Abstract
The steel oval hollow section (OHS) provides an aesthetic architecture and a greater local buckling strength. However, the existing design codes do not specify the effective width in calculating the load-bearing capacity of OHS members. This study aims to predict the axial compression capacity (ACC) of cold-formed steel OHS columns using artificial neural network (ANN) and adaptive neural fuzzy inference system (ANFIS) models. A total of 128 data sets collected from the literature were utilized to develop the ANN and ANFIS models. The performance of the two machine learning models was compared with three existing design codes. The results demonstrated that the developed ANN and ANFIS models predicted the ACC of steel OHS columns more accurately compared to the existing formulas. Specifically, the ANN model revealed a superior performance with the highest coefficient of determination and the smallest root means square errors. Moreover, the formulas based on ANN and ANFIS models, which accommodates all input parameters, were proposed to predict the ACC of cold-formed steel OHS columns. The thickness of the cross-section was the most influential parameter on the ACC of the OHS column. By contrast, the column length negatively affected the ACC value of the steel column. Finally, a graphical user interface tool was developed to readily calculate the ACC of the steel OHS columns.
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Appendix: Database used in developing ANN and ANFIS models
Appendix: Database used in developing ANN and ANFIS models
\(D\) (mm) | \(W\) (mm) | \(t\) (mm) | \(h/t\) | \(L\) (mm) | \(E\) (MPa) | \(\sigma_{u}\) (MPa) | \(\varepsilon_{f}\) (%) | \(\sigma_{0.2}\) (MPa) | \(P_{Test}\) (kN) |
|---|---|---|---|---|---|---|---|---|---|
120 | 48 | 2 | 36 | 360 | 202 | 403 | 18 | 359 | 181.2 |
120 | 48 | 2 | 36 | 360 | 202 | 403 | 18 | 359 | 185.9 |
120 | 48 | 2 | 36 | 600 | 202 | 403 | 18 | 359 | 196 |
120 | 48 | 2 | 36 | 1200 | 202 | 403 | 18 | 359 | 190.3 |
120 | 48 | 2 | 36 | 1200 | 202 | 403 | 18 | 359 | 188.5 |
120 | 48 | 2 | 36 | 1800 | 202 | 403 | 18 | 359 | 183.9 |
120 | 48 | 2 | 36 | 2400 | 202 | 403 | 18 | 359 | 173.1 |
120 | 48 | 2 | 36 | 3000 | 202 | 403 | 18 | 359 | 157.7 |
42 | 21 | 2.8 | 7.5 | 126 | 200 | 456 | 20 | 443 | 144.1 |
42 | 21 | 2.8 | 7.5 | 300 | 200 | 456 | 20 | 443 | 122.3 |
42 | 21 | 2.8 | 7.5 | 600 | 200 | 456 | 20 | 443 | 111 |
42 | 21 | 2.8 | 7.5 | 900 | 200 | 456 | 20 | 443 | 96.8 |
