Shear Behavior of Non-Stirrup Ultra-High-Performance Concrete Beams: Contribution of Steel Fibers and UHPC
Abstract
:1. Introduction
2. Research Significance
3. Experimental Programs
3.1. Specimens and Test Matrix
3.2. Mix Design and Beam Fabrication
3.3. Material Characterization
3.4. Test Setup and Instrumentation
4. Experimental Results and Discussion
4.1. Crack Patterns and Failure Modes
4.2. Load–Deflection Relationships
4.2.1. Effect of Shear Span-to-Effective-Depth
4.2.2. Effect of Steel Fiber Volume Content
4.2.3. Effect of Beam Height
4.3. Strain Response
4.3.1. Strain Response of Longitudinal Reinforcements
4.3.2. Strain Response of Stirrups
4.3.3. Strain Response of Concrete Diagonal Sections
4.4. Ultimate Shear Strengths
4.4.1. Influence of the Volume Content of Steel Fiber
4.4.2. Influence of the Shear Span-to-Effective-Depth Ratio
4.5. The Formation and Propagation of Shear Cracks
4.5.1. The Effect of Steel Fiber Volume Content on the Formation and Propagation of Shear Cracks
4.5.2. The Effect of Beam Height on the Formation and Propagation of Shear Cracks
4.6. Load–Concrete Strain Relationships in the Shear-Bending Section
5. Shear Design Recommendations for UHPC Beams
5.1. French Standard Formulae
5.2. PCI-2021 Formulae
5.3. Xu’s Formulae
5.4. Comparison of Calculated Values
6. Contribution of Steel Fiber and UHPC Matrix
6.1. Contribution of Steel Fiber and UHPC Matrix to the Shear Capacity of UHPC Beams
6.1.1. Effect of Shear Span-to-Effective-Depth Ratio
6.1.2. Effect of Steel Fiber Volume Content
6.1.3. Effect of Beam Height
6.1.4. Effect of Beam Width
6.2. Discussion of the Calculated Values for the Steel Fiber Contribution and UHPC Matrix Using Theoretical Formulas
6.2.1. The Calculated Values for the Steel Fiber Contribution
6.2.2. The Calculated Values for the UHPC Matrix Contribution
7. Conclusions
- (1)
- The addition of steel fibers in the concrete mix exerted a pivotal impact on the failure mode of the tested beams. The failure modes of UHPC beams without steel fibers were typically brittle, whereas those reinforced with steel fibers exhibited ductile failure. In particular, the tested beams generally exhibited shear compression failure at steel fiber volume contents of 2.0% and 1.5%. Conversely, the beams with steel fiber volume content of 0% exhibited diagonal tension failure or diagonal compression failure.
- (2)
- The shear resistance of UHPC beams could be significantly enhanced by the addition of steel fibers in the concrete mix. At a shear span-to-effective-depth ratio (λ) of 2.0, the ultimate shear strength can be increased by approximately 100% and 170% with the addition of 1.5% and 2.0% volume content of steel fibers, respectively. Furthermore, an increase in the shear span-to-effective-depth ratio (λ) was observed to result in a notable decline in the ultimate shear strength of the UHPC beams.
- (3)
- The addition of steel fibers in the concrete mix could markedly improve the post-cracking load-bearing performance of non-stirrup UHPC beams. As the steel fiber volume content increased from 1.5% to 2.0%, the crack deformation at the ultimate load of specimens B7 and B10 could be increased by up to 39% and 6%, compared to B8 and B11, respectively. The beam height had a minor effect on the crack deformation at the turning point; however, it could significantly influence the crack deformation at the ultimate load.
- (4)
- The maximum value of the tensile strain on the diagonal section of the concrete was found to be markedly influenced by the beam height, with this effect diminishing gradually with an increase in the volume content of steel fiber. This finding demonstrates that the volume content of steel fiber also has a significant impact on the tensile strain on the diagonal section of the concrete.
- (5)
- The French standard formulae are more accurate for a relatively larger beam height. Furthermore, the formulae demonstrated greater accuracy at a steel fiber volume content of 2.0% in comparison to 1.5%. The PCI formulae were more precise when the beam height is relatively lower. Xu’s formulae demonstrated greater accuracy at larger shear span-to-effective-depth ratios.
