Structural Performance of EB-FRP-Strengthened RC T-Beams Subjected to Combined Torsion and Shear Using ANN
Abstract
:1. Introduction
2. Material Modeling and Nonlinear Analysis
3. Results and Discussions
3.1. Evaluation of Strengthened RC T-Beams under Combined Torsion and Shear
3.2. Application of ANN
3.3. Model Evaluation Method
3.4. Comparison of ABAQUS and ANN Results
- : the weights between the -th and the -th layers;
- : the biases between the -th and the -th layers;
- : the weight from the -th neuron in the -th layer to the -th neuron in the -th layer;
- : the bias of the -th neuron in the -th layer.
4. Conclusions
- Regarding the figures and tables, numerical cracking torques, ultimate torques, the maximum angle of twist, cracking shear, and ultimate shear values are consistent with the experimental results for all beams.
- According to the numerical results, the ultimate structural strength of EB-FRP-strengthened RC T-beams depends on the volumetric ratio and fiber orientation of the employed FRP materials. For a certain angle of twist, beams with higher torsional reinforcement have greater torsional capacity, increased post-cracking stiffness, and ultimate angle of twist.
- The applications of ANN, MSE, and can evaluate the consistency of experimental and FEM results.
- The resultant values of MSE less than 0.0009 and greater than 0.9960 proved that the developed ANN model of this study fits the data precisely.
- The research methodology presented in this study can be adopted and applied in expensive and time-consuming structural experiments subjected to combined torsion, shear, and bending.
5. Possible Directions for Future Studies
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
References
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Beam | Wrapping Configurations | Strengthening Schemes | |
---|---|---|---|
TB1 | None (Un-retrofitted beam) | --- | |
TB1S1 | U-Jacket | ||
TB1S2 | Extended U-Jacket | ||
TB1S3 | Full Wrapping | ||
TB3 | None (Control beam) | --- | |
TB3S4 | Extended U-Jacket + Full Wrapping |
Designation | Combined Effects | Mean Concrete Strength (MPa) | FRP | Torsional Moment at First Crack | Maximum Torsional Resistance | Maximum Shear Resistance |
---|---|---|---|---|---|---|
TB1 | Torsion & Shear | 25 | -- | 10.5 | 23 | 44 |
TB1S1 | Torsion & Shear | 25 | CFRP | 19.5 | 34 | 60 |
TB1S2 | Torsion & Shear | 25 | CFRP | 14 | 38 | 80 |
TB1S3 | Torsion & Shear | 25 | CFRP | 18 | 39 | 83 |
TB3 | Torsion & Shear | 25 | -- | 3 | 10.75 | 109 |
TB3S4 | Torsion & Shear | 25 | CFRP | 16 | 17.5 | 173 |
FRP | E | Tensile Strength | Thickness |
---|---|---|---|
CFRP | 63,300 | 609 | 0.86 |
Beam | ||||||
---|---|---|---|---|---|---|
TB1 | 10.5 | 23 | 2.6 | 10 | 23.38 | 2.31 |
TB1S1 | 19.5 | 34 | 1.5 | 17.5 | 33.85 | 1.33 |
TB1S2 | 14 | 38 | 2.5 | 16 | 39 | 2 |
TB1S3 | 18 | 39 | 2.5 | 15.5 | 40 | 2 |
TB3 | 3 | 10.75 | 0.9 | 3.3 | 10.44 | 1.01 |
TB3S4 | 16 | 17.5 | 8 | 14.5 | 18 | 8.5 |
