频率法计算匀质竖直拉索索力的实用公式

PRACTICAL FORMULAS TO CALCULATE TENSIONS OF VERTICAL CABLE WITH UNIFORM PROPERTIES BY FREQUENCY METHOD

列举几种关于拉索索力测量的常用方法,指出频率法测量索力仍是实际工程最为经济、实用的方法,并对国内已有频率法计算索力实用公式做出评价与分析。基于轴向受拉梁振动方程,建立了适用于任意约束条件下的匀质竖直拉索索力实用计算公式模型,并将实用公式中的比例变量表示成为拉弯比的函数;采用有限单元法对拉索在相同拉弯比,不同拉索性质(索力、索长和抗弯刚度)情况下的比例变量进行大量的数值计算,验证了比例变量对拉弯比具有唯一性,同时说明了以拉弯比做为比例变量唯一自变量的正确性;仍然采用数值计算的方法将比例变量分段拟合成为拉弯比的反比例函数,最终给出频率法测量索力实用公式;根据已建立的实用公式,分析了约束条件和抗弯刚度对计算索力的影响,随着拉弯比的增大,约束条件和抗弯刚度对计算索力的影响逐渐减弱、直至可以忽略。与国内已有实用公式对比计算结果和实际工程应用情况均表明:该文建立的根据基频计算索力的实用公式能够对拉弯比大于1的拉索索力做出正确的计算,其计算精度满足实际工程要求。

This paper lists several methods for cable force measurement in practice and points out that the frequency method is still the most practical and convenient method of cable force measurement in actual engineering,and then evaluates and analyzes the domestic pre-existing practical formulas to calculate cable force by frequency method.Based on the vibration equation of tensile beam,the model of practical formula to calculate cable force of vertical cable with uniform properties is created,which can be used for any constraint conditions,and the proportion variable of practical formula is expressed as a function of the tension-to-bending rigidity ratio（TBR）;Using the finite element method,massive data about the proportion variable are obtained for cables with the same TBR but different cable properties（tension,length and bending rigidity）,which not only verifies the uniqueness of the proportion variable to TBR but also proves the rationality and validity of taking TBR as the unique independent variable of the proportion variable;Through numerical calculation,the proportion variable is piecewisely fitted to an inverse proportion function of the TBR,and at last according to the established practical formulas,the affections of constraint conditions and bending rigidity to cable force are analyzed,which gradually decreases and can be neglected along with the increase of TBR.Both of the comparative results of domestic pre-existing practical formulas and applications in actual engineering indicate： the practical formulas created according to the cable force calculated at fundamental frequency can make a correct calculation and the calculation precision can satisfy the requirement of actual engineering when TBR is more than one.