Determining the Shear Capacity of Steel Beams with Corrugated Webs by Using Optimised Regression Learner Techniques
Abstract
:1. Introduction
2. Theoretical Background
3. Assessment of SBCW Shear Capacity Formulas
4. Test Data
4.1. Test Data Published by Other Researchers
4.2. Test Data from the Authors
4.3. Test Setup
5. ORLTs
- The validation technique was selected, the cross-validation technique with 10 folds was chosen before the training process.
- The primary optimisation options were selected, and the option used was the BO technique, with an expected improvement per second plus and 30 iterations.
- One of the ORLTs was selected (DT, SVM, GPR or EN).
- The training process is started to determine the optimal parameters and predicted model of this method.
- The optimal parameters and performance model of the selected method were recorded.
- Finally, the ORLT model of the selected method was exported to be used in the prediction of the original and new datasets.
6. Model Validation and Comparison
7. Initial Comparison with Published Experimental Data
8. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Experimental Data
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
L1A | 994 | 974 | 2 | 140 | 50.03 | 50 | 292 | 512.37 |
L1B | 994 | 984 | 3 | 140 | 50.03 | 50 | 335 | 383.78 |
L2A | 1445 | 1503 | 2 | 140 | 50.03 | 50 | 282 | 744.85 |
L2B | 1445 | 1503 | 3 | 140 | 50.03 | 50 | 317 | 568.90 |
L3A | 2005 | 2005 | 2 | 140 | 50.03 | 50 | 280 | 997.51 |
L3B | 2005 | 2005 | 3 | 140 | 50.03 | 50 | 300 | 792.49 |
B1 | 600 | 798 | 2 | 140 | 50.03 | 50 | 341 | 285.71 |
B4 | 600 | 798 | 2 | 140 | 50.03 | 50 | 363 | 284.36 |
B4b | 600 | 798 | 2 | 140 | 50.03 | 50 | 363 | 284.36 |
B3 | 600 | 798 | 3 | 140 | 50.03 | 50 | 317 | 229.01 |
B2 | 600 | 702 | 3 | 140 | 50.03 | 50 | 315 | 229.01 |
M101 | 600 | 600 | 1 | 70 | 15.01 | 15 | 189 | 606.06 |
M102 | 800 | 800 | 1 | 70 | 15.01 | 15 | 190 | 808.08 |
M103 | 1000 | 1000 | 1 | 70 | 15.01 | 15 | 213 | 1052.63 |
M104 | 1200 | 1200 | 1 | 70 | 15.01 | 15 | 189 | 1212.12 |
L1 | 1000 | 1500 | 2 | 106 | 50.02 | 87 | 410 | 476.19 |
L1 | 1000 | 1490 | 3 | 106 | 50.02 | 87 | 450 | 333.33 |
L2 | 1498 | 2157 | 2 | 106 | 50.02 | 87 | 376 | 749.00 |
L2 | 1498 | 2142 | 3 | 106 | 50.02 | 87 | 402 | 499.33 |
No. 1 | 850 | 1131 | 2 | 102 | 55.55 | 86 | 355 | 425.00 |
No. 2 | 850 | 1131 | 2 | 91 | 56.30 | 72 | 349 | 425.00 |
V1/1 | 298 | 2819 | 2 | 144 | 102.06 | 102 | 298 | 145.37 |
V1/2 | 298 | 2000 | 2 | 144 | 102.06 | 102 | 283 | 141.90 |
V1/3 | 298 | 1001 | 2 | 144 | 102.06 | 102 | 298 | 149.00 |
V2/3 | 600 | 1650 | 3 | 144 | 102.06 | 102 | 279 | 200.00 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
