PSI - Issue 84

Allan Larsen et al. / Procedia Structural Integrity 84 (2026) 1103–1110

1106

The data in Fig. 2 (right) may be used to determine the likely amplitude of a hanger cable once the mass, outer diameter and structural damping is known. It may also be used in a reversed sense to estimate the structural damping for known amplitudes.

≈ − 2

Fig. 3. Spring suspended cable section model in the FORCE Tech wind tunnel (right). Vortex induced vibration of one of the longest hangers (200 m) of the 1915 Çanakkale bridge, Türkie (left). Overlay of two video frames captured at the extreme excursions of the cable / model. As an example, the 1915 Çanakkale bridge has an outer diameter = 0.108 m and a mass = 46 kg/m. For ⁄ ≈ 0.08 read of Fig. 3 (right), a Scruton number ≈ 9 – 10.5 depending on the turbulence level is obtained from Fig. 2 (right). Evaluating the Scruton number relation with respect to the decrement damping yields = 0.001 - 0.0016 for the hanger cable structure. This is about 1/4 of the damping decrement = 0.006 proposed by Eurocode for parallel wire cables. The width of the lock-in range 0.12 < < 0.15 implies that more vibration modes of a hanger cable can co exist to form beating vibrations. Taking as an example a = 122 m long hanger cable having a diameter = 84 mm, a linear mass = 30 kg/m and tensioned to an axial force = 1000 kN, the basic natural frequency is estimated from taut string theory as 1 = 0.76 Hz. The wind speed range for lock-in for the consecutive modes of the hanger as function of frequency is shown in Fig. 4 (shaded area).

Fig. 4. Lock-in wind speed range as function of frequency for 122 m hanger cable having a first mode eigenfrequency of 0.76 Hz