Comparing Different Techniques of Determining Cable Forces from Vibration Measurements on a Cable-Stayed Arch Bridge

As part of a reassessment of a cable-stayed arch bridge in The Netherlands, cable forces need to be determined. To this end vibration measurements are performed on each cable individually, from which the natural frequencies are derived. This paper describes three methods to determine cable forces from these vibration measurements, all using the relation between force and frequency according to the taut-string formula. In the first method the cable length as-is is used as vibrating length. A second method uses information on the mode shapes to determine the vibrating length and a third method uses the change in frequency due to an added point mass as a way to derive the vibrating length. Measurements on the shortest cable of the arch bridge show that using modal shapes leads to a vibrating length of almost one meter shorter than the full cable length (13.29 m instead of 14.32 m), while the third method leads to a much lower vibrating length (12.32 m) and thus to a different cable force. The two latter methods have as big advantage that they can be applied independent of the boundary condition of the cables, but the measurements have shown that their success is strongly related to the accuracy with which different parameters can be determined.