Tension prediction for straight cables based on effective vibration length with a two-frequency approach

Cost-efficient and theoretically simple vibration-based analyses are widely used to assess the axial forces of tensioned members. In the determination of cable forces, the applicability of an explicit-type formula depends on the suitability of the adopted theories and the accuracy of the known parameters. For straight cables, the sectional rigidity is generally assumed to be a known quantity and the end conditions are presumptive. Nevertheless, given data of these parameters could be vague or unreliable. Methodologies which omit the requirement of a priori data are thus preferable in practice. This paper illustrates an effective methodology for the tension prediction of cables with presumptive end conditions by making use of multiple measured mode frequencies. Simple yet accurate formulas are obtained from the exact expressions based on the Bernoulli beam theory. Due to the fact that this approach does not require the knowledge of the flexural rigidity of the testing cable and it can be performed using only a single sensor, the method is suitable to be implemented in a quick diagnosis scheme. Present research emphasizes developing an analytic basis to effectively correlate the proposed formulas with the concept of the effective vibration lengths. This concept has been widely recognized as a useful idea to interpret the dynamics of cable vibrations