42 | 21 | 2.8 | 7.5 | 900 | 200 | 456 | 20 | 443 | 92.8 |
42 | 21 | 2.8 | 7.5 | 1200 | 200 | 456 | 20 | 443 | 64.6 |
42 | 21 | 2.8 | 7.5 | 1500 | 200 | 456 | 20 | 443 | 51.5 |
115 | 38 | 2 | 38.5 | 345 | 202 | 387 | 27 | 359 | 163.3 |
115 | 38 | 2 | 38.5 | 600 | 202 | 387 | 27 | 359 | 156.2 |
115 | 38 | 2 | 38.5 | 1200 | 202 | 387 | 27 | 359 | 146.6 |
115 | 38 | 2 | 38.5 | 1800 | 202 | 387 | 27 | 359 | 131.6 |
115 | 38 | 2 | 38.5 | 2400 | 202 | 387 | 27 | 359 | 118.8 |
115 | 38 | 2 | 38.5 | 3000 | 202 | 387 | 27 | 359 | 103.5 |
30 | 15 | 1.6 | 9.4 | 90 | 199 | 454 | 21 | 432 | 58.4 |
30 | 15 | 1.6 | 9.4 | 300 | 199 | 454 | 21 | 432 | 51.1 |
30 | 15 | 1.6 | 9.4 | 600 | 199 | 454 | 21 | 432 | 38.9 |
30 | 15 | 1.6 | 9.4 | 900 | 199 | 454 | 21 | 432 | 30.4 |
30 | 15 | 1.6 | 9.4 | 900 | 199 | 454 | 21 | 432 | 28.4 |
30 | 15 | 1.6 | 9.4 | 1200 | 199 | 454 | 21 | 432 | 19 |
30 | 15 | 1.6 | 9.4 | 1500 | 199 | 454 | 21 | 432 | 12.7 |
300 | 60 | 2 | 120 | 500 | 202 | 387 | 27 | 359 | 223.4 |
300 | 60 | 2 | 120 | 1200 | 202 | 387 | 27 | 359 | 205 |
300 | 60 | 2 | 120 | 2000 | 202 | 387 | 27 | 359 | 202.3 |
300 | 60 | 2 | 120 | 2700 | 202 | 387 | 27 | 359 | 178.3 |
300 | 60 | 2 | 120 | 3500 | 202 | 387 | 27 | 359 | 171.7 |
300 | 60 | 2.4 | 100 | 500 | 202 | 387 | 27 | 359 | 299.9 |
300 | 60 | 2.4 | 100 | 1200 | 202 | 387 | 27 | 359 | 273.3 |
300 | 60 | 2.4 | 100 | 2000 | 202 | 387 | 27 | 359 | 267.1 |
300 | 60 | 2.4 | 100 | 2700 | 202 | 387 | 27 | 359 | 237.7 |
300 | 60 | 2.4 | 100 | 3500 | 202 | 387 | 27 | 359 | 227.3 |
300 | 60 | 3 | 80 | 500 | 202 | 387 | 27 | 359 | 429.4 |
300 | 60 | 3 | 80 | 1200 | 202 | 387 | 27 | 359 | 395.9 |
300 | 60 | 3 | 80 | 2000 | 202 | 387 | 27 | 359 | 380.7 |
300 | 60 | 3 | 80 | 2700 | 202 | 387 | 27 | 359 | 355.7 |
300 | 60 | 3 | 80 | 3500 | 202 | 387 | 27 | 359 | 326.5 |
300 | 60 | 4 | 60 | 500 | 202 | 387 | 27 | 359 | 700.6 |
300 | 60 | 4 | 60 | 1200 | 202 | 387 | 27 | 359 | 658.5 |
300 | 60 | 4 | 60 | 2000 | 202 | 387 | 27 | 359 | 626.3 |
300 | 60 | 4 | 60 | 2700 | 202 | 387 | 27 | 359 | 598.5 |
300 | 60 | 4 | 60 | 3500 | 202 | 387 | 27 | 359 | 562.8 |
300 | 60 | 10 | 24 | 500 | 202 | 387 | 27 | 359 | 2350.6 |
300 | 60 | 10 | 24 | 1200 | 202 | 387 | 27 | 359 | 2279.6 |
300 | 60 | 10 | 24 | 2000 | 202 | 387 | 27 | 359 | 2133.6 |
300 | 60 | 10 | 24 | 2700 | 202 | 387 | 27 | 359 | 1994.4 |
300 | 60 | 10 | 24 | 3500 | 202 | 387 | 27 | 359 | 1826.2 |
300 | 75 | 1.9 | 118.4 | 500 | 202 | 387 | 27 | 359 | 237.5 |
