Shape finding of suspension bridges with interacting matrix

Abstract

Reasonable determination of cable tensions and main cable configuration was the key issue in designing suspension bridges. Based on interacting matrix theory, an optimisation method of cable force in suspension bridges was deduced. For linear structure, interacting matrix was linear. But for non-linear structure, such as suspension bridge, large deformation effect was strong, superposition principle was not applicable. So the interacting matrix theory applied especially to linear structure. The interacting matrix of suspension bridge could be gotten taking into account dead load stiffness. Based on interacting matrix, cable forces were gotten after iterations by non-linear FEM. The procedure consists of two successive steps of non-linear analysis. The first step was interacting matrix formation procedure. The interacting matrix of suspension bridge could be gotten taking into account dead load stiffness. Successive non-linear analyses were then performed until the trial nodal coordinates and unstrained lengths of cable elements resulted in the target. The optimisation procedure with designated targets was achieved concerning the structure stiffness. The reasonable shape of suspension bridge was gotten. In addition, a case study on a suspension bridge was carried out to show the capability of the proposed method. It showed that the method had the advantages of mechanical significance, concise algorithm, and high accuracy. It was worth popularising in design practice.

Keywords:

• interacting matrix
• suspension bridges
• cable force

Acknowledgements

The authors would also like to thank the reviewers for their critical comments and valuable feedback which have been very useful in improving the work presented in this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology [grant number S13209]; the Liaoning Provincial Department of Education [grant number L2014027]; the Fundamental Research Funds for the Central Universities [grant number DUT15QY34].