Discrete analytical model for lateral mechanical behavior of cable-saddle system in suspension bridges

Abstract Frictional resistance, typically provided by the bottom and sides of saddle, is essential for counterpoising unbalanced cable tension between adjacent spans. In most practices, however, the friction from the saddle sides is ignored due to the lack of an effective calculation method of lateral forces, giving rise to serious anti-slip issues, especially for multi-tower suspension bridges. For this reason, the lateral forces between the main cable and saddle are studied in this paper. A similar formula of lateral force in specification is first investigated to reveal its theoretical basis and limitations. Considering each cable wire as an individual discrete body, an analytical model with recursive algorithm is then developed, which allows to calculate the contact forces layer by layer. Based on this, the effects of possible errors are quantified, and the sensitivity of lateral forces to key parameters, such as friction coefficient, extra pressure, arrangement and diameter of the wires, is subsequently discussed in detail. The results show that the existing formula evolved from the Janssen theory is insufficient for anti-slip assessment of the main cable. The transverse gap of saddle trough has a limited increase effect on the lateral force. As the wire arrangement widens, the lateral force grows rapidly and then approaches a certain value. The lateral force is negatively related with the friction coefficient, and the extra pressure can create great yet regular influence on the distribution of lateral pressure. Finally, the Taizhou Yangtze River Bridge is taken as a case example for an application of the proposed model. It is found that 32.2% of the total friction comes from the lateral friction when two vertical friction plates are used, confirming that the anti-slip capacity of cable-saddle system can be greatly improved by adequately utilizing the lateral friction.