V-PILOTA | 305 | 305 | 0.78 | 38.10 | 25.42 | 25.40 | 621 | 390.03 |
V-PILOTB | 305 | 305 | 0.79 | 38.10 | 25.42 | 25.40 | 638 | 388.54 |
V121216A | 305 | 305 | 0.64 | 38.10 | 25.42 | 25.40 | 676 | 478.06 |
V121216B | 305 | 305 | 0.77 | 38.10 | 25.42 | 25.40 | 665 | 398.69 |
V181216B | 457 | 305 | 0.61 | 38.10 | 25.42 | 25.40 | 618 | 749.18 |
V181216C | 457 | 305 | 0.76 | 38.10 | 25.42 | 25.40 | 679 | 602.11 |
V181816A | 457 | 457 | 0.64 | 38.10 | 25.42 | 25.40 | 591 | 719.69 |
V181816B | 457 | 457 | 0.74 | 38.10 | 25.42 | 25.40 | 614 | 620.08 |
V241216A | 610 | 305 | 0.64 | 38.10 | 25.42 | 25.40 | 591 | 960.63 |
V241216B | 610 | 305 | 0.79 | 38.10 | 25.42 | 25.40 | 588 | 775.10 |
V121221A | 305 | 305 | 0.63 | 41.90 | 33.45 | 23.40 | 665 | 484.13 |
V121221B | 305 | 305.00 | 0.79 | 41.90 | 33.45 | 23.40 | 665 | 388.54 |
V122421A | 305 | 609.60 | 0.68 | 41.90 | 33.45 | 23.40 | 621 | 451.18 |
V122421B | 305 | 609.60 | 0.78 | 41.90 | 33.45 | 23.40 | 638 | 390.03 |
V181221A | 457 | 305 | 0.61 | 41.90 | 33.45 | 23.40 | 578 | 749.18 |
V181221B | 457 | 305 | 0.76 | 41.90 | 33.45 | 23.40 | 606 | 599.74 |
V181821A | 457 | 457 | 0.64 | 41.90 | 33.45 | 23.40 | 552 | 719.69 |
V181821B | 457 | 457 | 0.74 | 41.90 | 33.45 | 23.40 | 596 | 620.08 |
V241221A | 610 | 305 | 0.61 | 41.90 | 33.45 | 23.40 | 610 | 1000.00 |
V241221B | 610 | 305 | 0.76 | 41.90 | 33.45 | 23.40 | 639 | 800.52 |
V121232A | 305 | 305 | 0.64 | 49.80 | 50.77 | 26.40 | 665 | 476.56 |
V121232B | 305 | 305 | 0.78 | 49.80 | 50.77 | 26.40 | 641 | 391.03 |
V121832A | 305 | 457 | 0.64 | 49.80 | 50.77 | 26.40 | 703 | 476.56 |
V121832B | 305 | 457 | 0.92 | 49.80 | 50.77 | 26.40 | 562 | 331.88 |
V122432A | 305 | 609.60 | 0.64 | 49.80 | 50.77 | 26.40 | 714 | 476.56 |
V122432B | 305 | 609.60 | 0.78 | 49.80 | 50.77 | 26.40 | 634 | 392.54 |
V181232A | 457 | 305 | 0.60 | 49.80 | 50.77 | 26.40 | 552 | 765.49 |
V181232B | 457 | 305 | 0.75 | 49.80 | 50.77 | 26.40 | 602 | 610.15 |
V181832A | 457 | 457 | 0.61 | 49.80 | 50.77 | 26.40 | 689 | 749.18 |
V181832B | 457 | 457 | 0.75 | 49.80 | 50.77 | 26.40 | 580 | 610.15 |
V241232A | 610 | 305.00 | 0.62 | 49.80 | 50.77 | 26.40 | 673 | 980.71 |
V241232B | 610 | 305.00 | 0.76 | 49.80 | 50.77 | 26.40 | 584 | 800.52 |
V121809A | 305 | 457.00 | 0.71 | 19.80 | 14.19 | 11.90 | 572 | 432.01 |
V121809C | 305 | 457.00 | 0.63 | 19.80 | 14.19 | 11.90 | 669 | 482.59 |
V122409A | 305 | 609.60 | 0.71 | 19.80 | 14.19 | 11.90 | 586 | 427.17 |
V122409C | 305 | 609.60 | 0.66 | 19.80 | 14.19 | 11.90 | 621 | 460.03 |
V181209A | 457 | 305.00 | 0.56 | 19.80 | 14.19 | 11.90 | 689 | 817.53 |