- (6)
- The contribution of steel fiber to the shear capacity of the UHPC beams was observed to increase as the shear span-to-effective-depth ratio (λ) increased. Moreover, the contribution of steel fiber to the shear capacity of the UHPC beams was found to be inversely proportional to the width of the beams.
- (7)
- The contribution of UHPC matrix to the shear capacity of the UHPC beams was found to decrease as the shear span-to-effective-depth ratio (λ) increased. Furthermore, it was observed that the contribution of UHPC matrix to the shear capacity of UHPC beams increased as the steel fiber volume content decreased. The beam height was found to have a minor effect on the contribution of UHPC matrix to the shear capacity of UHPC beams.
- (8)
- The French standard formulae demonstrated a tendency to overestimate the contribution of steel fibers as the beam height and beam width increased. The calculation results were found to be more accurate for UHPC beams with a moderate shear span-to-effective-depth ratio (around 2.0). As the shear span-to-effective-depth ratio increased, the calculated values of the formulae for the UHPC matrix contribution became increasingly accurate.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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NO. | Specimen Nomenclature | Concrete Type | b/(mm) | h/(mm) | Volume Content of Steel Fiber | /(mm) | /(mm) | λ | /(mm) | Stirrup Ratio |
---|---|---|---|---|---|---|---|---|---|---|
B1 | U-W150-H30-V2.0-1.2 | UHPC | 150 | 300 | 2.0% | 244.5 | 293.4 | 1.2 | 800 | 0% |
B2 | U-W150-H30-V2.0-1.8 | UHPC | 150 | 300 | 2.0% | 244.5 | 440.1 | 1.8 | 1100 | 0% |
B3 | U-W150-H30-V2.0-3.1 | UHPC | 150 | 300 | 2.0% | 244.5 | 758.0 | 3.1 | 1700 | 0% |
B4 | U-W150-H30-V0-1.2 | UHPC | 150 | 300 | 0% | 244.5 | 293.4 | 1.2 | 800 | 0% |
B5 | U-W150-H30-V0-1.8 | UHPC | 150 | 300 | 0% | 244.5 | 440.1 | 1.8 | 1100 | 0% |
B6 | U-W150-H30-V0-3.1 | UHPC | 150 | 300 | 0% | 244.5 | 758.0 | 3.1 | 1700 | 0% |
B7 | U-W200-H35-V2.0-2.0 | UHPC | 200 | 350 | 2.0% | 291.0 | 582.0 | 2.0 | 1800 | 0% |
B8 | U-W200-H35-V1.5-2.0 | UHPC | 200 | 350 | 1.5% | 291.0 | 582.0 | 2.0 | 1800 | 0% |
B9 | U-W200-H35-V0-2.0 | UHPC | 200 | 350 | 0% | 291.0 | 582.0 | 2.0 | 1800 | 0% |
B10 | U-W200-H40-V2.0-2.0 | UHPC | 200 | 400 | 2.0% | 341.0 | 682.0 | 2.0 | 1800 | 0% |
B11 | U-W200-H40-V1.5-2.0 | UHPC | 200 | 400 | 1.5% | 341.0 | 682.0 | 2.0 | 1800 | 0% |
B12 | U-W200-H40-V0-2.0 | UHPC | 200 | 400 | 0% | 341.0 | 682.0 | 2.0 | 1800 | 0% |
