Improved algorithm for determining cable saddle pre-offsets considering the coupling effect of tower and splay saddles

By analysing the mechanical and geometrical relations between the main cable, tower, and splay saddles, and considering the coupling effect of the tower and splay saddles, an improved algorithm is proposed to determine the cable saddles pre-offsets of suspension bridges. The equilibrium relationship of the cable saddles, the compatible deformation condition, and the basic equation of the main cable shape are considered to establish several coupled non-linear equations up to 19, and the tower and splay saddle pre-offsets are obtained by solving the above equations with the Newton–Raphson method. This paper presents the initial value selection principle and the constraint conditions for solving the cable saddle pre-offsets of the plane cable suspension bridge and the calculation process ensures convergence. The calculation example demonstrates that the improved algorithm without an exact initial value can achieve excellent convergence.