Keywords: patch load, steel structures, neural network, parametric analysis, web buckling, web crippling.

The structural optimum design involves, for economic reasons, the minimum amount of material necessary to ensure the required resistance and stiffness to the structure provided that an adequate safety is guaranteed. This fact implies that the design equations must properly consider the uncertainties related to the problem. This is done by using proper-calibrated design factors. On the other hand, as the problem knowledge increases, less severe safety margins can be used.

Patch load actions on steel girders are frequently encountered in civil engineering practice. This type of loading can be found in crane girders; secondary beams reactions acting over the primary girder system and other structural problems. When the location of the concentrated load is previously known, transversal web stiffeners can be used at this point to provide the necessary resistance. The extra work related to the stiffener use tends to make this solution uneconomic. In the case of moving loads, where the exact position of the concentrated load is not known in advance, it is necessary to evaluate the ultimate resistance of unstiffened webs.

This work presents the application of Neural Networks algorithms to forecast the ultimate resistance of steel beams subjected to concentrated loads. A single design formula for this structural engineering problem is very difficult to be obtained, due to the influence of several independent parameters. On the other hand, creating new experimental data in laboratory is very time consuming and expensive. Many studies have already been carried out with the available experimental data, however, a 20 error is still present in the current design formulae.

Preceding studies[1,2] has demonstrated that new data can be obtained from neural networks algorithms. In these investigations the ultimate resistance of beams was predicted using a data set composed of 155 experimental results with the ultimate load varying from 30 to 4010 kN. Due to the ultimate load large range, the data set was divided into three classes. The adopted model consisted of three prediction and one classifying neural networks. This subdivision granted a better normalisation in the training process. The first group ranged from 30kN to 120kN, the second ranged from 80kN to 250kN and the third from 150kN to 4010kN. The classifying neural network divided the data set from 30kN to 100kN, from 100kN to 200kN and from 200kN to 4010kN. This superposition was used to increase the data set of each group and to ensure that the complete range of experiments could be used and tested without any discontinuity. In that study, the results have been compared and calibrated with experimental data and existing design formulae, showing good agreement.

Despite the results achieved, the method used to separate the three groups did not properly consider the difference in behaviour of slender, intermediate and compact beams. As previously stated the division of classes was purely based on the load level basis and not on the beam's structural behaviour (web and flange yield, web buckling and web crippling). This strategy tends to produce distortions in the analysis because beams with the same ultimate load could have their failure associated to different modes of failure. The present paper describes a new methodology to overcome this setbacks. The new strategy uses a single neural network containing all the 155 experimental results using a different ultimate load normalisation technique. In this process the ultimate load is divided by a modified beam's web plastification capacity based on Lyse and Godfrey[3] equation. The back-propagation algorithm was used to train the neural net using 15 parameters as input and the normalised ultimate beam resistance as output.

In a preliminary analysis the best results were achieved with a single hidden layer and a sigmoid activation function. The Neural Networks presented a maximum error value lower than 30 40 trustworthy data. These new data, coupled with the existent experimental data, can surely help the production of a more consistent and accurate design formula.

1

E.T. Fonseca, M.M.B.R Vellasco, P.C.G. da S. Vellasco and S.A.L.de Andrade, "A Neural Network Evaluation of the Patch Load Phenomenon", Int. Conf. on Enhancement and Promotion of Comp. Methods in Eng. and Science, Macao, 797-806,1999.

2

E.T. Fonseca, M.M.B.R Vellasco, P.C.G.daS. Vellasco, S.A.L.de Andrade and M.A.C. Pacheco, "A Rule-based Neural Network System for Patch Load Prediction", Fifth Int. Conf. on Eng. Applications of Neural Networks, Warsaw, Poland, 81-86, 1999.

3

I. Lyse, H.J. Godfrey, "Investigation of Web Buckling in Steel Beams", ASCE Transactions, 100, paper 1907, 675-695, 1935.

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