Multidimensional forces and their quantitative relationships in cable-saddle system based on strand-unitized numerical model

The multidimensional mechanical behavior of cable-saddle systems, influenced by numerous steel wires, remains poorly understood, and the absence of quantifiable relationships complicates anti-slip design in these systems. This study develops a strand-unitized numerical model with five strand specifications, validated through two large-scale tests. It clarifies the internal and external forces and analyzes the competitive mechanism between lateral force ( F y ) and vertical force ( F z ). A ratio K (= F y / F z ) is introduced as a quantitative indicator to assess the influence of key parameters, with a practical formula fitted. Case studies on two multi-tower suspension bridges are conducted. Results indicate that as the wires accumulate, the internal contact force increases, forming a distinct diamond-shaped force chain, while vertical transmission occurs between strands. At the bottom, the lateral force sharply decreases, with the vertical force larger in the center and smaller at the sides. The wires generally reach a state of maximum friction. As the number of strands increases, vertical force rises linearly, while lateral force exhibits power function growth . Strand tension does not affect K , but reducing friction and increasing wire diameter enhance it. In actual cable-saddle systems, vertical force shows an arrow-shaped distribution, with a similar distribution for lateral force occurring when vertical plates are absent or fully installed. When the saddle is divided into sub-saddles, the lateral force shows an interleaved distribution; K remains nearly constant within sub-saddles but changes abruptly between them. Increasing the vertical plates significantly enhances the frictional component of lateral force, effectively addressing the anti-slip challenges of multi-tower suspension bridges. The existing lateral force formula is insufficient in this regard, whereas the proposed numerical model and practical formulas offer valuable tools for this purpose.