300 | 75 | 1.9 | 118.4 | 1200 | 202 | 387 | 27 | 359 | 231.1 |
300 | 75 | 1.9 | 118.4 | 2000 | 202 | 387 | 27 | 359 | 220.6 |
300 | 75 | 1.9 | 118.4 | 2700 | 202 | 387 | 27 | 359 | 212.8 |
300 | 75 | 1.9 | 118.4 | 3500 | 202 | 387 | 27 | 359 | 182.1 |
300 | 75 | 2.2 | 102.3 | 500 | 202 | 387 | 27 | 359 | 286 |
300 | 75 | 2.2 | 102.3 | 1200 | 202 | 387 | 27 | 359 | 284.8 |
300 | 75 | 2.2 | 102.3 | 2000 | 202 | 387 | 27 | 359 | 266.2 |
300 | 75 | 2.2 | 102.3 | 2700 | 202 | 387 | 27 | 359 | 263.1 |
300 | 75 | 2.2 | 102.3 | 3500 | 202 | 387 | 27 | 359 | 245.7 |
300 | 75 | 2.8 | 80.4 | 500 | 202 | 387 | 27 | 359 | 415.5 |
300 | 75 | 2.8 | 80.4 | 1200 | 202 | 387 | 27 | 359 | 406.2 |
300 | 75 | 2.8 | 80.4 | 2000 | 202 | 387 | 27 | 359 | 387.8 |
300 | 75 | 2.8 | 80.4 | 2700 | 202 | 387 | 27 | 359 | 373.2 |
300 | 75 | 2.8 | 80.4 | 3500 | 202 | 387 | 27 | 359 | 348.9 |
300 | 75 | 3.8 | 59.2 | 500 | 202 | 387 | 27 | 359 | 678.9 |
300 | 75 | 3.8 | 59.2 | 1200 | 202 | 387 | 27 | 359 | 648.1 |
300 | 75 | 3.8 | 59.2 | 2000 | 202 | 387 | 27 | 359 | 621.9 |
300 | 75 | 3.8 | 59.2 | 2700 | 202 | 387 | 27 | 359 | 603.4 |
300 | 75 | 3.8 | 59.2 | 3500 | 202 | 387 | 27 | 359 | 579.7 |
300 | 75 | 10 | 22.5 | 500 | 202 | 387 | 27 | 359 | 2433.9 |
300 | 75 | 10 | 22.5 | 1200 | 202 | 387 | 27 | 359 | 2380.1 |
300 | 75 | 10 | 22.5 | 2000 | 202 | 387 | 27 | 359 | 2266.4 |
300 | 75 | 10 | 22.5 | 2700 | 202 | 387 | 27 | 359 | 2147.8 |
300 | 75 | 10 | 22.5 | 3500 | 202 | 387 | 27 | 359 | 2016.8 |
300 | 100 | 1.7 | 117.6 | 500 | 202 | 387 | 27 | 359 | 228.3 |
300 | 100 | 1.7 | 117.6 | 1200 | 202 | 387 | 27 | 359 | 226.3 |
300 | 100 | 1.7 | 117.6 | 2000 | 202 | 387 | 27 | 359 | 222.4 |
300 | 100 | 1.7 | 117.6 | 2700 | 202 | 387 | 27 | 359 | 216.8 |
300 | 100 | 1.7 | 117.6 | 3500 | 202 | 387 | 27 | 359 | 208.8 |
300 | 100 | 2 | 100 | 500 | 202 | 387 | 27 | 359 | 283.7 |
300 | 100 | 2 | 100 | 1200 | 202 | 387 | 27 | 359 | 282.4 |
300 | 100 | 2 | 100 | 2000 | 202 | 387 | 27 | 359 | 278.1 |
300 | 100 | 2 | 100 | 2700 | 202 | 387 | 27 | 359 | 271.8 |
300 | 100 | 2 | 100 | 3500 | 202 | 387 | 27 | 359 | 261.3 |
300 | 100 | 2.5 | 80 | 500 | 202 | 387 | 27 | 359 | 385.9 |
300 | 100 | 2.5 | 80 | 1200 | 202 | 387 | 27 | 359 | 384.1 |
300 | 100 | 2.5 | 80 | 2000 | 202 | 387 | 27 | 359 | 376.7 |
300 | 100 | 2.5 | 80 | 2700 | 202 | 387 | 27 | 359 | 369.5 |
300 | 100 | 2.5 | 80 | 3500 | 202 | 387 | 27 | 359 | 356.4 |
300 | 100 | 3.3 | 60.6 | 500 | 202 | 387 | 27 | 359 | 578 |
