Using spatial graphic statics method to find funicular forms for curved-deck arch bridges

Abstract

Bridges with curved decks are often used decrease the slant of a bridge without changing the span or to produce aesthetically interesting bridges, but finding funicular forms for arch and suspension bridges of this type can be complicated because the form is three-dimensional and the forces on the arch depend on the angle of the members connecting the arch to the deck, and therefore the shape of the arch. Other iterative tools for finding these forms have been created using finite element method, force density method, and 3D graphic statics, but these methods involve a lot of complicated mathematics. In this thesis, I demonstrate the usefulness of the spatial graphic statics method (SGSM, a method in which graphic statics in performed in 2D on two planes and then combined using projections) for finding these forms by creating an iterative form-finding tool. The tool created allows for the use of any deck shape so long as its supports are at the same height, and allows the user to alter parameters such as the load on the deck, the arch self-weight, and the horizontal force in arch, and to optimize for parameters from a predetermined list or based on a function created by the user. To determine the appropriateness of the use of SGSM to model spatial arch bridges, the forces determined by SGSM were compared to those found using FEM, and the difference was within 4\% except in cases where the arch was very tall or its supports were shifted too far past the deck. The moments in arches with different angles of inclination, found using FEM, were also compared, and the form produced by the SGSM form-finding tool was found to have the least moment, which confirms that the tool accurately finds the funicular form. This tool may be useful for structural engineers trying to find a basic shape for an arch or suspension cable and for researchers looking to learn more about these structures. This tool may also serve as a basis for more robust applications that use SGSM in the future.