Neural networks for modelling ultimate pure bending of steel circular tubes

The behaviour of steel circular tubes under pure bending is complex and highly nonlinear. The literature has a number of solutions to predict the response of steel circular tubes under pure bending; however, most of these solutions are complicated and difficult to use in routine design practice. In this paper, the feasibility of using artificial neural networks (ANNs) for developing more accurate and simple-to-use models for predicting the ultimate pure bending of steel circular tubes is investigated. The data used to calibrate and validate the ANN models are obtained from the literature and comprise a series of 49 pure bending tests conducted on fabricated steel circular tubes and 55 tests carried out on cold-formed tubes. Multilayer feed-forward neural networks that are trained with the back-propagation algorithm are constructed using four design parameters (i.e. tube thickness, tube diameter, yield strength of steel and modulus of elasticity of steel) as network inputs and the ultimate pure bending as the only output. A sensitivity analysis is conducted on the ANN models to investigate the generalization ability (robustness) of the developed models, and predictions from the ANN models are compared with those obtained from most available codes and standards. To facilitate the use of the developed ANN models, they are translated into design equations suitable for spreadsheet programming or hand calculations. The results indicate that ANNs are capable of predicting the ultimate bending capacity of steel circular tubes with a high degree of accuracy, and outperform most available codes and standards.