Optimization of Concrete Cable-Stayed Bridges with Discrete Design Variables

Abstract

This work presents a procedure for finding the discrete optimum design of concrete cable-stayed bridges. The behaviour of this type of structures is governed by the stiffness of the load-bearing elements (towers, deck and cable stays) and the cable force distribution. In concrete bridges the stresses and deformations are significantly influenced by the construction sequence and by the concrete time-dependent effects. Furthermore, the geometrical nonlinear behaviour that arises when dealing with cables, large and flexible structures should also be considered in the analysis. A finite-element approach is used for structural analysis. It includes a direct analytic sensitivity analysis module, which provides the structural behavior responses to changes in the design variables. The optimum design of cable-stayed bridges involves a significant amount of design variables and design objectives. It can be stated as the minimization of stresses, displacements and bridge cost. To solve the continuous design problem an equivalent multi-criteria approach was used transforming the original problem into the sequential minimization of unconstrained convex scalar functions, from which a Pareto optimum can be obtained. This is followed by the rounding up or down of the continuous cross section variables to the nearest available discrete sections to find a discrete solution. Once the discrete design variables are fixed the solution is then improved by optimizing the cable installation forces (continuous variables) to meet the stress and displacements criteria. If this solution is infeasible, the segmental method is used to find the sizing variables which need to be modified. A concrete cable-stayed bridge example is presented to illustrate the proposed procedure.