Tension force identification for cable of various end-restraints using equivalent effective vibration lengths of mode pairs

Vibration-based approaches have been widely adopted in determining the cable tension force. The development of effective length concept has been successfully applied in revealing the cable force regardless type of end-restraints. Simultaneously, the two-mode frequency approach can determine the tension force without knowing the bending stiffness of cables, but the formulas are limited only for the cable with hinged-hinged restraints. By taking advantage of these two methods, the present study aims to extend the two-mode frequency approach by introducing equivalent effective length for any mode pairs regardless type of end-restraints. To verify the proposed formula, three cases of cable end-restraints: hinged–hinged, fixed–fixed and hinged–fixed with the same tensioning force and cross-sectional properties, are studied. Validation using laboratory data and demonstration in a real cable force identification are also presented.