Beam | |||
---|---|---|---|
TB1 | 0.95 | 1.016 | 0.888 |
TB1S1 | 0.897 | 0.995 | 0.886 |
TB1S2 | 1.14 | 1.026 | 0.8 |
TB1S3 | 0.861 | 1.025 | 0.8 |
TB3 | 1.1 | 0.971 | 1.12 |
TB3S4 | 0.906 | 1.028 | 1.062 |
Beam | ||||||
---|---|---|---|---|---|---|
TB1 | 17 | 44 | 16.3 | 42 | 0.959 | 0.95 |
TB1S1 | 24 | 60 | 28 | 68.7 | 1.16 | 1.14 |
TB1S2 | 35 | 80 | 33 | 73.03 | 0.94 | 0.91 |
TB1S3 | 45 | 83 | 38 | 88.4 | 0.84 | 1.06 |
TB3 | 58 | 109 | 60 | 119.2 | 1.034 | 1.09 |
TB3S4 | 70 | 173 | 81 | 184.47 | 1.157 | 1.066 |
Beam | TB1 | (a) | ||
Structural Response | Torsion | (b) | (c) | (d) |
Shear | (e) | (f) | (g) | |
Beam | TB1S1 | (a) | ||
Structural Response | Torsion | (b) | (c) | (d) |
Shear | (e) | (f) | (g) | |
Beam | TB1S2 | (a) | ||
Structural Response | Torsion | (b) | (c) | (d) |
Shear | (e) | (f) | (g) | |
Beam | TB1S3 | (a) | ||
Structural Response | Torsion | (b) | (c) | (d) |
Shear | (e) | (f) | (g) | |
Beam | TB3 | (a) | ||
Structural Response | Torsion | (b) | (c) | (d) |
Shear | (e) | (f) | (g) | |
Beam | TB3S4 | (a) | ||
Structural Response | Torsion | (b) | (c) | (d) |
Shear | (e) | (f) | (g) |
Structural Loading | Beam Model | Evaluation Index | |||||
---|---|---|---|---|---|---|---|
Training Set | Test Set | All Set | |||||
MSE | R2 | MSE | R2 | MSE | R2 | ||
Torsion | TB1 | 0.000218 | 0.999584 | 0.000208 | 0.999572 | 0.000216 | 0.999582 |
TB1S1 | 0.000010 | 0.999942 | 0.000010 | 0.999934 | 0.000010 | 0.999941 | |
TB1S2 | 0.000855 | 0.998568 | 0.000853 | 0.998567 | 0.000854 | 0.998568 | |
TB1S3 | 0.000120 | 0.999586 | 0.000113 | 0.999617 | 0.000119 | 0.999592 | |
TB3 | 0.000012 | 0.999880 | 0.000010 | 0.999861 | 0.000011 | 0.999879 | |
TB3S4 | 0.000015 | 0.999997 | 0.000017 | 0.999996 | 0.000016 | 0.999997 | |
Shear | TB1 | 0.000204 | 0.999619 | 0.000130 | 0.999742 | 0.000189 | 0.999643 |
TB1S1 | 0.000282 | 0.998268 | 0.000196 | 0.998732 | 0.000265 | 0.998359 | |
TB1S2 | 0.000894 | 0.996909 | 0.001667 | 0.996277 | 0.000949 | 0.996775 | |
TB1S3 | 0.000291 | 0.999200 | 0.000214 | 0.999500 | 0.000276 | 0.999270 | |
TB3 | 0.000016 | 0.999808 | 0.000030 | 0.999677 | 0.000019 | 0.999780 | |
TB3S4 | 0.000846 | 0.998700 | 0.000617 | 0.998963 | 0.000800 | 0.998749 |
Layers | Variables | Weights | Biases | ||||||
---|---|---|---|---|---|---|---|---|---|
Input Layer– Hidden Layer 1 | 0.9055 | 0.1368 | −2.1926 | 0.3227 | 0.1869 | 0.2014 | 0.2081 | 0.0113 | |
−0.4744 | −0.5172 | 0.2766 | 0.4934 | 0.2912 | 0.2610 | 0.0833 | −0.1754 | ||
Hidden Layer 1– Hidden Layer 2 | −0.4782 | −0.2169 | −0.2380 | −0.2013 | |||||
−0.2345 | 0.5501 | 0.1987 | 0.8133 | ||||||
0.3647 | 0.1677 | 0.5850 | 0.5514 | ||||||
0.4934 | −0.3571 | 0.1958 | 0.6721 | ||||||
0.4643 | −0.9118 | −0.1101 | −0.2964 | ||||||
−0.5442 | 0.0397 | −1.9594 | 0.9148 | ||||||
0.1914 | 0.4342 | −0.0231 | −0.3457 | ||||||
0.8302 | −0.8049 | 0.1371 | 0.2899 | 0.0000 | 0.2942 | 0.0000 | 0.2942 | ||
