Neural network models for the critical bending moment of uniform and tapered beams

Abstract

Most design standards require the calculation of the elastic critical bending moment for the design and verification of steel beams. Formulae exists for uniform beams with double or mono-symmetric cross-sections but, for tapered beams, simple design formulae are yet to be developed because of the complexity associated with the non-uniform geometry of these members.This work proposes a neural network model to calculate the critical moment. The model is developed using the Backpropagation and Levenberg–Marquardt algorithms and considering 60549 data samples for training and 8526 samples for validation. The samples are generated by a numerical model using the Finite Element Method (FEM). An innovative methodology to reduce the number of samples necessary to train the model is implemented based on the concept of random sample generation with constrained geometric proportions.The accuracy of the developed model is further illustrated on some particular cases and against the FEM results of other authors. For the uniform beams, the results of the proposed model are compared against those from existing formulae for uniform members showing its improved accuracy.Finally, it is expected that this investigation demonstrates the benefits of the use of neural networks based solutions as fast assessment tools during the search of optimal structural solutions in the early design stages.