V181209C | 457 | 305.00 | 0.61 | 19.80 | 14.19 | 11.90 | 592 | 749.18 |
V181809A | 457 | 457.00 | 0.61 | 19.80 | 14.19 | 11.90 | 618 | 749.18 |
V181809C | 457 | 457.00 | 0.62 | 19.80 | 14.19 | 11.90 | 559 | 734.73 |
V241209A | 610 | 305.00 | 0.62 | 19.80 | 14.19 | 11.90 | 606 | 980.71 |
V241209C | 610 | 305.00 | 0.64 | 19.80 | 14.19 | 11.90 | 621 | 960.63 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
CW1 | 440.36 | 730.92 | 3.06 | 180 | 45.01 | 44.99 | 320 | 143.91 |
CW2 | 437.92 | 730.92 | 3.29 | 180 | 45.01 | 44.99 | 312 | 133.11 |
CW3 | 437.18 | 940.92 | 3.26 | 250 | 45.01 | 44.99 | 284 | 134.10 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
SP1 | 800 | 1750 | 2 | 146 | 104.07 | 104 | 307 | 400 |
SP2 | 800 | 1750 | 2 | 170 | 80.05 | 80 | 299 | 400 |
SP3 | 800 | 1750 | 2 | 185 | 65.04 | 65 | 292 | 400 |
SP4 | 800 | 1800 | 2 | 117 | 83.05 | 83 | 298 | 400 |
SP5 | 800 | 1800 | 2 | 136 | 64.04 | 64 | 291 | 400 |
SP6 | 800 | 1800 | 2 | 148 | 52.03 | 52 | 294 | 400 |
SP2-2-400 1 | 400 | 1000 | 2 | 170 | 80.05 | 80 | 263 | 200 |
SP2-2-400 2 | 400 | 1000 | 2 | 170 | 80.05 | 80 | 263 | 200 |
SP2-2-800 1 | 800 | 1000 | 2 | 170 | 80.05 | 80 | 272 | 400 |
SP2-2-800 2 | 800 | 1000 | 2 | 170 | 80.05 | 80 | 272 | 400 |
SP2-3-600 1 | 600 | 1000 | 3 | 170 | 80.05 | 80 | 294 | 200 |
SP2-3-600 2 | 600 | 1000 | 3 | 170 | 80.05 | 80 | 294 | 200 |
SP2-3-1200 1 | 1200 | 1000 | 3 | 170 | 80.05 | 80 | 294 | 400 |
SP2-3-1200 2 | 1200 | 1000 | 3 | 170 | 80.05 | 80 | 294 | 400 |
SP2-4-800 1 | 800 | 1000 | 4 | 170 | 80.05 | 80 | 326 | 200 |
SP2-4-800 2 | 800 | 1000 | 4 | 170 | 80.05 | 80 | 326 | 200 |
SP2-4-1600 1 | 1600 | 1000 | 4 | 170 | 80.05 | 80 | 328 | 400 |
SP2-4-1600 2 | 1600 | 1000 | 4 | 170 | 80.05 | 80 | 328 | 400 |
SP2-8-800 1 | 800 | 1000 | 8 | 170 | 80.05 | 80 | 270 | 100 |
SP2-8-800 2 | 800 | 1000 | 8 | 170 | 80.05 | 80 | 270 | 100 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
G7A | 1500 | 4500 | 6 | 300 | 150 | 200 | 465 | 250 |
G8A | 1500 | 4500 | 6 | 300 | 150 | 200 | 465 | 250 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
L1 | 1500 | 3000 | 4.80 | 450 | 200.00 | 300 | 250 | 312.50 |
L2 | 1500 | 3400 | 4.80 | 550 | 188.80 | 300 | 250 | 312.50 |
L3 | 1500 | 3000 | 4.80 | 450 | 49.60 | 300 | 250 | 312.50 |
L4 | 1500 | 3400 | 4.80 | 550 | 55.60 | 300 | 250 | 312.50 |
I1 | 2000 | 3600 | 4.80 | 320 | 44.60 | 100 | 250 | 416.67 |
I2 | 2000 | 3600 | 3.80 | 350 | 28.60 | 100 | 250 | 526.32 |
G1 | 2000 | 3000 | 4.80 | 200 | 45.40 | 180 | 250 | 416.67 |
G2 | 2000 | 3000 | 3.80 | 160 | 33.00 | 50 | 250 | 526.32 |
G3 | 2000 | 3000 | 3.80 | 160 | 26.90 | 100 | 250 | 526.32 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
