Direct Evaluation of Effective Lengths of Vibrating Cables Using Responses from Dual/Three Transducers

In this study, a direct calculation formula using frequency amplitudes for the first two modes at two or three locations is proposed to compute the effective lengths of vibration for pre-stressed members. Derivation of the proposed formulas is based on the assumption that vibration mode shapes of cables are simple sinusoidal functions. This paper describes the use of the proposed formulas to reasonably recover the designated effective lengths for simulated cable members. The proposed formulas work well with a recent developed scheme for assessing cable forces in which good estimations can be obtained in a relatively more accurate yet simpler way than the traditional approach. It is concluded that such calculation is an alternative way in giving reference values for the lengths of tensioned members and especially useful when using in the determination of cable forces.