Tension estimation of cables with different boundary conditions by means of the added mass technique

When analyzing cable vibration, both the tension and the bending stiffness must be taken into account; in fact, the cable can be considered as an intermediate case between the beam (no tension) and the string (no bending stiffness). Moreover, one of the most important issues for this approach is the right definition of the boundary conditions, since they can be very different from one structure to another. Taking into account the aforementioned issues, the paper presents an overview of all possible scenarios, especially focusing on the relationships between the cable properties and its boundary conditions, summarized by the introduction of the modal length concept. Successively, a method for the estimation of the cable tension has been developed, just based on two simple measurements: one with the cable in its standard configuration and one with an added mass on it. This supplementary information allows to well estimate the modal lengths and consequently the tension. The procedure is applied both to a numerical example and to an experimental test done on a stay-cable bridge.