PG2 | 2000 | 2600 | 4 | 250 | 60 | 220 | 296 | 500 |
PG1 | 2000 | 2800 | 4 | 220 | 60 | 180 | 296 | 500 |
PG3 | 2000 | 2800 | 4 | 220 | 75 | 180 | 296 | 500 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
TP20-300-30 | 3050 | 664.90 | 2 | 60 | 20.01 | 34.64 | 290 | 152.50 |
A20-410-30-N | 410 | 578.10 | 2 | 40 | 20.01 | 34.64 | 290 | 205.00 |
A20-410-45-N | 410 | 524.80 | 2 | 40 | 28.29 | 28.28 | 290 | 205.00 |
A20-505-30-N | 505 | 575.70 | 2 | 40 | 20.01 | 34.64 | 290 | 252.50 |
A20-505-45-N | 505 | 525.20 | 2 | 40 | 28.29 | 28.28 | 290 | 252.50 |
B20-305-30 | 305 | 427.00 | 2 | 40 | 20.01 | 34.64 | 680 | 152.50 |
B20-305-45 | 305 | 390.40 | 2 | 40 | 28.29 | 28.28 | 680 | 152.50 |
B20-505-45 | 505 | 388.85 | 2 | 40 | 28.29 | 28.28 | 680 | 252.50 |
B20-505-45-N | 505 | 388.85 | 2 | 40 | 28.29 | 28.28 | 290 | 252.50 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
W1 | 1200 | 2000 | 3 | 110 | 55 | 90 | 400 | 400 |
SC1 | 1500 | 4500 | 6.27 | 300 | 150 | 200 | 465 | 239.23 |
V1b | 500 | 1000 | 2.50 | 30 | 40 | 47 | 270 | 200 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
L1A | 0.953 | 0.53 | 1.09 | 0.70 | 1.255 | 281.72 | 280.93 | 1.01 |
L1B | 0.765 | 0.53 | 0.93 | 0.80 | 1.238 | 495.08 | 501.34 | 0.98 |
L2A | 0.937 | 0.76 | 1.21 | 0.63 | 1.222 | 347.69 | 337.50 | 1.04 |
L2B | 0.759 | 0.75 | 1.07 | 0.71 | 1.182 | 571.69 | 563.51 | 1.00 |
L3A | 0.901 | 1.04 | 1.38 | 0.52 | 1.384 | 465.59 | 451.22 | 1.05 |
L3B | 0.741 | 1.02 | 1.26 | 0.60 | 1.460 | 776.65 | 773.57 | 0.99 |
B1 | 0.952 | 0.34 | 1.01 | 0.75 | 1.056 | 202.53 | 208.04 | 0.94 |
B4 | 0.977 | 0.35 | 1.04 | 0.73 | 1.062 | 203.28 | 183.46 | 1.12 |
B4b | 0.977 | 0.35 | 1.04 | 0.73 | 1.062 | 203.28 | 217.66 | 0.95 |
B3 | 0.735 | 0.31 | 0.80 | 0.88 | 1.008 | 255.36 | 246.01 | 1.04 |
B2 | 0.733 | 0.31 | 0.80 | 0.88 | 1.061 | 263.45 | 273.42 | 0.98 |
M101 | 0.751 | 0.74 | 1.05 | 0.72 | 1.153 | 53.46 | 52.96 | 1.02 |
M102 | 0.753 | 0.99 | 1.24 | 0.60 | 1.507 | 79.10 | 79.19 | 1.00 |
M103 | 0.831 | 1.32 | 1.56 | 0.41 | 1.751 | 83.79 | 83.95 | 1.00 |
M104 | 0.751 | 1.48 | 1.66 | 0.36 | 2.168 | 102.33 | 103.98 | 0.98 |
L1 | 0.790 | 0.66 | 1.03 | 0.74 | 1.045 | 383.35 | 380.08 | 1.01 |
L1 | 0.579 | 0.63 | 0.86 | 0.84 | 0.945 | 617.09 | 610.72 | 1.01 |
L2 | 0.794 | 0.96 | 1.25 | 0.60 | 1.506 | 592.39 | 600.20 | 0.98 |
L2 | 0.548 | 0.90 | 1.05 | 0.72 | 1.202 | 899.87 | 905.32 | 1.00 |
No. 1 | 0.743 | 0.48 | 0.88 | 0.83 | 0.948 | 272.59 | 275.01 | 0.99 |
No. 2 | 0.657 | 0.47 | 0.81 | 0.87 | 0.918 | 272.46 | 264.27 | 1.04 |
V1/1 | 0.939 | 0.10 | 0.94 | 0.79 | 0.820 | 67.96 | 67.98 | 1.00 |
V1/2 | 0.894 | 0.09 | 0.90 | 0.82 | 0.837 | 69.87 | 69.84 | 1.00 |
