Keywords: cable-stayed bridges, under-deck cable-stayed bridges, combined cable-stayed bridges, optimization, concrete, cable prestressing forces, sizing design variables, shape design variables.

This paper presents an optimization-based approach for the automated design of combined cable-stayed concrete bridges. This approach combines an automated multi-start procedure with a gradient-based algorithm to solve the original non-convex optimization problem. The finite element method is used for the three-dimensional analysis considering dead load, road traffic live load and concrete time-dependent effects. The design is formulated as a cost minimization problem subject to constraints on the displacements and stresses considering service and strength criteria defined according to the provisions of the Eurocodes. A constraint aggregation approach is adopted to solve this problem by minimizing a convex scalar function obtained through an entropy-based approach. The discrete direct method of sensitivity analysis provides the structural response to changes in the design variables. The design variables are the deck and tower sizes, the cable-stays' and under-deck cables’ prestressing forces and cross-sectional areas, the tower height, the maximum strut length and the distance from the tower to the backstays’ anchor point. The optimization of a 90 m span bridge illustrates the features and applicability of the proposed approach. The optimum design features a deck slenderness of 1/72.1, maximum strut length-to-span ratio of 1/10.8 and height of the tower-to-span ratio of 1/4.4.

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