Abstract
The rack column is one of the essential elements in the pallet rack system. However, due to its distinctive perforation feature, it is challenging to analyze its stability using traditional theories for cold-formed steel structures. In this paper, we are interested in the comparison analysis of strength prediction on the perforated columns using finite element method (FEM), regression analysis (RA) and artificial neural network (ANN) methods respectively. First, a refined finite element (FE) model considering the perforation and nonlinearity behavior was generated and calibrated against the experimental results. Subsequently, the validated FE model was used to perform the parametric analysis for the different holes in columns. Given experimental and simulated data, a regression model with an equivalent thickness was proposed for the design strength prediction of thin-walled steel perforated sections. For comparison of the RA model, two powerful tools such as the FEM and ANN are also employed to predict the design strength of different perforated sections. Four indicators were used to assess the accuracy and generalization performance of the three models, including the root mean square error, the mean absolute percentage error, the correlation coefficient and the mean relative percentage. The obtained results show that although they both have good consistency, FEM still slightly outperforms the other two models. Since the values calculated from ANN and regression models are usually smaller than the experimental data, they are reasonably recommended as effective and safer design tools than FEM models from the perspective of engineering applications.
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Acknowledgements
The writers gratefully acknowledge the financial support provided by National Key R&D Program of China (2017YFB1304000), Shanghai Sailing Program (19YF1401600), Research Program of Shanghai Science and Technology Committee (17DZ2283800).
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Appendix
Appendix
Column type | Parameter | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
WW (mm) | CT (mm) | FW (mm) | OS (mm) | CL (mm) | RHA (%) | BN | RAN | RN | DSC (MPa) | |
M45-1.5 | 45 | 1.5 | 45 | 25 | 300 | 18.205 | 8 | 4 | 0 | 225.24 |
M45-1.5 | 45 | 1.5 | 45 | 25 | 300 | 16.472 | 8 | 4 | 0 | 228.85 |
M45-1.5 | 45 | 1.5 | 45 | 25 | 300 | 15.605 | 8 | 4 | 0 | 229.27 |
M60-1.8 | 60 | 1.8 | 55 | 34 | 350 | 16.525 | 8 | 4 | 0 | 300.16 |
M60-1.8 | 60 | 1.8 | 55 | 34 | 350 | 14.951 | 8 | 4 | 0 | 303.07 |
M60-1.8 | 60 | 1.8 | 55 | 34 | 350 | 14.164 | 8 | 4 | 0 | 303.89 |
M60-2 | 60 | 2.0 | 55 | 34 | 350 | 16.525 | 8 | 4 | 0 | 316.94 |
M60-2 | 60 | 2.0 | 55 | 34 | 350 | 14.951 | 8 | 4 | 0 | 315.39 |
M60-2 | 60 | 2.0 | 55 | 34 | 350 | 14.164 | 8 | 4 | 0 | 316.6 |
M75-1.8 | 75 | 1.8 | 58 | 45 | 400 | 14.222 | 12 | 4 | 1 | 302.28 |
M75-1.8 | 75 | 1.8 | 58 | 45 | 400 | 12.868 | 12 | 4 | 1 | 312.62 |
M75-1.8 | 75 | 1.8 | 58 | 45 | 400 | 12.190 | 12 | 4 | 1 | 313.68 |
M75-2 | 75 | 2.0 | 58 | 45 | 400 | 14.222 | 12 | 4 | 1 | 317.84 |
M75-2 | 75 | 2.0 | 58 | 45 | 400 | 12.868 | 12 | 4 | 1 | 322.13 |
M75-2 | 75 | 2.0 | 58 | 45 | 400 | 12.190 | 12 | 4 | 1 | 323.76 |
M90A-1.8 | 90 | 1.8 | 65 | 50 | 400 | 11.852 | 12 | 4 | 1 | 289.59 |
M90A-1.8 | 90 | 1.8 | 65 | 50 | 400 | 10.723 | 12 | 4 | 1 | 292.44 |