V1/3 | 0.963 | 0.10 | 0.97 | 0.77 | 0.992 | 79.08 | 80.93 | 0.97 |
V2/3 | 0.621 | 0.17 | 0.64 | 0.97 | 0.844 | 236.78 | 234.89 | 1.01 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
V-PILOTA | 0.939 | 0.52 | 1.07 | 0.71 | 1.284 | 76.65 | 82.73 | 0.94 |
V-PILOTB | 0.948 | 0.52 | 1.08 | 0.70 | 1.290 | 78.78 | 71.17 | 1.12 |
V121216A | 1.200 | 0.57 | 1.33 | 0.55 | 1.249 | 50.51 | 50.05 | 1.05 |
V121216B | 0.993 | 0.54 | 1.13 | 0.67 | 1.300 | 80.36 | 87.63 | 0.90 |
V181216B | 1.200 | 0.82 | 1.46 | 0.47 | 1.870 | 89.05 | 93.41 | 0.94 |
V181216C | 1.011 | 0.82 | 1.30 | 0.57 | 1.537 | 117.97 | 119.47 | 1.00 |
V181816A | 1.128 | 0.80 | 1.38 | 0.52 | 1.492 | 75.66 | 74.73 | 1.03 |
V181816B | 0.990 | 0.78 | 1.26 | 0.59 | 1.370 | 96.48 | 96.17 | 1.01 |
V241216A | 1.128 | 1.06 | 1.55 | 0.42 | 1.423 | 77.15 | 75.57 | 1.04 |
V241216B | 0.908 | 1.01 | 1.35 | 0.54 | 1.494 | 133.19 | 133.35 | 0.98 |
V121221A | 1.326 | 0.45 | 1.40 | 0.51 | 1.238 | 47.01 | 46.26 | 1.01 |
V121221B | 1.064 | 0.42 | 1.15 | 0.67 | 1.188 | 75.75 | 72.50 | 1.00 |
V122421A | 1.194 | 0.42 | 1.27 | 0.59 | 1.034 | 44.47 | 43.28 | 1.04 |
V122421B | 1.046 | 0.41 | 1.13 | 0.68 | 1.017 | 61.61 | 61.20 | 0.99 |
V181221A | 1.277 | 0.63 | 1.42 | 0.49 | 1.380 | 64.04 | 61.83 | 1.02 |
V181221B | 1.046 | 0.61 | 1.21 | 0.62 | 1.301 | 99.89 | 97.86 | 1.01 |
V181821A | 1.198 | 0.61 | 1.34 | 0.54 | 1.208 | 58.44 | 56.49 | 1.07 |
V181821B | 1.073 | 0.61 | 1.23 | 0.61 | 1.269 | 92.84 | 93.41 | 0.96 |
V241221A | 1.312 | 0.86 | 1.57 | 0.41 | 1.481 | 78.46 | 77.26 | 1.02 |
V241221B | 1.075 | 0.84 | 1.36 | 0.53 | 1.403 | 130.66 | 126.72 | 1.01 |
V121232A | 1.782 | 0.30 | 1.81 | 0.31 | 1.702 | 39.58 | 41.14 | 0.95 |
V121232B | 1.436 | 0.28 | 1.46 | 0.47 | 1.460 | 59.92 | 61.16 | 0.98 |
V121832A | 1.833 | 0.31 | 1.86 | 0.29 | 1.493 | 34.40 | 34.47 | 0.99 |
V121832B | 1.141 | 0.25 | 1.17 | 0.65 | 0.994 | 54.68 | 53.38 | 1.10 |
V122432A | 1.847 | 0.31 | 1.87 | 0.28 | 1.360 | 31.35 | 31.14 | 1.00 |
V122432B | 1.434 | 0.28 | 1.46 | 0.47 | 1.175 | 49.14 | 48.93 | 0.98 |
V181232A | 1.741 | 0.42 | 1.79 | 0.31 | 1.848 | 49.76 | 51.60 | 0.97 |
V181232B | 1.449 | 0.41 | 1.51 | 0.44 | 1.536 | 79.59 | 80.06 | 1.00 |
V181832A | 1.904 | 0.47 | 1.96 | 0.26 | 1.810 | 52.07 | 52.93 | 0.99 |
V181832B | 0.939 | 0.52 | 1.07 | 0.71 | 1.284 | 76.65 | 82.73 | 0.94 |
V241232A | 1.422 | 0.41 | 1.48 | 0.46 | 1.505 | 78.12 | 78.64 | 1.00 |
V241232B | 1.845 | 0.61 | 1.94 | 0.26 | 1.765 | 69.16 | 69.08 | 1.00 |
V121809A | 1.403 | 0.54 | 1.50 | 0.44 | 1.485 | 103.31 | 101.46 | 1.01 |
V121809C | 0.519 | 0.78 | 0.94 | 0.79 | 1.070 | 62.39 | 63.16 | 0.95 |