B13 | C-W200-H35-V0-2.0 | C40 | 200 | 350 | 0% | 291.0 | 582.0 | 2.0 | 1800 | 0.584% |
B14 | C-W200-H40-V0-2.0 | C40 | 200 | 400 | 0% | 341.0 | 682.0 | 2.0 | 1800 | 0.599% |
Property (kg/m3) | Cement | Silica Fume | Quartz Powder | Quartz Sand | Steel Fiber | Water | Water Reducer |
---|---|---|---|---|---|---|---|
UHPC 2.0% | 868 | 181 | 102 | 941 | 161 | 153 | 46 |
UHPC 1.5% | 868 | 181 | 102 | 941 | 121 | 153 | 46 |
UHPC 0% | 868 | 181 | 102 | 941 | / | 153 | 46 |
Property (kg/m3) | Cement | Fly Ash | Mineral Powder | Sand | Stone | Water | Water Reducer |
---|---|---|---|---|---|---|---|
C40 | 280 | 65 | 61 | 688 | 1099 | 158 | 8 |
Concrete Type | Volume Content of Steel Fiber | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) | (MPa) |
---|---|---|---|---|---|---|---|---|---|---|
UHPC-T1-0 | 0% | 126.1 | 106.3 | / | 3.10 | 2.48 | 1.94 | 10.7 | 4.0 | 40,518 |
UHPC-T1-2.0 | 2.0% | 158.8 | 142.0 | / | 8.94 | 7.15 | 5.50 | 28.1 | 10.5 | 42,780 |
UHPC-T2-0 | 0% | 113.8 | 90.9 | 5.46 | 3.10 | 2.48 | 1.94 | 9.6 | 3.6 | 40,518 |
UHPC-T2-1.5 | 1.5% | 155.0 | 139.1 | 10.33 | 5.62 | 5.00 | 3.46 | 30.3 | 11.4 | 42,500 |
UHPC-T2-2.0 | 2.0% | 160.3 | 148.5 | 13.85 | 8.94 | 7.15 | 5.50 | 42.3 | 15.9 | 42,780 |
C40 | 0% | 31.7 | / | / | / | / | / | / | / | 34,500 |
Specimen | Reinforcing Steel Type | Diameter (mm) | Yield Strength (MPa) | Ultimate Strength (MPa) |
---|---|---|---|---|
Stirrup | HRB400 | 8 | 415 | 623 |
Longitudinal reinforcement | HRB400 | 25 | 425 | 611 |
Longitudinal reinforcement | HRB400 | 32 | 419 | 624 |
NO. | (kN) | (kN·m) | (MPa) | (kN) | (MPa) | (kN) | (kN) | (MPa) | (mm) | (kN) | (mm) | (kN) | (mm) | PSCR | Failure Pattern | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
B1 | 200 | 29.3 | 20.2 | 519 | 7.1 | 1475 | 737.5 | 20.1 | 2.97 | 1180 | 3.83 | 1402 | 2.86 | 1.34 | 45 | 65% | SC |
B2 | 134 | 29.5 | 20.3 | 480 | 6.5 | 1076 | 538 | 14.7 | 5.00 | 861 | 6.53 | 998 | 4.14 | 1.58 | 33 | 55% | SC |
B3 | 94 | 35.6 | 24.5 | 420 | 5.7 | 748 | 374 | 10.2 | 21.59 | 745 | 23.98 | 705 | 7.34 | 3.26 | 35 | 44% | FF |
B4 | 104 | 15.3 | 10.2 | 141 | 1.9 | 868 | 434 | 11.8 | 2.73 | 694 | 2.79 | 851 | 2.63 | 1.06 | 43 | 83% | DC |
B5 | 80 | 17.6 | 11.7 | 101 | 1.4 | 225 | 112.5 | 3.1 | 1.84 | 180 | 2.25 | 202 | 1.58 | 1.42 | 31 | 55% | DT |
B6 | 56 | 21.2 | 14.2 | 56 | 0.8 | 346 | 173 | 4.7 | 5.98 | 69 | 8.45 | 323 | 5.56 | 1.52 | 34 | 83% | DT |
B7 | 501 | 145.8 | 52.2 | 901 | 7.7 | 2500 | 1250 | 21.5 | 5.56 | 1074 | 8.67 | 2480 | 5.12 | 1.69 | 32 | 64% | SC |
B8 | 298 | 86.7 | 30.9 | 420 | 3.6 | 1862 | 931 | 16.0 | 4.23 | 1104 | 4.66 | 1841 | 3.99 | 1.16 | 38 | 77% | SC |
