Sustainability of Using Steel Fibers in Reinforced Concrete Deep Beams without Stirrups
Abstract
:1. Introduction
2. Shear Strength Models of SFRC Deep Beams
2.1. Background
2.2. Available Shear Strength Models
3. Research Significance
4. Methodology
4.1. Available Experimental Database
4.2. Comparison between RC and SFRC Databases
4.3. Development of the Nonlinear Regression-Based Model and Features Selection
4.4. Derivation and Evaluation of the Nonlinear Regression Model
5. Results and Discussions
5.1. Performance of the Proposed Model
5.2. Importance of Key Parameters
5.3. Effect of Selected Parameters on the Proposed Model
6. Summary and Conclusions
- Longitudinal steel reinforcement significantly boosts the shear strength of SFRC deep beams without stirrups. This can be justified, as the steel fibers improve deep beams’ capacity to carry loads by helping them bridge cracks.
- Even though the shear stresses are inversely related to the span-to-depth ratio, SFRC deep beams experience higher shear loads than RC deep beams because when the span-to-depth ratio of beams rises, the failure mode shifts from crushing of struts to diagonal shear failure.
- The results also show that the concrete compressive strength and depth of beams have only a small impact on the performance of SFRC and RC beams, which is understandable given that the strut-and-tie model, which primarily relies on the concrete compressive strength, provides the most accurate simulation of the shear strength of deep beams.
- A survey was conducted to explore the input parameters of the available shear strength models in literatures, and the investigation revealed the three variables , and are significant to quantify the shear strength contribution of steel reinforcement, concrete, and steel fibers ratio. Therefore, these three variables were utilized to build the proposed shear strength model for SFRC deep beams without stirrups.
- The proposed model outperformed the other equations in the literature, since it was able to anticipate the shear strength of SFRC deep beams with the lowest RMSE (=1.58) and lowest scatteredness, demonstrating the model’s high accuracy.
- The shear stresses predictions using the proposed model revealed that the trendlines of a/d, , and versus the predicted shear stresses match the test results in terms of the average fitting line and the scatteredness of data. This demonstrates the suggested model’s superior performance when considering various crucial factors that affect the shear strength of SFRC deep beams without stirrups.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Reference | No. of Specimens | d (mm) |
(MPa) | ρ (%) | Vf (%) | a/d | lf/df |
---|---|---|---|---|---|---|---|
[6] | 1 | 102 | 22.7 | 1.1 | 1.0 | 1.5 | 60 |
[7] | 2 | 197 | 29.1;29.9 | 1.34 | 0.5; 0.75 | 2.0 | 60 |
[13] | 5 | 221 | 34 | 1.1; 2.2 | 0.5; 1.0 | 1.5; 2.5 | 60 |
[10] | 8 | 130; 126 | 49–78.8 | 2.0, 5.72 | 0.25–2.0 | 2.0 | 100;133 |
[5] | 8 | 215 | 92–99.1 | 0.37–4.58 | 0.5–1.5 | 1.0;2.0 | 75 |
[14] | 9 | 345 | 37.8–68.2 | 3.55 | 0.25–1.0 | 0.7–0.93 | 100 |
[15] | 2 | 175 | 80 | 3.59 | 0.5; 1.0 | 2.0 | 100 |
[16] | 4 | 186 | 23–26 | 1.2 | 0.5; 1.0 | 2.0 | 50;100 |
[17] | 6 | 557 | 40.8–56.5 | 2.15 | 0.4–1.5 | 1.35 | 60;100 |
[11] | 3 | 212 | 30.8–68.6 | 1.5 | 0.5;0.75 | 2.0 | 62.5 |
[18] | 3 | 127 | 39.8 | 3.09 | 1.76 | 1.2;1.8 | 66.8 |