V122409A | 0.626 | 0.87 | 1.07 | 0.71 | 1.101 | 56.55 | 55.16 | 1.05 |
V122409C | 0.519 | 0.79 | 0.95 | 0.79 | 1.026 | 59.74 | 57.82 | 1.03 |
V181209A | 0.575 | 0.83 | 1.01 | 0.75 | 1.061 | 57.65 | 57.82 | 1.00 |
V181209C | 0.719 | 1.37 | 1.54 | 0.42 | 1.880 | 79.95 | 80.95 | 0.99 |
V181809A | 0.611 | 1.24 | 1.38 | 0.52 | 1.766 | 87.08 | 88.78 | 0.99 |
V181809C | 0.624 | 1.27 | 1.41 | 0.50 | 1.626 | 83.94 | 82.29 | 0.99 |
V241209A | 0.582 | 1.20 | 1.33 | 0.55 | 1.584 | 77.56 | 77.62 | 1.03 |
V241209C | 0.606 | 1.67 | 1.77 | 0.32 | 1.737 | 71.90 | 70.77 | 1.04 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
CW1 | 0.813 | 0.34 | 0.88 | 0.83 | 0.660 | 133.74 | 126.59 | 1.07 |
CW2 | 0.747 | 0.33 | 0.82 | 0.87 | 0.669 | 152.26 | 150.56 | 1.00 |
CW3 | 0.999 | 0.35 | 1.06 | 0.72 | 0.667 | 110.05 | 100.22 | 1.12 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
SP1 | 0.996 | 0.26 | 1.03 | 0.74 | 1.077 | 224.99 | 225.00 | 1.00 |
SP2 | 1.136 | 0.35 | 1.19 | 0.64 | 1.202 | 213.74 | 215.30 | 0.98 |
SP3 | 1.222 | 0.44 | 1.30 | 0.57 | 1.324 | 205.69 | 209.50 | 0.97 |
SP4 | 0.783 | 0.30 | 0.84 | 0.85 | 0.999 | 232.31 | 230.80 | 1.02 |
SP5 | 0.897 | 0.41 | 0.99 | 0.76 | 1.095 | 222.07 | 220.50 | 1.02 |
SP6 | 0.981 | 0.53 | 1.11 | 0.68 | 1.177 | 218.68 | 220.00 | 0.99 |
SP2-2-400 1 | 1.066 | 0.16 | 1.08 | 0.71 | 0.981 | 84.29 | 80.25 | 1.05 |
SP2-2-400 2 | 1.066 | 0.16 | 1.08 | 0.71 | 0.981 | 84.29 | 88.13 | 0.95 |
SP2-2-800 1 | 1.084 | 0.33 | 1.13 | 0.67 | 1.060 | 178.87 | 178.88 | 1.00 |
SP2-2-800 2 | 1.084 | 0.33 | 1.13 | 0.67 | 1.060 | 178.87 | 177.75 | 1.01 |
SP2-3-600 1 | 0.751 | 0.24 | 0.79 | 0.89 | 1.121 | 302.98 | 301.50 | 1.00 |
SP2-3-600 2 | 0.751 | 0.24 | 0.79 | 0.89 | 1.121 | 302.98 | 308.63 | 0.98 |
SP2-3-1200 1 | 0.751 | 0.47 | 0.89 | 0.82 | 1.221 | 614.51 | 611.25 | 1.01 |
SP2-3-1200 2 | 0.751 | 0.47 | 0.89 | 0.82 | 1.221 | 614.51 | 625.13 | 0.98 |
SP2-4-800 1 | 0.593 | 0.31 | 0.67 | 0.96 | 1.056 | 603.28 | 601.50 | 1.01 |
SP2-4-800 2 | 0.593 | 0.31 | 0.67 | 0.96 | 1.056 | 603.28 | 603.38 | 1.01 |
SP2-4-1600 1 | 0.595 | 0.62 | 0.86 | 0.84 | 1.197 | 1218.89 | 1215.38 | 1.00 |
SP2-4-1600 2 | 0.595 | 0.62 | 0.86 | 0.84 | 1.197 | 1218.89 | 1227.00 | 0.99 |
SP2-8-800 1 | 0.270 | 0.24 | 0.36 | 1.00 | 1.330 | 1332.58 | 1308.38 | 1.01 |
SP2-8-800 2 | 0.270 | 0.24 | 0.36 | 1.00 | 1.330 | 1332.58 | 1374.75 | 0.97 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
G7A | 0.834 | 0.37 | 0.91 | 0.81 | 1.084 | 2190.70 | 2299.82 | 0.92 |
G8A | 0.834 | 0.37 | 0.91 | 0.81 | 1.084 | 2190.70 | 2155.05 | 0.98 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
L1 | 1.146 | 0.22 | 1.17 | 0.65 | 1.097 | 743.50 | 745.62 | 1.00 |
