Keywords: bracing systems, bracing members, multi-storey buildings, lateral loads, wind load, minimum cost, optimum bracing system, neural networks.

This paper proposes a technique for the selection of optimum bracing systems and the corresponding sections for the bracing members at a minimum cost. Based on a list of criteria and design requirements, selected bracing systems and the corresponding section of the bracing members are evaluated for optimum performance and cost for a given project.

Multi-storey buildings located in Egypt are used as case studies. They consist of multi-storey frames, with different numbers of bays. Different vertical bracing systems are used in this study; V-bracing, A-bracing and X-bracing. For each case, three types of sections are used for the bracing members; a single-angle, double-angles back-to-back and star-shaped sections. The study includes six steel profiles used for the bracing members. Twenty different buildings are considered in this study. The first building consists of one storey, the second consists of two storeys etc. The twentieth building consists of twenty storeys. These twenty buildings are studied taking into consideration one bay, three bays, five bays and finally seven bays. These bracing systems are analysed according to the allowable stress design requirements to resist lateral loads, at minimum cost, for wind pressure intensities of 70kg/m2, 80 kg/m2 and 90 kg/m2. If the section succeeds in sustaining the internal forces in the bracing members, the optimum cost for the bracing members can be achieved by selecting the section with the lowest cost. That section can be a single-angle, double-angles back-to-back or star-shaped angles.

The type of artificial neural networks (ANNs) that are used in this study are a feed forward artificial multilayer perceptron (MLP) models, that map sets of input data onto sets of appropriate output. The computer program Neural Connection 2.0 is used to train the artificial neural networks; the program uses 80% of the records for training, 10% for validation and 10% for testing.

The comprehensive database that was obtained from the structural analysis of all the cases that were studied was used to train five artificial neural networks to determine the three required target outputs; type of bracing system, optimum section for the bracing members and the corresponding profile of that section. The first network determines the required type of bracing system and according to this result either the second or third network in case of a V-braced building or the fourth or fifth network in the case of the X-braced building were used to determine the required section and profile of the bracing members. The (second and fourth) networks are used to determine the optimum section for the bracing members, while the (third and fifth) are used to determine the corresponding profile of that section.

The size of the training sets for each of the neural networks is about 30% of the collected records which range from 12000 to 15000 records for each neural network. This number is the actual limit for the program used to train networks. Each neural network in the developed model was tested and validated to ensure that the output matches the actual records for different cases in the study. The final organisation of the artificial neural network model developed has been successfully trained, tested and validated to determine the target outputs with a high degree of accuracy. The degree of accuracy of the developed ANN model is 94%, while the error rate is only 6%.

This paper shows that artificial neural networks are very effective tools to determine the optimum type of bracing systems, the optimum required section for the bracing members and the optimum cost for each storey for different types of buildings, with a very high degree of accuracy.

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