GENETIC ALGORITHM BASED OPTIMUM DESIGN OF CABLE STAYED BRIDGES

Abstract

Modern cable stayed bridges are at present considered to be the most interesting development in bridge design. These structural systems are statically highly indeterminate. Cable stayed bridges are large and sophisticated structures which may greatly benefit from the use of structural optimization techniques for design improvements. Due to their efficient utilization of structural materials, aesthetic appearance and other notable advantages, cable stayed bridges have gained much popularity in recent decades. Due to the large number and a mixed type of design variables it poses challenge to the designer to choose appropriate parameters. This challenge is addressed in the present thesis by developing an optimization procedure for the design of cable stayed bridges. Finite element stiffness-based approach has been adopted for the analysis of 2D frame of cable stayed bridge. Uniformly distributed superimposed dead load (apart from self weight of structure), live load, seismic load and flutter have been considered for analysis. Cables as linear truss element have been considered in the linear analysis and the modulus of elasticity modified as equivalent modulus of elasticity has been considered in the nonlinear analysis. The tower and girder have been modeled as a beam element. Two types of deck-pylon connection have been modeled - one with rigid connection and another with a sliding connection in the longitudinal direction. The bridge coordinates are assigned in such a way that bridge can be analyzed for both the radiating type and the harp type, without re-meshing the geometry. In the modeling, deck has been treated as a single cell box section and the tower as a box section. The material for the girder and tower is assumed same, either steel or concrete. Geometric nonlinearities - cable sag effect, beam column effect and large deformation effect, have been incorporated in the analysis. For seismic response of cable stayed bridges, response spectrum analysis method has been adopted. Flutter is one of the important factors to be considered in the design of cables stayed bridges. Hence safety against flutter phenomenon has been incorporated in the present thesis work. In order to calculate the critical flutter velocity at bridge location, flutter derivatives for the given bridge deck are essential. The most reliable method of working out the flutter derivates is through wind tunnel test. Since it is very costly and time consuming to get the flutter derivatives for every deck section, a Support Vector Machine (SVM) based approach has been adopted. In this approach, an SVM has been developed and validated with the flutter derivatives given in the literature. The flutter velocity at bridge location has been calculated using the flutter analysis and validated with three major bridges as reported in the literature. Then, the developed SVM was combined with Genetic Algorithm (GA) for optimization. The responses obtained for each load case have been analyzed for constraint satisfaction and used to obtain a minimum cost. A GA program has been developed to incorporate the design optimization for cable stayed bridge with large design variables and important design constraints. The cost of deck, tower (considered of that above the girder level) and cables together has been taken as the objective function. Size and configuration levels of optimization have been carried out. The design variables considered for the present thesis work are viz. cable areas, girder depth, girder bottom width, girder web thickness, tower width, tower depth, tower web thickness, tower height-to-main span ratio, side-to-main span ratio, central unsupported length-to-main span ratio, number of cables, cable layout. The optimum design has to satisfy strength, stability and stiffness related constraints. For optimization, the cables in the bridge are grouped into four zones according to cable positions with respect to tower. The grouping of cables resulted in a reduction in the optimum cost of cable stayed bridges. The effect of connection between deck and pylon was studied and it was observed that in the seismic case, deck supported on the pylon makes it economical and in the static case, deck fixed with pylon makes it economical. When the nonlinearity is taken into consideration in the analysis, the relative optimum cost is 13% more as compared to that in the linear analysis for optimization. In the optimization process the effect of cable layout has been demonstrated. In case of longer spans, the radial type layout proves economical while in case of short span bridges, the harp type cable layout makes it economical. In the present work, restricting the tower height-to-main span ratio, the design of extradosed bridges has been carried out. The extradosed bridges are economical for bridge lengths less than 250 m. A complete database has been prepared for the relative optimum cost of cable stayed bridges for different cost ratios both for steel bridge and concrete bridge. The cost break-ups for each component of the bridge have been presented for different cost ratios, both for steel and concrete bridges. vi