Multi-objective optimization of polyester-rope and steel-rope suspended footbridges

• Multi-objective optimization of polyester-rope and steel-rope suspended footbridges.
• Novel methodology combining a multi-objective genetic algorithm with dynamic relaxation and eigenanalysis.
• Span is maximized while volume is minimized.
• Includes two-dimensional systems with or without prestress and unstayed or stayed from below the deck.
• Optimized polyester-rope bridges have higher volumes, but lower self-weights than steel-rope bridges.

Historically, suspended footbridges have been built from ropes (i.e., cables) constructed of a variety of materials including iron and natural fibers. However, contemporary suspended footbridges are typically constructed with steel rope. One exception, a 64 m span polyester-rope footbridge completed in 2013, demonstrates the potential for alternative rope materials in contemporary footbridge design and construction. The first goal of this paper is to support the idea that polyester rope has promise in future footbridge applications by comparing minimum rope volume and self-weight results for polyester-rope and steel-rope footbridges with spans ranging from 15 to 64 m in two multi-objective optimization problems. In both problems the competitive objective functions are span which is maximized and rope volume which is minimized. The results are minimum volume systems for spans in the defined range. Minimizing volume reduces rope cost and eases material transport and handling. To provide an alternative measure of rope quantity, volume results are scaled to find the equivalent self-weights. This study focuses on in-plane structural behavior and investigates two-dimensional rope systems with or without prestress and with or without under-deck stays. A combination of static and natural frequency constraints is considered in the optimization problems. The second goal of this paper is to describe the novel methodology developed to evaluate these optimization problems. This methodology combines a non-dominated sorting genetic algorithm for searching the design space with dynamic relaxation and eigenanalysis algorithms for the structural analysis. Results indicate that polyester-rope systems have higher volumes, but lower self-weights than steel-rope systems. This observation supports the premise that polyester-rope footbridges are potential alternatives to steel-rope footbridges. The presented methodology can be adapted to evaluate how other unconventional materials compare to more conventional counterparts that are well established in bridge applications.