Determining the Reasonable Completed Bridge State of a Self-Anchored Suspension Bridge with a Spatial Cable System Based on Minimum Bending Strain Energy: An Analytical Algorithm

The main cable of a self-anchored suspension bridge (SSB) is directly anchored to the two ends of a stiffening girder, and the stiffening girder is therefore subjected to enormous axial force and bending moment. This paper proposes a new method to determine the reasonable completed bridge state of the SSB in preliminary design. This method can accurately find the main cable shape that satisfies the minimum bending strain energy of the stiffening girder without being trapped in a local optimum. The method is suitable for the SSB with three-dimensional cables. Based on the segmental catenary theory, the relational expression of the component of the main cable tension in the longitudinal direction and the hanger tension is derived. Also, the partial differential equations for the condition at which the stiffening girder has minimum bending strain energy are also presented, which innovatively incorporates the effect of the vertical curve of the stiffening girder. The problem of solving simultaneous equations is converted into an optimization problem, which is then solved using the generalized reduced gradient method to obtain the hanger tensions and the main cable shape in the completed bridge state. The solving process is clear and has explicit physical meaning. Besides, there is no need to build a finite-element model. A calculation example is used to verify the applicability and accuracy of the proposed method. The mechanical behaviors of the cable-only system are further analyzed. On this basis, the approximate expressions of the component of the main cable tension in the longitudinal direction and the partial derivative of this tension component with respect to each vertical component of the hanger tension are provided.