L2 | 1.401 | 0.23 | 1.42 | 0.50 | 1.209 | 624.38 | 625.56 | 1.00 |
L3 | 1.146 | 0.63 | 1.31 | 0.57 | 0.921 | 540.06 | 532.02 | 1.02 |
L4 | 1.401 | 0.56 | 1.51 | 0.44 | 1.052 | 480.55 | 474.73 | 1.01 |
I1 | 0.815 | 0.86 | 1.18 | 0.64 | 1.463 | 1302.50 | 1313.50 | 0.99 |
I2 | 1.126 | 1.26 | 1.69 | 0.35 | 1.475 | 565.15 | 565.66 | 1.00 |
G1 | 0.509 | 0.91 | 1.04 | 0.73 | 1.077 | 1087.70 | 1095.96 | 0.99 |
G2 | 0.515 | 1.14 | 1.25 | 0.60 | 1.392 | 916.69 | 912.94 | 1.01 |
G3 | 0.515 | 1.39 | 1.48 | 0.46 | 1.759 | 888.05 | 929.62 | 0.94 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
PG2 | 0.831 | 0.85 | 1.19 | 0.64 | 0.998 | 869.56 | 873.60 | 0.99 |
PG1 | 0.732 | 0.87 | 1.13 | 0.67 | 0.946 | 864.75 | 843.20 | 1.03 |
PG3 | 0.732 | 0.73 | 1.03 | 0.74 | 1.053 | 1052.21 | 1052.80 | 1.01 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
TP20-300-30 | 0.395 | 0.38 | 0.55 | 1.00 | 0.833 | 84.89 | 84.72 | 1.00 |
A20-410-30-N | 0.263 | 0.45 | 0.52 | 1.00 | 0.899 | 122.74 | 125.09 | 0.99 |
A20-410-45-N | 0.263 | 0.34 | 0.43 | 1.00 | 0.857 | 118.28 | 116.46 | 1.01 |
A20-505-30-N | 0.263 | 0.56 | 0.62 | 0.99 | 0.915 | 153.69 | 154.23 | 0.99 |
A20-505-45-N | 0.263 | 0.42 | 0.50 | 1.00 | 0.895 | 152.72 | 152.49 | 0.99 |
B20-305-30 | 0.403 | 0.51 | 0.65 | 0.97 | 1.006 | 233.51 | 233.20 | 1.00 |
B20-305-45 | 0.403 | 0.39 | 0.56 | 1.00 | 1.044 | 248.99 | 251.72 | 0.99 |
B20-505-45 | 0.403 | 0.64 | 0.76 | 0.90 | 0.976 | 335.82 | 329.34 | 1.06 |
B20-505-45-N | 0.263 | 0.42 | 0.50 | 1.00 | 0.852 | 150.59 | 150.43 | 0.96 |
Scheme 1. | λL | λG | λI,1 | ρ e | ζ | V (kN) | VT (kN) | V/VT |
---|---|---|---|---|---|---|---|---|
W1 | 0.567 | 0.66 | 0.87 | 0.83 | 0.858 | 587.62 | 567.00 | 1.05 |
SC1 | 0.798 | 0.36 | 0.88 | 0.83 | 1.088 | 2127.47 | 2007.53 | 1.14 |
V1b | 0.314 | 0.24 | 0.39 | 1.00 | 1.028 | 200.94 | 206.50 | 0.97 |
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Specimen ID | hw (mm) | a (mm) | tw (mm) | Corrugation Dimensions (mm) | Fyw MPa | Web Slenderness | Variables | ||
---|---|---|---|---|---|---|---|---|---|
b | hr | d | |||||||
3PCW350 | 384 | 900 | 2.80 | 350 | 100 | 100 | 325 | 137.14 | b, Load |
4PCW275 | 384 | 750 | 3.00 | 275 | 100 | 100 | 357 | 128.00 | a,tw, Fyw |
3PCW200 | 384 | 900 | 2.80 | 200 | 100 | 100 | 325 | 137.14 | b, Load |
ORLTs | Optimal Parameters |
---|---|
DT | Minimum leaf size: 12 |
SVM | Box constraints: 992.584 Epsilon: 0.00031804 Kernel function: Linear Standardised data: False |
GPR | Sigma: 0.16623 Basis function: Zero Kernel function: Isotropic exponential Kernel scale: 0.66404 Standardised data: True |
EN | Ensemble method: Bag Number of learners: 57 Minimum leaf size: 2 Number of predictors to samples: 8 |
