Abstract:

Today, post-graduate engineering education faces multiple challenges in our country and most of Europe. Traditional post-graduate courses used to deal with well-established knowledge not covered at the undergraduate level. These courses led to the Master´s degree or as in most European countries to a higher degree in engineering. Besides, research tools and ongoing advances were given at doctoral courses leading to the degree of Ph.D. Following the Bolonia’s declaration, post-graduate courses are reshaping into a mix of both well-established knowledge courses, together with the tools and knowledge of ongoing research topics. Such is the case of the recent Concrete Engineering Master course of the ‘Universidad Politécnica de Valencia’ that started in October 2007. This paper presents the main ingredients of a recent post-graduate course in automated design and multiobjective optimization of reinforced concrete structures. This topic is the teaching consequence of the research done by the authors on this topic. The course is concerned first with the basic heuristic algorithms for structural optimization, such as simulated annealing, tabu search, threshold acceptance, genetic algorithms, ant colonies, variable neighbourhood search, neural networks, etc. And it then moves to the application of such algorithms to the practical design of real structures such as walls, road portal and box frames, building frames, vaults, bridge piers, abutments and decks. The paper presents the field of research, an overall view of the course, some of the algorithms used and three case studies that give an insight in the applied part of the course. Threshold accepting (TA) heuristic is firstly applied to RC road vault underpasses of 12.40 m of diameter. The structure is defined by 49 discrete design variables, 5 geometrical, 3 different grades of concrete, and 41 reinforcement variables following a standard setup. Penalty functions are used for unfeasible solutions. The TA method indicates savings of about 10% with respect to a traditional design. The second structure analysed is a 24 m RC vertical height bridge pier of hollow rectangular cross-section, which supports the main span of a prestressed concrete road bridge of 60-90-60 meters of longitudinal spans. This example has 95 discrete variables, 15 geometrical, 7 types of concrete and 73 types of reinforcement bars of fixed length. The evaluation module includes the limit states that are commonly checked in design: flexure, shear, deflections, buckling, etc. Ant colonies results indicate savings of about 30% with respect to the design based on the experience of the bridge designers. The third type of structure analysed is RC symmetrical building frame with two bays and five flours. This example has 96 discrete variables. Apart from the cost function, an additional constructability function based on de number of bars of the structure is considered. The results demonstrate the potential of multiobjective simulated algorithms for the design of real building frames taking into account the cost and the constructability. Finally, case studies indicate that heuristic optimization is a forthcoming option for improving the design costs of real RC structures.

Keywords:

post-graduate education, structural design, multiobjective optimization, heuristic.