Optimum weight analysis of steel grid bridges

Abstract

Bridges include different types, mainly, the truss, the plate girder, the box, the cabled systems, and the grid type. In this research work the main objective will be to analyze the grid type bridges consisting of main girders and cross girders. Optimization techniques have been utilized in order to determine the minimum weight of the steel grid bridges. The purpose of this research work is to accomplish the following: (1) To determine the ideal number of main girders supporting a reinforced concrete slab for the same geometrical dimensioning, the same conditions of live loads, the same number of cross girders, and the same type of steel. (2) To determine for the previous ideal number of main girders, whether or not the spacing between cross girders is changing, the optimum situation. (3) To determine the optimum type of steel. Three different types of steel, 37, 44, and 52, are used for both main girders and cross girders. (4) To determine to what extent the model of optimization is influenced by the restrictions of side constraints. The problem here is to find the optimum weight of steel grid bridges. Different grid bridges having two, three, four, and five main girders have been analyzed. The objective function is given by the weight of the structure and the design variables are the dimensions of the cross section. The design and side constraints are respected. The unconstrained formulation using the interior penalty function technique is selected. Powell's algorithm is chosen for the generation of the search vector and the quadratic interpolation technique is chosen for the determination of the step size. The conclusions are (1) The optimum solution for the different cases of steel types 37, 44, and 52 was the use of three main girders. (2) The use of steel type 52 with the cases of two, three, four, and five main girders would provide a saving in steel weight amounting to 20% and 25% relative to steel types 44 and 37, respectively. (3) Practically speaking, steel type 52 is more expensive than steel types 44 and 37. Nevertheless, this factor being considered, there would be a saving of 18.8% and 22% if steel type 52 is used instead of steel types 44 and 37, respectively. (4) When three main girders are used with steel types 52, 44, and 37, the weight of cross girders amounted to 10.7%, 7.1%, and 10.8%, respectively.