300 | 100 | 3.3 | 60.6 | 1200 | 202 | 387 | 27 | 359 | 574 |
300 | 100 | 3.3 | 60.6 | 2000 | 202 | 387 | 27 | 359 | 560.6 |
300 | 100 | 3.3 | 60.6 | 2700 | 202 | 387 | 27 | 359 | 550.9 |
300 | 100 | 3.3 | 60.6 | 3500 | 202 | 387 | 27 | 359 | 535.7 |
300 | 100 | 10 | 20 | 500 | 202 | 387 | 27 | 359 | 2514.8 |
300 | 100 | 10 | 20 | 1200 | 202 | 387 | 27 | 359 | 2487.9 |
300 | 100 | 10 | 20 | 2000 | 202 | 387 | 27 | 359 | 2422.6 |
300 | 100 | 10 | 20 | 2700 | 202 | 387 | 27 | 359 | 2338.4 |
300 | 100 | 10 | 20 | 3500 | 202 | 387 | 27 | 359 | 2234 |
300 | 150 | 1.3 | 115.4 | 500 | 202 | 387 | 27 | 359 | 211.5 |
300 | 150 | 1.3 | 115.4 | 1200 | 202 | 387 | 27 | 359 | 208.5 |
300 | 150 | 1.3 | 115.4 | 2000 | 202 | 387 | 27 | 359 | 206.6 |
300 | 150 | 1.3 | 115.4 | 2700 | 202 | 387 | 27 | 359 | 204.3 |
300 | 150 | 1.3 | 115.4 | 3500 | 202 | 387 | 27 | 359 | 203.5 |
300 | 150 | 1.5 | 100 | 500 | 202 | 387 | 27 | 359 | 255.9 |
300 | 150 | 1.5 | 100 | 1200 | 202 | 387 | 27 | 359 | 253.3 |
300 | 150 | 1.5 | 100 | 2000 | 202 | 387 | 27 | 359 | 252.1 |
300 | 150 | 1.5 | 100 | 2700 | 202 | 387 | 27 | 359 | 249.4 |
300 | 150 | 1.5 | 100 | 3500 | 202 | 387 | 27 | 359 | 240 |
300 | 150 | 1.8 | 83.3 | 500 | 202 | 387 | 27 | 359 | 325.3 |
300 | 150 | 1.8 | 83.3 | 1200 | 202 | 387 | 27 | 359 | 322.7 |
300 | 150 | 1.8 | 83.3 | 2000 | 202 | 387 | 27 | 359 | 318 |
300 | 150 | 1.8 | 83.3 | 2700 | 202 | 387 | 27 | 359 | 313.9 |
300 | 150 | 1.8 | 83.3 | 3500 | 202 | 387 | 27 | 359 | 307.8 |
300 | 150 | 2.5 | 60 | 500 | 202 | 387 | 27 | 359 | 499.5 |
300 | 150 | 2.5 | 60 | 1200 | 202 | 387 | 27 | 359 | 482.1 |
300 | 150 | 2.5 | 60 | 2000 | 202 | 387 | 27 | 359 | 479.5 |
300 | 150 | 2.5 | 60 | 2700 | 202 | 387 | 27 | 359 | 473.5 |
300 | 150 | 2.5 | 60 | 3500 | 202 | 387 | 27 | 359 | 466.8 |
300 | 150 | 10 | 15 | 500 | 202 | 387 | 27 | 359 | 2788.1 |
300 | 150 | 10 | 15 | 1200 | 202 | 387 | 27 | 359 | 2755.4 |
300 | 150 | 10 | 15 | 2000 | 202 | 387 | 27 | 359 | 2694.9 |
300 | 150 | 10 | 15 | 2700 | 202 | 387 | 27 | 359 | 2638.7 |
300 | 150 | 10 | 15 | 3500 | 202 | 387 | 27 | 359 | 2566.9 |
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Nguyen, TH., Tran, NL. & Nguyen, DD. Prediction of Axial Compression Capacity of Cold-Formed Steel Oval Hollow Section Columns Using ANN and ANFIS Models. Int J Steel Struct 22, 1–26 (2022). https://doi.org/10.1007/s13296-021-00557-z
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DOI: https://doi.org/10.1007/s13296-021-00557-z