悬索桥索鞍位置的分离计算法

Separate calculation method on suspension bridge saddle's position

关于索鞍位置计算,已有的计算方法较为繁琐或仅适用于单圆曲线索鞍,针对这种情况,将单圆曲线索鞍位置计算的分离计算法推广到复合圆曲线索鞍位置的计算中,从力学关系和几何关系出发推导得到了复合圆曲线索鞍位置计算的解析公式和由解析公式求解的牛顿-拉斐森迭代算法。改进约束条件,给出合理的迭代初值计算公式,确保了索鞍位置迭代计算快速收敛于真实解。归纳提出了理论顶点的顺延悬链线交点定义法和切线交点定义法的概念,探讨了两种定义法所得的索鞍位置计算公式或计算结果之间的必然联系。算例表明:该精确方法正确可行,近似方法也具有较高的精度,可供悬索桥施工、设计人员参考。

The calculation on saddle's position is one of important contents of the design for suspension bridge. All the presented methods are either complicated or only applied to the single arc saddle. To this fact, authors apply the separate calculation method used in the calculation of the single arc saddle's position to calculation of combined arc saddle's position. The analytic equation and NEWTON-RAPHSON iterating equation are derived from mechanical relationship and geometrical relationship. Improving the constraint condition, the formula of the reasonable iterative initial value is obtained, which ensures the iteration quickly to converge at the true solution. Two conception of the suspension theoretical apex which are defined as extensive catenary crossing point and tangent lines crossing point are presented, and the certain relations of the equations or results between the two definition methods are put forward. The samples show that the two methods are feasible and preferable precision, and both of them are reference for designer and worker on suspension bridge.