Optimization of Cable System for a Cable-stayed Suspension Bridge using a Simplified Analysis Model

Abstract

A cable-stayed suspension bridge is a hybrid structural system that is a combination of a cable-stayed bridge and a suspension bridge. In the cable-stayed suspension bridge, the cable-stayed system is generally allocated near pylons to reduce the loads supported by the suspension cables and to improve the stiffness of the bridge. Therefore, the span length can be extended and the structural behavior can be improved. Since the suspension system and the cable-stayed system present different structural behaviors due to the discrepancy in their load carrying path and the structural discontinuity taking place at the border between both systems, the design of the cable system is a complex and time consuming work. Particularly, designers should deal with the design variables of both cable-stayed system and suspension system and analyze various combinations of the variables to secure safety, stability, and economic feasibility. However, there is no generally optimized cable system for such a structural type since a few projects have been just completed in the past century and because of the scarcity of related researches. Accordingly, in this study, an optimization procedure to find an optimal cable system with minimized construction cost of superstructure for a cable-stayed suspension bridge using Genetic Algorithm (GA) is presented, and the optimal cable systems for a roadway bridge and a railway bridge are proposed. The proposed optimal cable system is defined using several design variables including a side span length (Ls), a main span length (Lsp), an overlapping length (Lov), a cable sag (f), and a dead load distribution factor (r). The application of the proposed optimal cable system to the practical design can enhance the efficiency of the design process as well as reduce much time, cost and manpower for numerous iteration works. Generally, the optimization procedure based on a GA dealing with several design variables necessitates a lot of iteration works mobilizing tremendous time, cost and manpower. This study proposes a new simplified analysis model enabling to analyze efficiently a cable-stayed suspension bridge. The proposed simplified analysis model uses the two-dimensional truss elements for all members, and the cables in the side spans are replaced with an equivalent horizontal cable spring at the pylon top. Through the comparison with FEM analysis using a commercial software, the applicability of the proposed model to the structural analysis of cable supported bridges is verified, and the simplified analysis model is employed to the proposed optimization procedure. As a result, time for assembling and analyzing a structural model for a cable-stayed suspension bridge is remarkably reduced. Using the simplified analysis model, parametric investigations are performed to understand the effects of design modifications including the change of a side span length, the composition of a suspension section and an overlapping section, the cable sag, and the dead load distribution factor on the structural behavior under traffic load and rail load. The 3rd Bosphorus Bridge with a main span length of 1,408 m is adopted as example bridge. The results of the parametric investigations are applied to set the range of design variables in the proposed optimization procedure. Finally, the optimization problem for the design of the cable system of a cable-stayed suspension bridge is defined as a cost optimization for finding the minimum construction cost of superstructures. GA is employed for the optimization, design criteria for stress and deformation from the design specification of KBDC and Eurocode are employed to examine the structural safety in the optimization procedure. The optimal cable systems are proposed for both roadway and railway bridges, and a sensitivity analysis is performed to investigate the effects of the change of design constraints and variables on the optimized result. It appears that the angular change of suspension cables among the constraints and the suspension section length among the design variables are very dominant on the optimal design of cable system. The proposed optimization procedure to find an optimal cable system for a cable-stayed suspension bridge using the simplified analysis model is so reasonable and efficient that it can be applied to the practical design process with reduced time, cost and manpower for numerous iteration works. Also, the proposed optimal cable systems for a roadway bridge and a railway bridge help design engineers avoid heavy iteration works to find a conceptual design in the preliminary design stage.