Iterative Nonlinear Cable Shape and Force Finding Technique of Suspension Bridges Using Elastic Catenary Configuration

It is important from the safety and economical perspectives that a suspension bridge should have minimal deformation under the self-weight of the bridge while the tension forces of the main cable and hangers remain at the lowest required level to achieve this goal. Most existing studies require establishing force equilibrium equations on the main cable joints and substituting equivalent forces. A new iterative nonlinear shape-finding technique is developed for suspension bridges to seek the target bridge profile under gravity. Different from most existing studies, nonlinear analysis is conducted on the whole bridge structure directly to avoid the complexities and induced errors associated with existing approaches. A detailed analyzation of a three-dimensional catenary cable element is first conducted based on the analytical equilibrium equations of elastic catenary. Two iteration schemes are proposed to find the solutions of cables with known undeformed length or known tension force at one end to serve different design needs. The proposed shape-finding technique is composed of iterations in three levels to comprehensively consider the nonlinear effects involved in the process. Numerical studies are conducted to demonstrate the behavior of a single cable element and the proposed shape-finding process on a prototype suspension bridge. The iteration results show that the proposed direct shape-finding technique is effective and accurate to determine the optimal target bridge profile by overcoming the limitations of the existing approaches. Although developed for suspension bridges, the proposed iteration technique for target cable shape and cable tension can also be extended to the optimal design of other types of cable-supported structures.