Abstract
MARTÍ ALBIÑANA, J.V. (2010) Optimal design bridges boards of prestressed concrete precast beams. Doctoral Thesis. School of Civil Engineering. 282 pages. jvmartia@upv.es.
The boards of prestressed concrete precast beams are typically used around the world to solve structures of viaducts and overpasses on roads. Scarce research work aimed at economic optimization of these structures, where the majority have focused on the reduction of forces of prestressed and suffered a considerable theoretical sign without a better use of resources that require, which has hindered its implementation on engineering design. Bibliographic search, not found any work focused on the optimization heuristic economic of this type of structures.
Before the gap in the spectrum of research, the focus of this work has been implementing optimization techniques economic to this typology. Applied metaheuristic technical in order to define the problem as complete as possible, where it is defined all the board and its reinforcement, and checked according to the Spanish code.
Different projects with this typology, where different manufacturers U-shape beams designs have been studied have been analysed by choosing one of them as a model for the present study, and leaving the option to adapt the typology to any of the designs that are produced. Then has developed a computer program in FORTRAN language that includes different modules: generation of the structure, structural testing, and economic evaluation. In addition, there is a module that generates the board CAD files. The study is on a board of 12 m wide, with 11 m road, 35 m of span lengths between supports and separation between beams of 6 m. 
The study of the heuristic methods applied to the board, is performed by comparison of eight different types of algorithms: random walk (RW), three local search methods and four evolutionary algorithms. Local search methods make it up descent local search (DLS), simulated annealing (SA) and threshold accepting (TA). Regarding the evolutionary algorithms, three variants of genetic optimization (GA1, GA2 and GA3) and one memetic algorithm (MA) were used. The lowest cost solution was the SA with 108,008 €, being 0.6% less than TA, 7% less than DLS and MA, and 13% less than the GA variants. As for the process times for the best calibrations, the minor values them lead the DLS with 8,122 seconds, later with 18,322 seconds for the SA, followed by three GA, with values around 21,000 seconds, them 36,233seconds of the TA, and finally already very remote they are 129,441 seconds of the MA. Results have shown the SA as better heuristics of them all.
Once selected the best calibration of the SA, we have studied the number of restart required to achieve quality solutions with a sufficiently high probability, using a stabilization of averages and standard deviations criterion. Thus designed an algorithm optimization combined nine restarts.
Conducted a study on the sensitivity of the model to the variation in the price of the materials. Percentage increases in prices of the active and passive reinforcement of  5, 10, 15 and 20%, doing the same with the concrete has been taken. The results show a sensibility more accused with the price of the steel that with that of the concrete, and that the board design adapts to reduce its cost, increasing the volume of concrete and by reducing the weight of steel when increases the price of the latter, and vice-versa when the price increase is concrete.
For the parametric study board there have taken span lengths of 20, 25, 30, 35 and 40 meters. There have been analyzed the cross-sectional geometry, the active steel ratios, the passive steel ratios, the amount of concrete and the types of concrete in beam and slab. There has appeared a substantially linear correlation of the cost, of the beam depth and the number of strands with regard to the span lengths board. The results show small thickness sections and high depths, allowing savings in the volume of concrete and increasing its inertia, needing less active steel, and a better quality of the concrete, among 40 and 50 Mpa, in beam. 
Simultaneously the parametric study for a concrete reinforced with steel fibers (HPF) in the beams has spread by comparing the results with those obtained previously. There has been analyzed the effect of the reinforcement of the fibers that produces on the design of the board with longitudinal and transverse solicitations, the variation in the number of strands, in the concrete volume, in the transverse steel ratio. Also the most suitable quantity of fibers, etc. Their economic competitiveness to conventional concrete has been verified.