Evaluation Techniques | DT | SVM | GPR | EN | ANN |
---|---|---|---|---|---|
MSE | 0.04212 | 0.03962 | 0.00074 | 0.00391 | 0.01088 |
RMSE | 0.20522 | 0.19906 | 0.02723 | 0.06253 | 0.10432 |
Number of Test Data | Mean | Std. Dev. | Co. Var. | Max. | Min. |
---|---|---|---|---|---|
116 | 1.0018 | 0.021 | 0.021 | 1.10 | 0.926 |
76 out of 116 (65%) | 0.987 | 0.015 | 0.015 | 1.015 | 0.986 |
38 out of 116 (32%) | 1.0033 | 0.029 | 0.028 | 1.055 | 0.955 |
3 out of 116 (3%) | 1.0185 | 0.071 | 0.07 | 1.10 | 0.926 |
Specimen ID | hw | a | tw | Corrugation Dimensions | Fyw | Web Slenderness | ||
---|---|---|---|---|---|---|---|---|
b | hr | d | ||||||
Moussa et al. [32] | ||||||||
A12-305-30 | 305 | 557.0 | 1.20 | 40 | 20.00 | 34.64 | 230 | 254.17 |
A12-410-30 | 410 | 557.0 | 1.20 | 40 | 20.00 | 34.64 | 230 | 341.67 |
A12-505-30 | 505 | 557.0 | 1.20 | 40 | 20.00 | 34.64 | 230 | 420.83 |
A12-505-45 | 505 | 526.5 | 1.20 | 40 | 28.28 | 28.28 | 230 | 420.83 |
Nie et al. [33] | ||||||||
S2-1 | 260 | 1200 | 0.90 | 80 | 48 | 64 | 385.50 | 288.89 |
S2-2 | 360 | 1200 | 0.90 | 80 | 48 | 64 | 385.50 | 400.00 |
Specimen ID | λL | λG | λI,1 | ρ e | ζ | Vn (kN) | VT (kN) | Vn/VT |
---|---|---|---|---|---|---|---|---|
Moussa et al. [32] | ||||||||
A12-305-30 | 0.391 | 0.34 | 0.52 | 1.00 | 0.94 | 45.60 | 49.8 | 0.92 |
A12-410-30 | 0.391 | 0.46 | 0.60 | 1.00 | 0.98 | 64.21 | 66.3 | 0.97 |
A12-505-30 | 0.391 | 0.56 | 0.69 | 0.95 | 1.03 | 78.46 | 72 | 1.09 |
A12-505-45 | 0.391 | 0.43 | 0.58 | 1.00 | 1.03 | 82.99 | 89.1 | 0.93 |
Nie et al. [33] | ||||||||
S2-1 | 1.349 | 0.21 | 1.37 | 0.53 | 0.90 | 24.88 | 25.24 | 0.99 |
S2-2 | 1.349 | 0.29 | 1.38 | 0.52 | 0.97 | 36.58 | 39.31 | 0.93 |
Authors | ||||||||
3PCW350 | 1.74 | 0.16 | 1.75 | 0.327 | 1.56 | 102.94 | 105.00 | 0.98 |
4PCW275 | 1.339 | 0.15 | 1.35 | 0.54 | 1.16 | 149.36 | 147.50 | 1.01 |
3PCW200 | 0.995 | 0.13 | 1.00 | 0.752 | 0.80 | 121.45 | 117.50 | 1.03 |
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Elamary, A.S.; Taha, I.B.M. Determining the Shear Capacity of Steel Beams with Corrugated Webs by Using Optimised Regression Learner Techniques. Materials 2021, 14, 2364. https://doi.org/10.3390/ma14092364
Elamary AS, Taha IBM. Determining the Shear Capacity of Steel Beams with Corrugated Webs by Using Optimised Regression Learner Techniques. Materials. 2021; 14(9):2364. https://doi.org/10.3390/ma14092364
Chicago/Turabian StyleElamary, Ahmed S., and Ibrahim B. M. Taha. 2021. "Determining the Shear Capacity of Steel Beams with Corrugated Webs by Using Optimised Regression Learner Techniques" Materials 14, no. 9: 2364. https://doi.org/10.3390/ma14092364