0.2652 | −0.0362 | −0.1578 | −0.5761 | 0.1679 | −0.0291 | 0.1679 | −0.0291 | ||
−0.0078 | 0.6746 | 0.3158 | −1.9715 | ||||||
0.1724 | 0.0492 | 0.7593 | −0.0956 | ||||||
0.1656 | 0.2187 | 1.2919 | −0.0056 | ||||||
0.4801 | 0.4057 | −0.6696 | −0.1514 | ||||||
0.4514 | 0.8221 | −0.4599 | 0.4107 | ||||||
0.4930 | 0.0647 | 0.5120 | −1.7222 | ||||||
−0.1700 | −0.4075 | 0.0203 | 0.4248 | ||||||
Hidden Layer 2– Hidden Layer 3 | −0.0330 | 0.8583 | 0.2370 | −0.5885 | |||||
0.2429 | −0.4196 | −0.8351 | −0.1537 | ||||||
−0.2964 | 0.1166 | −0.0714 | −0.8275 | ||||||
0.0003 | 0.2155 | −0.1605 | 0.2042 | ||||||
0.2977 | −0.6194 | 0.6551 | −0.1769 | ||||||
−0.1414 | −0.5998 | 0.1234 | 0.1651 | ||||||
0.3675 | 0.0010 | −0.0161 | 0.9348 | ||||||
0.1266 | 0.0796 | −0.0199 | −0.3759 | 0.218 | 0.2706 | 0.218 | 0.2706 | ||
−0.4590 | 0.3589 | −0.3686 | 0.2192 | −0.2659 | 0.0000 | −0.2659 | 0.0000 | ||
0.8897 | 0.2254 | −0.1640 | 0.0363 | ||||||
−1.4055 | 0.1166 | 0.6798 | −0.2132 | ||||||
0.0544 | 0.1966 | −0.1423 | −0.8834 | ||||||
−0.9197 | 0.4698 | −1.0743 | 0.2524 | ||||||
−0.3382 | −0.3060 | 0.4118 | −0.3654 | ||||||
0.3631 | 0.3432 | 0.4255 | −0.0669 | ||||||
0.2511 | −0.3471 | 0.4713 | 0.0675 | ||||||
Hidden Layer 3– Hidden Layer 4 | −0.0978 | 0.3359 | −0.0234 | −0.2039 | |||||
0.3257 | −0.5964 | 0.1834 | 0.1567 | ||||||
0.1030 | 0.0933 | −0.3127 | 0.2791 | ||||||
0.6889 | −0.1012 | 0.1629 | 0.0561 | ||||||
0.3922 | 0.3585 | 0.6967 | 0.0493 | ||||||
−0.0747 | 1.6836 | −0.2026 | 0.5889 | ||||||
−0.1932 | 0.2583 | 0.3790 | −0.098 | ||||||
−0.1582 | 0.2372 | 0.0852 | 0.5036 | −0.0060 | 0.1727 | −0.006 | 0.1727 | ||
0.0680 | 0.1110 | −0.3814 | −0.0323 | 0.1675 | −0.0533 | 0.1675 | −0.0533 | ||
0.0911 | 0.1246 | −0.2549 | −0.3707 | ||||||
−1.0282 | −0.0705 | 0.5200 | 0.1239 | ||||||
0.4415 | 0.3857 | 0.0975 | 0.1955 | ||||||
0.1195 | −0.0460 | 0.2357 | 0.2504 | ||||||
−0.2813 | −0.4536 | −0.3516 | −0.4265 | ||||||
0.0556 | 0.0410 | −0.4205 | 0.2033 | ||||||
−0.2370 | −0.5362 | −0.4228 | −0.2052 | ||||||
Hidden Layer 4– Output Layer | −1.1736 | 0.5198 | −1.1736 | 0.5198 | 0.1462 | ||||
0.6921 | -0.6953 | 0.6921 | −0.6953 |
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Amini Pishro, A.; Zhang, Z.; Amini Pishro, M.; Liu, W.; Zhang, L.; Yang, Q. Structural Performance of EB-FRP-Strengthened RC T-Beams Subjected to Combined Torsion and Shear Using ANN. Materials 2022, 15, 4852. https://doi.org/10.3390/ma15144852
Amini Pishro A, Zhang Z, Amini Pishro M, Liu W, Zhang L, Yang Q. Structural Performance of EB-FRP-Strengthened RC T-Beams Subjected to Combined Torsion and Shear Using ANN. Materials. 2022; 15(14):4852. https://doi.org/10.3390/ma15144852
Chicago/Turabian StyleAmini Pishro, Ahad, Zhengrui Zhang, Mojdeh Amini Pishro, Wenfang Liu, Lili Zhang, and Qihong Yang. 2022. "Structural Performance of EB-FRP-Strengthened RC T-Beams Subjected to Combined Torsion and Shear Using ANN" Materials 15, no. 14: 4852. https://doi.org/10.3390/ma15144852