Cable Force Identification for Pre-Stressed Steel Structures Based on a Multi-Frequency Fitting Method

As cables are the most critical components of pre-stressed steel structures, accurate identification of the cable force is necessary. This paper established a vibration equation of a multi-brace strut cable, which ignores the influence of sagging and changes in the cable force during the vibration. The form of cable vibration was also developed based on the vibration theory of cables. The analytical solutions of cable vibration equations under different boundary conditions were derived by studying the vibration models of single-span cables. The cable vibration under arbitrary boundary conditions was discussed. Additionally, based on the multi-span cable element vibration theory, the theoretical model of multi-span cable vibration and a cable force calculation method were proposed. A realization principle and an algorithm of the multi-frequency fitting method were proposed to calculate and identify the cable force. Further, the accuracy of the cable force calculated by the proposed method was verified based on a multi-span cable model test and two practical project experiments. The results show that the cable force was calculated with a relative error of 8%. Finally, a cable safety monitoring system was developed and established.