Gravity stiffness of a three-tower suspension bridge: Analytical solution via double-span bridge reduction to a single-span one with elastic constraints

Abstract

Suspension bridge’s main cable under live load undergoes deformation depending on its gravity stiffness, i.e., work done against gravity under the initial dead load. In three-tower suspension bridges (3TSB), the middle tower's effect on the main cable's gravity stiffness is crucial but hard to assess. In this paper, the 3TSB model was simplified to the 2TSB with elastic constraints. The main cable shape was then calculated via the ratio between the simply supported beam's bending moment and the horizontal force component. The 2TSB model results were used to derive the 3TSB main cable's deflection using the middle tower's stiffness under vertical load. The analytical formula for gravity stiffness of 3TSB was derived by matching the latter with the simply supported beam's deflection formula. For a case-study 3TSB with main spans of 248 m + 1060 m + 1360 m + 380 m, analytical predictions were verified by FEM numerical results obtained via ANSYS. Linear relationships between live load and increments of the main cable's deflection and horizontal force component were derived. Besides, the main cable's deflection under live load can be reduced by increasing its sag-to-span ratio and cross-sectional area.