VTOP. An improved software for design optimization of prestressed concrete beams

Optimum tendon layout of prefabricated prestressed concrete beams was an early application of design optimization methodologies. However, most of the approaches found in the literature were not suitable to be implemented in real life bridge engineering. To fill the existing gap research has been conducted in past years by the authors to optimize prefabricated concrete beams formulating the problem in such a way that could be applied directly by bridge designers in beam and slab bridge decks. The software produced, labelled VTOP, contains the necessary capabilities for daily applications and possesses a user friendly graphical interface. This paper describes the problem formulation carried out and includes several examples to show the efficiency of the computer code implemented. Some of them are examples of single prefabricated concrete beams, and also an example showing the overall analysis of a bridge deck and the subsequent optimization of the prefabricated beam subjected to the internal forces produced by the external loading is included in the paper. 1 Beam and slab bridge decks Beam and slab decks are used for a wide variety of modern bridges. Many highway overpasses or urban bridges are designed with such arrangement. While the upper slab is always made in concrete, beams can be of steel or concrete. Also concrete beams can be prefabricated or built at the bridge site at the same time than slab producing a monolithic deck. But this latter technique, while sometime common in past times, is rarely used nowadays. Currently concrete beams are made in factories by means of a delicate mixture of cement and aggregates that produces a material with quite high strength to compressive stresses. The design is completed with prestressed steel tendons that translate Computer Aided Optimum Design in Engineering X 151 © 2007 WIT Press WIT Transactions on The Built Environment, Vol 91, www.witpress.com, ISSN 1743-3509 (on-line) doi:10.2495/OP070151 compressive forces to the concrete allowing this material to support future tensile stresses created by the bending moment originated by the external loads. Figure 1 shows two examples of beam and slab bridges, one having steel beams and other one with prefabricated concrete beams. In this paper only deck bridges built with concrete beams will be considered. (a) (b) Figure 1: Beam and slab bridge decks. (a) Steel beams deck and (b) concrete beams deck. 2 Structural models of beam and slab decks A computer picture of a beam and slab deck composed by a set of prefabricated prestressed concrete beams and an upper concrete slab is shown in Figure 2. This kind of structures needs to withstand traffic loads located at different points of the deck. Structural analysis aimed to proper dimensioning of the bridge requires create a structural model of the deck. Many approaches can be used for this purpose and it is very important to define one that can produce accurate results of the structural behaviour of the bridge and is also easy enough to be a tool for most bridge designers. This objective can be accommodated by defining a structural model composed of a two level grillage as indicated in this figure. In that grillage the top level of beams is an idealization of slab by two families of transversal and longitudinal beams. The bottom level of longitudinal elements idealizes the prefabricated beams. The set of vertical bars connecting both level of grillage are fictitious elements of great rigidity that make compatible the displacement restraints between beams and slab. With this arrangement, that represents very adequately the real behaviour of deck, the values of internal forces in slab and beams can be calculated. Bending deformation produced by external forces is supported by the deck an indicated in Figure 3. In that figure it can be observed that the total value of bending moment due to external loads is balanced not only by such kind on internal force in the slab and beams but also by a pair of compressive and tensile axial forces in slab and beam. That couple of axial forces is an important component in the internal equilibrium. Therefore the design of the prefabricated beams needs to take in account not only the bending moment but also the axial force described. © 2007 WIT Press WIT Transactions on The Built Environment, Vol 91, www.witpress.com, ISSN 1743-3509 (on-line) 152 Computer Aided Optimum Design in Engineering X