B9 | 197 | 57.3 | 19.9 | 242 | 2.1 | 919 | 459.5 | 7.9 | 2.55 | 627 | 3.30 | 883 | 2.38 | 1.39 | 44 | 74% | DC |
B10 | 501 | 170.8 | 49.1 | 701 | 5.1 | 2167 | 1083.5 | 15.9 | 4.69 | 1413 | 6.29 | 2140 | 4.46 | 1.41 | 38 | 68% | SC |
B11 | 400 | 136.4 | 39.0 | 600 | 4.4 | 1603 | 801.5 | 11.8 | 4.25 | 952 | 5.49 | 1579 | 4.10 | 1.34 | 38 | 63% | SC |
B12 | 203 | 69.2 | 19.2 | 301 | 2.2 | 794 | 397 | 5.8 | 2.75 | 519 | 3.36 | 761 | 2.39 | 1.41 | 42 | 62% | DT |
B13 | 80 | 23.3 | 7.4 | 259 | 2.2 | 591 | 295.5 | 5.1 | 3.93 | 573 | 5.66 | 582 | 3.27 | 1.73 | 39 | 56% | DC |
B14 | 80 | 27.3 | 6.9 | 298 | 2.2 | 606 | 303 | 4.4 | 2.78 | 521 | 4.99 | 600 | 2.67 | 1.87 | 36 | 51% | DC |
Experimental Results | French Standard Formulae | PCI-2021 Formulae | Xu’s Formulae | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
NO. | |||||||||||||||
B1 | 737.5 | 97.1 | 0 | 287.2 | 384.2 | 0.53 | 550.7 | 0 | 550.7 | 0.75 | 1398.5 | 0 | 186.6 | 1585.1 | 2.15 |
B2 | 538 | 97.1 | 0 | 442.2 | 539.2 | 1.00 | 550.7 | 0 | 550.7 | 1.02 | 445.0 | 0 | 256.1 | 701.1 | 1.30 |
B3 | 374 | 97.1 | 0 | 421.4 | 518.5 | 1.39 | 550.7 | 0 | 550.7 | 1.47 | 14.6 | 0 | 352.2 | 366.8 | 0.98 |
B4 | 434 | 86.5 | 0 | 0 | 86.5 | 0.20 | 209.8 | 0 | 209.8 | 0.48 | 1210.0 | 0 | 0 | 1210.0 | 2.79 |
B5 | 112.5 | 86.5 | 0 | 0 | 86.5 | 0.77 | 209.8 | 0 | 209.8 | 1.86 | 385.0 | 0 | 0 | 385.0 | 3.42 |
B6 | 173 | 86.5 | 0 | 0 | 86.5 | 0.50 | 209.8 | 0 | 209.8 | 1.21 | 12.6 | 0 | 0 | 12.6 | 0.07 |
B7 | 1250 | 154.7 | 0 | 749.4 | 904.1 | 0.72 | 1323.4 | 0 | 1323.4 | 1.06 | 523.7 | 0 | 457.6 | 981.4 | 0.79 |
B8 | 931 | 152.2 | 0 | 376.8 | 528.9 | 0.57 | 948.8 | 0 | 948.8 | 1.02 | 506.9 | 0 | 428.7 | 935.6 | 1.00 |
B9 | 459.5 | 130.4 | 0 | 0 | 130.4 | 0.28 | 299.6 | 0 | 299.6 | 0.65 | 409.8 | 0 | 0 | 409.8 | 0.89 |
B10 | 1083.5 | 181.3 | 0 | 702.4 | 883.7 | 0.82 | 1550.8 | 0 | 1550.8 | 1.43 | 613.7 | 0 | 536.3 | 1150.0 | 1.06 |
B11 | 801.5 | 178.3 | 0 | 441.5 | 619.8 | 0.77 | 1111.9 | 0 | 1111.9 | 1.39 | 594.0 | 0 | 502.3 | 1096.3 | 1.37 |
B12 | 397 | 152.8 | 0 | 0 | 152.8 | 0.38 | 351.1 | 0 | 351.1 | 0.88 | 480.2 | 0 | 0 | 480.2 | 1.21 |
Average: | 0.59 | Average: | 1.07 | Average: | 1.26 | ||||||||||
STDEV: | 0.24 | STDEV: | 0.43 | STDEV: | 0.71 | ||||||||||
CV: | 0.42 | CV: | 0.40 | CV: | 0.56 |
NO. | (kN) | (kN) | (kN) | (MPa) | ||
---|---|---|---|---|---|---|
B1 | 737.5 | 434.0 | 303.5 | 9.2 | 0.59 | 0.41 |
B2 | 538.0 | 112.5 | 425.5 | 12.9 | 0.21 | 0.79 |
B15 | 935.5 | 783.0 | 152.5 | 3.5 | 0.84 | 0.16 |