M90A-1.8 | 90 | 1.8 | 65 | 50 | 400 | 10.159 | 12 | 4 | 1 | 294.01 |
M90A-2 | 90 | 2.0 | 65 | 50 | 400 | 11.287 | 12 | 4 | 1 | 276.06 |
M90A-2 | 90 | 2.0 | 65 | 50 | 400 | 11.852 | 12 | 4 | 1 | 275.33 |
M90A-2 | 90 | 2.0 | 65 | 50 | 400 | 10.723 | 12 | 4 | 1 | 277.98 |
M90A-2 | 90 | 1.8 | 78 | 50 | 400 | 11.287 | 12 | 4 | 1 | 282.89 |
M90B-1.8 | 90 | 1.8 | 78 | 50 | 400 | 11.852 | 12 | 4 | 1 | 274.31 |
M90B-1.8 | 90 | 1.8 | 78 | 50 | 400 | 10.723 | 12 | 4 | 1 | 282.59 |
M90B-1.8 | 90 | 1.8 | 78 | 50 | 400 | 10.159 | 12 | 4 | 1 | 283.99 |
M90B-1.8 | 90 | 2.0 | 78 | 50 | 400 | 11.287 | 12 | 4 | 1 | 282.54 |
M90B-2 | 90 | 2.0 | 78 | 50 | 400 | 11.852 | 12 | 4 | 1 | 273.19 |
M90B-2 | 90 | 2.0 | 78 | 50 | 400 | 10.723 | 12 | 4 | 1 | 275.43 |
M90B-2 | 90 | 2.0 | 78 | 50 | 400 | 10.159 | 12 | 4 | 1 | 276.71 |
M100A-2 | 100 | 2.0 | 90 | 52 | 400 | 10.667 | 20 | 4 | 3 | 279.81 |
M100A-2 | 100 | 2.0 | 90 | 52 | 400 | 9.651 | 20 | 4 | 3 | 289.77 |
M100A-2 | 100 | 2.0 | 90 | 52 | 400 | 9.143 | 20 | 4 | 3 | 290.68 |
M100A-2.5 | 100 | 2.5 | 90 | 52 | 400 | 10.667 | 20 | 4 | 3 | 251.97 |
M100A-2.5 | 100 | 2.5 | 90 | 52 | 400 | 9.651 | 20 | 4 | 3 | 254.15 |
M100A-2.5 | 100 | 2.5 | 90 | 52 | 400 | 9.143 | 20 | 4 | 3 | 255.42 |
M100A-2.5 | 100 | 2.0 | 100 | 52 | 400 | 10.159 | 12 | 4 | 1 | 260.49 |
M100B-2 | 100 | 2.0 | 100 | 52 | 400 | 10.667 | 12 | 4 | 1 | 236.7 |
M100B-2 | 100 | 2.0 | 100 | 52 | 400 | 9.651 | 12 | 4 | 1 | 238.26 |
M100B-2 | 100 | 2.0 | 100 | 52 | 400 | 9.143 | 12 | 4 | 1 | 239.85 |
M100B-2 | 100 | 2.5 | 100 | 52 | 400 | 10.159 | 12 | 4 | 1 | 249.98 |
M100B-2.5 | 100 | 2.5 | 100 | 52 | 400 | 10.667 | 12 | 4 | 1 | 255.99 |
M100B-2.5 | 100 | 2.5 | 100 | 52 | 400 | 9.651 | 12 | 4 | 1 | 256.78 |
M100B-2.5 | 100 | 2.5 | 100 | 52 | 400 | 9.143 | 12 | 4 | 1 | 259.57 |
M100C-2 | 100 | 2.0 | 130 | 52 | 500 | 10.159 | 20 | 4 | 3 | 236.12 |
M100C-2 | 100 | 2.0 | 130 | 52 | 500 | 10.667 | 20 | 4 | 3 | 234.98 |
M100C-2 | 100 | 2.0 | 130 | 52 | 500 | 9.651 | 20 | 4 | 3 | 237.25 |
M100C-2 | 100 | 2.0 | 130 | 52 | 500 | 9.143 | 20 | 4 | 3 | 235.52 |
M100C-3 | 100 | 3.0 | 130 | 52 | 500 | 10.667 | 20 | 4 | 3 | 281.78 |
M100C-3.5 | 100 | 3.0 | 130 | 52 | 500 | 9.651 | 20 | 4 | 3 | 304.92 |
M100C-3.5 | 100 | 3.0 | 130 | 52 | 500 | 9.143 | 20 | 4 | 3 | 305.71 |
M120-2.5 | 120 | 2.5 | 95 | 76 | 500 | 8.466 | 12 | 4 | 1 | 274.23 |
M120-2.5 | 120 | 2.5 | 95 | 76 | 500 | 8.042 | 12 | 4 | 1 | 275.73 |
M120-2.5 | 120 | 2.5 | 95 | 76 | 500 | 7.619 | 12 | 4 | 1 | 276.97 |
M120-3 | 120 | 3.0 | 95 | 76 | 500 | 8.466 | 12 | 4 | 1 | 257.01 |
M120-3 | 120 | 3.0 | 95 | 76 | 500 | 8.889 | 12 | 4 | 1 | 256.75 |
M120-3 | 120 | 3.0 | 95 | 76 | 500 | 8.042 | 12 | 4 | 1 | 259.56 |
M120-3 | 120 | 3.0 | 95 | 76 | 500 | 7.619 | 12 | 4 | 1 | 262.63 |
M120-3.5 | 120 | 3.5 | 150 | 76 | 500 | 8.889 | 20 | 4 | 3 | 264.12 |
M120-3.5 | 120 | 3.5 | 150 | 76 | 500 | 8.042 | 20 | 4 | 3 | 267.17 |
M120-3.5 | 120 | 3.5 | 150 | 76 | 500 | 7.619 | 20 | 4 | 3 | 268.12 |
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Lyu, Z., Zhang, J., Zhao, N. et al. A Comparative Study on the Performance of FEM, RA and ANN Methods in Strength Prediction of Pallet-Rack Stub Columns. Int J Steel Struct 20, 1509–1526 (2020). https://doi.org/10.1007/s13296-020-00386-6
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DOI: https://doi.org/10.1007/s13296-020-00386-6