悬链线柔索索长的计算

Computation of the Length of Flexible Cable of Catenary Curve

假设悬索自重沿弧长均匀分布 ,由悬索微元力学平衡关系 ,推导悬索曲线方程。对悬索微元进行积分 ,进一步推出悬索有应力索长计算公式的显示表达。根据虎克定律 ,分别推出悬索无应力索长的精确计算公式和一阶近似公式。对索长各公式间关系进行了讨论 。

Given than the self weight of suspension cable is uniformly distributed along the whole length of the curve, the equation of cable curve was deduced according to infinitesimal mechanical balance relation. The infinitesimal of suspension cable was integrated, and the explicit expression for computation equation of the length of suspension cable with stress cable was deduced. The accurate computation equation and first approximation equation of suspension cable without stress cable were respectively deduced according to Hooke's law. A discussion was conducted of the correlation of equations, and computation results indicated the correctness of these equations.