B16 | 723.0 | 317.0 | 406.0 | 9.2 | 0.44 | 0.56 |
B17 | 570.5 | 174.5 | 396.0 | 9.0 | 0.31 | 0.69 |
B7 | 1250.0 | 459.5 | 790.5 | 15.1 | 0.37 | 0.63 |
B8 | 931.0 | 459.5 | 471.5 | 9.0 | 0.49 | 0.51 |
B10 | 1083.5 | 397.0 | 686.5 | 11.2 | 0.37 | 0.63 |
B11 | 801.5 | 397.0 | 404.5 | 6.6 | 0.50 | 0.50 |
B18 | 670.0 | 259.5 | 410.5 | 7.8 | 0.39 | 0.61 |
B19 | 739.0 | 259.5 | 479.5 | 9.2 | 0.35 | 0.65 |
B20 | 770.0 | 247.5 | 522.5 | 8.5 | 0.32 | 0.68 |
B21 | 742.5 | 248.0 | 494.5 | 8.1 | 0.33 | 0.67 |
Average: | 0.42 | 0.58 | ||||
STDEV: | 0.15 | 0.15 | ||||
CV: | 0.36 | 0.26 |
NO. | (kN) | (kN) | (kN) | (kN) | ||
---|---|---|---|---|---|---|
B1 | 737.5 | 303.5 | 287.2 | / | 1.06 | / |
B2 | 538.0 | 425.5 | 442.2 | / | 0.96 | / |
B15 | 935.5 | 152.5 | 321.3 | / | 0.47 | / |
B16 | 723.0 | 406.0 | 567.7 | / | 0.72 | / |
B17 | 570.5 | 396.0 | 637.2 | / | 0.62 | / |
B7 | 1250.0 | 790.5 | 749.4 | / | 1.05 | / |
B8 | 931.0 | 471.5 | 376.8 | / | 1.25 | / |
B10 | 1083.5 | 686.5 | 702.4 | / | 0.98 | / |
B11 | 801.5 | 404.5 | 441.5 | / | 0.92 | / |
B18 | 670.0 | 410.5 | 743.1 | / | 0.55 | / |
B19 | 739.0 | 479.5 | 434.1 | / | 1.10 | / |
B20 | 770.0 | 522.5 | 1056.0 | / | 0.49 | / |
B21 | 742.5 | 494.5 | 613.4 | / | 0.81 | / |
B4 | 434.0 | 0 | 0 | 411.8 | / | 1.05 |
B5 | 112.5 | 0 | 0 | 411.8 | / | 0.27 |
B6 | 173.0 | 0 | 0 | 411.8 | / | 0.42 |
B15 * | 783.0 | 0 | 0 | 549.0 | / | 1.43 |
B16 * | 317.0 | 0 | 0 | 549.0 | / | 0.58 |
B17 * | 174.5 | 0 | 0 | 549.0 | / | 0.32 |
B9 | 459.5 | 0 | 0 | 620.9 | / | 0.74 |
B12 | 397.0 | 0 | 0 | 727.5 | / | 0.55 |
B22 | 259.5 | 0 | 0 | 633.6 | / | 0.41 |
B23 | 247.5 | 0 | 0 | 742.4 | / | 0.33 |
Average: | 0.84 | 0.61 | ||||
STDEV: | 0.23 | 0.37 | ||||
CV: | 0.27 | 0.61 |
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Deng, B.; Zhang, L.; Wu, S.; Jiang, H.; Tian, Y.; Fang, J.; Zhou, C. Shear Behavior of Non-Stirrup Ultra-High-Performance Concrete Beams: Contribution of Steel Fibers and UHPC. Buildings 2024, 14, 2705. https://doi.org/10.3390/buildings14092705
Deng B, Zhang L, Wu S, Jiang H, Tian Y, Fang J, Zhou C. Shear Behavior of Non-Stirrup Ultra-High-Performance Concrete Beams: Contribution of Steel Fibers and UHPC. Buildings. 2024; 14(9):2705. https://doi.org/10.3390/buildings14092705
Chicago/Turabian StyleDeng, Bowen, Lifeng Zhang, Shengze Wu, Haibo Jiang, Yueqiang Tian, Junfa Fang, and Chengan Zhou. 2024. "Shear Behavior of Non-Stirrup Ultra-High-Performance Concrete Beams: Contribution of Steel Fibers and UHPC" Buildings 14, no. 9: 2705. https://doi.org/10.3390/buildings14092705