Abstract:
Optimum design of a two-span continuous post-tensioned prestressed concrete I-girder of a bridge super-structure is presented in the thesis. The objective is to minimize the total cost of the girders of the bridge considering the cost of materials, fabrication and installation. The design variables considered for the cost minimization of the girders of the bridge, are girder spacing, various cross sectional dimensions of the girder, number of strands per tendon, number of tendons, tendon configuration, slab thickness and ordinary reinforcement for deck slab and girder. Explicit constraints on the design variables are considered on the basis of geometric requirements, practical dimension for construction and code restrictions. Implicit constraints for design are considered according to AASHTO LRFD 2007.
The present optimization problem is characterized by having mixed continuous, discrete and integer design variables and having multiple local minima. Hence a global optimization algorithm called EVOP, is adopted which is capable of locating directly with high probability the global minimum without any requirement for information on gradient or sub-gradient. A computer program is developed to formulate optimization problem which consists of mathematical expression required for the design and analysis of the bridge system, three functions: an objective function, an implicit constraint function and an explicit constraint function and input control parameters required by the optimization algorithm. To determine the design moment and shear for the two-span continuous girder at various positions of the span, the computer program was incorporated with computer application of stiffness method to solve the indeterminate girder. No generalized equation for influence line of indeterminate girders was used, rather coordinates of the non-linear influence line were determined using basic stiffness method concept and were used to determine design live load moment and shear. Finally, to solve the problem, the program is linked to the optimization algorithm.
As constant design parameters have influence on the optimum design, the optimization approach is performed for various such parameters resulting in considerable cost savings. Parametric studies are performed for various girder spans (40 m, 60 m and 80m), girder concrete strengths (40 MPa and 50 MPa) and three different unit costs of the materials including fabrication and installation. From the parametric study, it is found that, optimum girder depth increases with increase in cost of steels. On an average, girder depth increases 22% with increase in cost of steel for 40 MPa concrete. On the other hand, for 50 MPa concrete, the average increase in girder depth comes out to be 19%. Optimum number of strand is higher in higher span girder. Number of strand decreases 17% with increase in cost of steel for 40 MPa concrete. In case of 50 MPa concrete, the average decrease in number of strand is 16%. Girder spacing is found to be higher in smaller span than larger span girder and optimum deck slab thickness comes out to be higher in shorter span as the girder spacing is higher in shorter span.
