Practical formulas to calculate tensions of vertical cable with uniform properties by frequency method

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.