 | 16.4 | 16.3 (+50.9%) | 1.15 | 1.22 (−40.3%) | 7.36 | 7.55 (−24.0%) |
C2 | 186.3 | 1.42 | 265.1 | 2.35 | 282.9 | 3.02 | 18.17 | 29.28 | 16.2 | 1.29 | 7.75 | ||||
D1 | 139.5 | 1.06 | 255.8 | 2.51 | 280.8 | 299.8 | 3.77 | 17.89 | 24.00 | 12.4 | 12.6 (+16.67%) | 1.50 | 1.58 (−22.5%) | 7.14 | 8.27 (−16.7%) |
D2 | 128.8 | 0.90 | 255.5 | 2.26 | 318.7 | 3.76 | 21.26 | 27.25 | 12.8 | 1.66 | 9.40 | ||||
E1 | 169.0 | 1.19 | 321.1 | 3.18 | 355.1 | 339.3 | 4.68 | 22.99 | 27.17 | 15.6 | 15.8 (+46.3%) | 1.47 | 1.34 (−34.5%) | 7.24 | 8.38 (−15.6%) |
E2 | 170.2 | 0.85 | 309.8 | 2.44 | 323.5 | 2.93 | 23.19 | 24.75 | 16.0 | 1.20 | 9.52 | ||||
F1 | 170.4 | 1.21 | 301.4 | 2.93 | 341.2 | 335.2 | 3.83 | 24.79 | 23.03 | 16.8 | 18.4 (+70.4%) | 1.31 | 1.24 (−39.1%) | 8.47 | 9.07 (−8.7%) |
F2 | 158.4 | 1.03 | 308.3 | 2.97 | 329.1 | 3.49 | 28.65 | 22.21 | 20.0 | 1.18 | 9.66 |
1.23 | −0.0262 | 0.0516 | 0.435 | 1.31 | 66 × 10−6 | −676 × 10−6 | −0.01356 | −0.472 |
77 × 10−6 | −12.49 × 10−4 | 0.0037 | 0.0035 | −0.044 | −0.161 |
Beam | (MPa) | (1) | (2) | (1)/(2) | ||||
---|---|---|---|---|---|---|---|---|
Test | Predicted | |||||||
Authors | B1 | 172.6 | 18.4 | 1.206 | 0.833 | 0.0738 | 0.0784 | 0.94 |
B2 | 172.6 | 18.4 | 1.206 | 0.833 | 0.0762 | 0.0784 | 0.97 | |
C1 | 185.8 | 24.9 | 1.311 | 0.767 | 0.0713 | 0.0839 | 0.85 | |
C2 | 185.8 | 24.9 | 1.311 | 0.767 | 0.0794 | 0.0839 | 0.95 | |
D1 | 179.3 | 20.0 | 1.587 | 0.633 | 0.0989 | 0.1143 | 0.87 | |
D2 | 179.3 | 20.0 | 1.587 | 0.633 | 0.1123 | 0.1143 | 0.98 | |
E1 | 186.7 | 27.6 | 1.774 | 0.567 | 0.1343 | 0.1339 | 1.00 | |
E2 | 186.7 | 27.6 | 1.774 | 0.567 | 0.1223 | 0.1339 | 0.91 | |
F1 | 187.5 | 25.1 | 2.011 | 0.500 | 0.1456 | 0.1436 | 1.01 | |
F2 | 187.5 | 25.1 | 2.011 | 0.500 | 0.1404 | 0.1436 | 0.98 | |
[1] | R12-1 | 196.7 | 32.7 | 0.599 | 0.870 | 0.0035 | 0.0052 | 0.67 |
R13-1 | 192.2 | 29.4 | 0.899 | 0.870 | 0.0040 | 0.0172 | 0.23 | |
R14-1 | 196.1 | 29.3 | 1.198 | 0.870 | 0.0047 | 0.0091 | 0.51 | |
[20] | S6 × 6-2.6-0.85 | 145.0 | 9.6 | 2.600 | 0.850 | 0.1570 | 0.1583 | 0.99 |
S6 × 6-1.7-0.85 | 145.0 | 9.6 | 1.700 | 0.850 | 0.1215 | 0.1358 | 0.89 | |
S6 × 6-1.7-0.65 | 145.0 | 9.6 | 1.700 | 0.650 | 0.1315 | 0.1283 | 1.02 | |
S6 × 6-0.6-0.85 | 145.0 | 9.6 | 0.600 | 0.850 | 0.0656 | 0.0784 | 0.84 | |
S4 × 6-3.9-0.75 | 145.0 | 9.6 | 3.900 | 0.750 | 0.1805 | 0.1912 | 0.94 | |
S2 × 6-1.8-0.50 | 145.0 | 9.6 | 1.800 | 0.500 | 0.0812 | 0.0930 | 0.87 | |
[51] | F1 | 146.0 | 7.9 | 2.301 | 0.868 | 0.1324 | 0.1353 | 0.98 |
F2 | 146.0 | 7.9 | 1.690 | 0.868 | 0.0936 | 0.1163 | 0.80 | |
F3 | 146.0 | 7.6 | 1.174 | 0.868 | 0.0730 | 0.0894 | 0.82 | |
F4 | 146.0 | 7.4 | 0.751 | 0.868 | 0.0616 | 0.0616 | 1.00 | |
[52] | U-B3 | 193.0 | 7.1 | 0.941 | 0.870 | 0.0035 | 0.0124 | 0.28 |
U-B5 | 193.0 | 7.1 | 1.255 | 0.870 | 0.0046 | 0.0122 | 0.38 | |
Min | 170.0 | 17.0 | 1.555 | 0.755 | 0.83 | |||
Max | 196.7 | 32.7 | 3.900 | 0.870 | 0.23 |
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Khan, M.I.; Fares, G.; Abbas, Y.M. Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Depth. Appl. Sci. 2021, 11, 11168. https://doi.org/10.3390/app112311168
Khan MI, Fares G, Abbas YM. Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Depth. Applied Sciences. 2021; 11(23):11168. https://doi.org/10.3390/app112311168
Chicago/Turabian StyleKhan, Mohammad Iqbal, Galal Fares, and Yassir M. Abbas. 2021. "Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Depth" Applied Sciences 11, no. 23: 11168. https://doi.org/10.3390/app112311168
APA StyleKhan, M. I., Fares, G., & Abbas, Y. M. (2021). Behavior of Non-Shear-Strengthened UHPC Beams under Flexural Loading: Influence of Reinforcement Depth. Applied Sciences, 11(23), 11168. https://doi.org/10.3390/app112311168