Keywords: under-deck, cable-stayed, bridges, optimization, concrete, prestressing.

This paper presents an optimization-based procedure for the design of under-deck cable-stayed concrete bridges. The proposed optimization strategy comprises a convex optimization algorithm combined with a multi-start procedure to generate local optimum solutions and the best of which is selected as the optimum design. The finite element method is used for the three-dimensional analysis of the structure under dead and road traffic live loads including concrete time-dependent effects. The optimum design of under-deck cable-stayed concrete bridges is posed as a multicriteria optimization problem with objectives of minimum cost, deflections and stresses considering service and strength criteria defined according to the Eurocodes provisions. This minimax optimization problem, which is discontinuous and nondifferentiable, is solved indirectly via the minimization of a convex scalar function from which a Pareto solution is obtained. This function is obtained following entropy principles and creates an inside convex approximation of the original nonconvex domain. The analytical discrete direct method is used to obtain the structural response to changes in the design variables, these derivatives are needed in the optimization algorithm used. The design variables considered are: the depth and width of the longitudinal beams of the deck beam-and-slab cross-section, cross-sectional sizes of the struts, under-deck cables cross-sectional area and prestressing force. The geometric design variable representing the strut length was fixed defining three different values corresponding to strut length-to-main span length ratios of 1/8, 1/10 and 1/12. The optimization of a single-span real-sized under-deck cable-stayed concrete bridge illustrates the features and applicability of the proposed method. The optimization-based procedure proposed allows finding minimum cost solutions that balance the deck flexure and the suspension effect provided by the under-deck cablestaying system. For the analysed example, the optimum design is governed by the cable stresses and the deck normal stresses for service conditions. The optimum solution features a deck slenderness of 1/37 and a strut length-to-main span length ratio of 1/10.

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