Keywords: structural engineering, semi-rigid connections, steel structures, neural network, semi-rigid behaviour, connection stiffness.

The traditional non-sway frame design usually adopts flexible connections. Unfortunately, when sway frame design is required, rigid stiffened connections have to be used. On the other hand, rigid connections have higher associated fabrication costs and give rise to a number of questions about their real structural behaviour. To overcome these difficulties the semi-rigid connection fit as a natural solution, reducing the final cost and presenting a more realistic structural behaviour. The bolted end-plate connections are, probably, the most common type of steel connections. They are widely used in constructional steel design because they can cover a wide range of structural solutions, from pinned to rigid connections, by minor modification of connection details. In general, the required initial stiffness and the flexural connection resistance can be obtained using an appropriate configuration of the connection elements, such as number of bolts, end-plate thickness and its geometrical configuration[1].

The artificial neural networks (ANN)[2] are computing systems that simulate the biological neural systems of the human brain. They are based on a simplified modelling of the brain's biological functions exhibiting the ability to learn and generalise its knowledge to solve specific problems.

A neural network is represented by weighted interconnections between processing elements (PEs). These weights are the parameters that actually define the non-linear function performed by the neural network. The process of determining such parameters is called training or learning[2], relying on the presentation of many training patterns. Thus, neural networks are inherently adaptive, conforming to the imprecise, ambiguous and faulty nature of real-world data[3].

This work proposes the use of artificial neural networks to predict the flexural resistance and initial stiffness of beam to column end plate connections. This civil engineering problem is characterised by the influence of several factors and for the difficulty of generation of new laboratory data. This was the main motivation for using artificial neural networks.

In this work, the Back Propagation supervised learning algorithm has been used, where the network is presented with a set of input vectors and their respective desired output vectors. The back-propagation algorithm[3] defines a systematic way to update the synaptic weights of multi-layer Perceptron (MLP) networks. The supervised learning is based on the gradient descent method, minimizing the global error on the output layer. The learning algorithm is performed in two stages: feed- forward and feed-backward. In the first phase the inputs are propagated through the layers of processing elements, generating an output pattern in response to the input pattern presented. In the second phase, the errors calculated in the output layer are then back propagated to the hidden layers and the synaptic weights updated, so the error value is reduced. This learning process is repeated until the output error value, for all patterns in the training set, are below a specified value.

The topology of the MPL network presented: twenty-one input data, three hidden layers with eight processors each and one output layer composed the neural network used to predict the flexural resistance. The prediction of the initial stiffness comprised: one hidden layer with fifteen processors. The results of 26 experimental tests (21 for training and 5 for testing) were used[3], producing satisfactory results.

The mean errors obtained were 8.5 resistance and the initial stiffness of beam to column connections, respectively. The results confirmed that the performance of the neural network for the prediction of flexural resistance was good. The initial stiffness prediction pointed out the necessity to improve the neural networks process.

1

C. Faella, V. Piluso, and G. Rizzano, "Structural Steel Semi-Rigid Connections � Theory, Design and Software", CRC Press, 1999.

2

K. Hornik, M Stinchcombe and H. White, "Multilayer Feedforward Networks are Universal Approximators", Neural Networks, 2, 359-366, 1989. doi:10.1016/0893-6080(89)90020-8

3

C.H. Barbosa, M.M.B.R. Vellasco, M.A.C. Pacheco, A.C. Bruno and C.S. Camerini, "Non-destructive Evaluation of Steel Structures Using a SQUID Magnetometer and a Neural Network System", Review of Scientific Instruments, American Institute of Physics, 71(10), 3806-3815, 2000. doi:10.1063/1.1313796

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