Praticial Formulas For Estimation Of Cable Tension By Vibration Method

The cable tension plays an important role in the construction control and long-term monitoring of cable-supported structures. The engineering implementation of a vibration-based cable tension evaluation is mostly carried out based on the taut string theory where the cable tension is estimated from measured natural frequencies by use of a simple explicit formula. However, the taut string theory may cause unacceptable errors in many applications by ignoring the cable sag and bending stiffness. The main work of this thesis includes: 1. Using energy theory, the cable sag and bending stiffness effects are investigated on the determination of cable tension forces through cable's fundamental frequency. Based on the curve fitting, the practical formulas are proposed where the cable tension can be easily estimated using measured fundamental frequency. It is demonstrated that the error between the proposed formulas with the theoretical solutions is less than .2. The cable sag and bending stiffness effects are studied on the higher natural frequencies of cable vibration. It is found that the differences of the higher adjacent frequencies go to the fundamental frequency of the taut string theory even though the cable sag or bending stiffness is included. This unique characteristic of cable vibration is used to determine the cable tension with the well-known taut string theory. 3. The frequency differences are determined by both the power spectral density (PSD) and Cepstrum of ambient vibration measurements. A MATLAB-based toolbox is developed, in which the differences of the higher adjacent frequencies can be easily evaluated. A field ambient vibration test of the Qingzhou Mingjiang cable-stayed bridge was carried out, and all the 168 stay cables' tensions are obtained by the proposed frequency differences method.