Analytical Calculation Method for Anti-Slip of Main Cables in Three-Tower Suspension Bridges with Spatial Cable Systems

To investigate the anti-slip characteristics of the main cables in a three-tower suspension bridge with spatial cable systems, this paper proposes an analytical calculation method for the anti-slip safety factor of the main cables and establishes an equivalent mechanical analysis model for multi-tower suspension bridges with spatial cable systems. Based on the deformation of the towers and cables under live load, as well as the equilibrium relationship of the main cable forces in loaded and unloaded spans, analytical formulas for the anti-slip safety factor of the main cables at the middle tower saddle are derived. A finite element model is developed to validate the formulas. The influence of parameters such as the spatial cable inclination angle, tower-to-cable stiffness ratio, dead-to-live load ratio, sag-to-span ratio, span length, and friction coefficient between the main cable and saddle on the anti-slip safety factor is analyzed. The results indicate that the formula proposed in this paper provides a highly accurate estimation of the slip resistance safety factor for main cables in spatial cable multi-tower suspension bridges. The adoption of spatial main cable configuration enhances the stability of the slip resistance safety factor at the intermediate tower saddle. The slip resistance safety factor of the main cable decreases with the increase in the tower-to-cable stiffness ratio, while it increases with the rise in the sag-to-span ratio. Moreover, the influence of the sag-to-span ratio on the slip resistance stability of the main cable becomes more pronounced with higher tower stiffness. The slip resistance safety factor of the main cable exhibits an approximately linear increase with the rise in the dead-to-live load ratio and the coefficient of friction. Furthermore, the slip resistance safety factor increases with the span length, and this rate of increase becomes more pronounced with smaller sag-to-span ratios. The research findings presented in this paper provide a theoretical basis for the design of spatial cable multi-tower suspension bridges.