Construction of suspension bridges and their structural analysis are challenged by the presence of elements (chains or main cables) capable of large deflections leading to a geometric nonlinearity. For an accurate prediction of the main cable geometry of a suspension bridge, an innovative iterative method is proposed in this article. In the iteration process, hanger tensions and the cable shape are, in turns, used as inputs. The cable shape is analytically predicted with an account of the pylon saddle arc effect, while finite element method is employed to calculate hanger tensions with an account of the combined effects of the cable-hanger-stiffening girder. The cable static equilibrium state is expressed by three coupled nonlinear governing equations, which are solved by their transformation into a form corresponding to the unconstrained optimization problem. The numerical test results for the hanger tensions in an existing suspension bridge were obtained by the proposed iterative method and two conventional ones, namely, the weight distribution and continuous multiple-rigid-support beam methods. The latter two reference methods produced the respective deviations of 10% and 5% for the side hangers, respectively, which resulted in significant errors in the elevations of the suspension points. To obtain more accurate hanger tensile forces, especially for the side hangers, as well as the cable shape, the iterative method proposed in this article is recommended.

During the construction of suspension bridges, the stress state of the pylon (tower) is improved by pushing the pylon saddle by an appropriate distance at the proper time. An analytical algorithm for the assessment of the required timing and displacements for the pylon saddle pushing at particular construction stages is proposed and verified in this study. The timing calculation is based on the assessment of current hanger tensile forces at each construction stage and the pylon stress state, while the pushing distance/displacement is derived from the conditions of elevation difference closure and the conservation of unstrained length of the main cable segments. This algorithm was successfully applied during the construction of a particular suspension bridge in China with a main span of 730 m. The results obtained strongly indicate that the bending moment in the pylon bottom is contributed by both horizontal and vertical forces of the main cable. The horizontal constituent is dominant and its share gradually increases in the bridge construction process. In a suspension bridge with side spans of various lengths, the stresses in the pylon bottom on the side with a larger side span is more likely to exceed the limit. Therefore, the respective strength criterion controls the pylon saddle-pushing schedule. The proposed analytical algorithm is quite straightforward and is recommended for wider application.

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