Efficient combination of a TCUD method and an initial force method for determining initial shapes of cable-supported bridges

The TCUD method (Kim and Lee, 2001) can provides the reasonable initial shape of cable-supported bridges under full dead load by including the unstrained lengths of the cable members as unknowns and introducing additional constraint conditions equal to the total number of the cable members. However, the axial deformations in the girder and main tower members are not avoidable which result in some difference from a target configuration when long-span cable-supported bridges are considered. In this study, an effective method to be able to eliminate those axial deformations as well as to preserve merits of the TCUD method is newly proposed. For this purpose, the TCUD method and the initial force method with successive substitution are reviewed based on an elastic catenary cable element, respectively, and a new algorithm combining two methods efficiently is presented. In addition, a truss-cable element for modeling hangers and a beam-column element for the girder and main tower members are supplementarily developed, respectively. The proposed method is applied for two suspension bridges and a cable-stayed bridge to demonstrate its accuracy and effectiveness.