[19] | 1 | 300 | 109.5 | 3.08 | 0.75 | 1.75 | 75 |
[20] | 9 | 135 | 60–64.2 | 1.16 | 0.5;1.0 | 2.2 | 65;80 |
[21] | 2 | 210 | 44.6;57.2 | 1.5 | 0.5 | 2.0 | 62.5 |
[22] | 4 | 222 | 40.4–45.6 | 1.43 | 0.5;0.75 | 1.8;2.25 | 80 |
[23] | 2 | 219 | 40.9;43.2 | 1.9 | 1.0;2.0 | 2.0 | 60 |
[24] | 4 | 260 | 34.5–37.1 | 2.52 | 0.5–2.0 | 2.0 | 35 |
[25] | 3 | 175 | 82–83.8 | 1.0 | 0.5–1.5 | 1.5 | 80 |
[26] | 6 | 170 | 31.3;38.3 | 2.35 | 0.85;1.3 | 0.8–2.4 | 100 |
[27] | 1 | 219 | 80 | 1.91 | 1.0 | 2.0 | 55 |
[28] | 1 | 275 | 28.4 | 0.35 | 0.5 | 2.0 | 75 |
[8] | 12 | 165 | 25.3–89.4 | 1.3;2.9 | 0.5;1.0 | 1.45 | 60 |
[29] | 11 | 260–305 | 26.5–50 | 0.93–1.64 | 0.25–0.75 | 1.54–2.48 | 45–80 |
[30] | 4 | 127 | 20.7 | 2.0 | 1.0 | 2.0;2.4 | 62.5–100 |
[31] | 6 | 360–657 | 33.5 | 1.06–1.78 | 1.0 | 0.46–1.11 | 60 |
[32] | 9 | 275 | 24.9–31.2 | 0.63–2.47 | 1.0–3.0 | 1.5;2.0 | 60 |
[33] | 18 | 362 | 38.4–47.4 | 1.11–2.32 | 0.4–1.2 | 1.0–2.0 | 37.5 |
[34] | 9 | 170;178 | 52.5–54.6 | 1.23;1.35 | 0.5–1.5 | 1.97;2.35 | 80 |
[35] | 4 | 250 | 53.1;55.4 | 0.53 | 0.5;1.0 | 2.4 | 50 |
[36] | 8 | 270 | 40.4;43.2 | 1.21 | 0.26;0.51 | 0.5;1.5 | 50 |
[37] | 7 | 80–280 | 45.8–51.5 | 2.0–3.54 | 0.75;1.5 | 2.0 | 60;67.7 |
Total | 172 |
Statistical Measure | Features | |||||
---|---|---|---|---|---|---|
d (mm) | bw (mm) | a/d | fcm (MPa) | ρ (%) | Vu (kN) | |
Mean | 425 | 183 | 1.35 | 33.5 | 2.02 | 283.4 |
Median | 356 | 178 | 1.36 | 27.9 | 1.82 | 220.8 |
Mode | 305 | 178 | 1 | 31.4 | 1.13 | 192.7 |
Standard deviation | 234 | 64 | 0.4 | 16.7 | 1.1 | 206 |
Minimum | 132 | 51 | 0.5 | 11.3 | 0.26 | 20.7 |
Maximum | 1559 | 460 | 2 | 87 | 5.04 | 1240 |
Count | 281 | 281 | 281 | 281 | 281 | 281 |
Reference | Variable | Parameter | Note |
---|---|---|---|
[10] | X1 | X2 is dependent on X1, therefore, X2 will be dropped | |
X2 | |||
X3 | |||
[5] | X4 | ||
X5 | |||
X6 | |||
[6] | X7 | ||
[11] | X8 | X8 is dependent on X1, therefore, X8 will be dropped | |
[12] | X9 | ||
X10 | |||
Proposed in this study | X11 | ||
X12 |
Variable | X1 | X3 | X4 | X5 | X6 | X7 | X9 | X10 | X11 | X12 |
---|---|---|---|---|---|---|---|---|---|---|
X1 | 1 | |||||||||
X3 | 0.23 | 1 | ||||||||
X4 | 0.20 | 0.96 | 1 | |||||||
X5 | −0.04 | −0.75 | −0.78 | 1 | ||||||
X6 | 0.10 | 0.24 | 0.23 | −0.05 | 1 | |||||
X7 | 0.29 | 0.69 | 0.78 | −0.26 | 0.32 | 1 | ||||
X9 | 0.12 | 0.23 | 0.23 | −0.05 | 0.99 | 0.33 | 1 | |||
X10 | 0.70 | 0.45 | 0.50 | −0.10 | 0.17 | 0.73 | 0.18 | 1 | ||
X11 | 0.10 | 0.23 | 0.23 | −0.05 | 1.00 | 0.33 | 0.99 | 0.17 | 1 | |
X12 | 0.79 | 0.03 | 0.06 | 0.04 | −0.05 | 0.20 | −0.04 | 0.69 | −0.05 | 1 |
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Almasabha, G.; Murad, Y.; Alghossoon, A.; Saleh, E.; Tarawneh, A. Sustainability of Using Steel Fibers in Reinforced Concrete Deep Beams without Stirrups. Sustainability 2023, 15, 4721. https://doi.org/10.3390/su15064721
Almasabha G, Murad Y, Alghossoon A, Saleh E, Tarawneh A. Sustainability of Using Steel Fibers in Reinforced Concrete Deep Beams without Stirrups. Sustainability. 2023; 15(6):4721. https://doi.org/10.3390/su15064721
Chicago/Turabian StyleAlmasabha, Ghassan, Yasmin Murad, Abdullah Alghossoon, Eman Saleh, and Ahmad Tarawneh. 2023. "Sustainability of Using Steel Fibers in Reinforced Concrete Deep Beams without Stirrups" Sustainability 15, no. 6: 4721. https://doi.org/10.3390/su15064721