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Vibration method has been widely applied to estimate cable force in bridge engineering since because of simplicity and speediness as presented in Nugroho, Priyosulistyo, and Suhendro (2014). It was applied on tensioned cable structure such as of suspension bridge as well as of cable-stayed bridge. On the suspended cable structure, such as hanger-on a suspension bridge, a vibration method is the most common approach used for the force measurement of hanger cables. Evaluation of force of hanger cables is very important to ensure the stability of the structure. Recently, vibration methods are not only applied to evaluate the force of the cable but also to develop the analitical formula based on the fundamental theory of string as well as theory of beam. A formula that considers sagextensibility, derived from the modern cable theory, was proposed by Russell and Lardner (1998). This method requires unstrained length of the cable as well as the solution of a nonlinear frequency equation using trial-and-error. This method was limited by the unavailable data of unstrained length in practice. Zui et al. (1998) solved the limitation of the Russell and Lardner (1998) by proposing a practical formulas for the vibration method was proposed by taking into account the effects of flexural rigidity and sag of a cable. This method was not limited by the unavailable data of unstrained length in practice. The approximate solutions with high accuracy for the equation of inclined cable with flexural rigidity was used to consider in these pactical formulation. The force of Abstract: Health monitoring using vibration technique is usually conducted on cable structure. The hanger cable on the suspension bridge has a difference of span. To predict axial force of cable, the beam-string theory includes a parameter of bending stiffness. However, string theory has neglected the effect of bending stiffness. The shorter the span of the cable the greater the effect of the bending stiffness would be. This paper raises parameter moment of inertia to span ratio (I/L) to determine the apropriate analytical formula between string and beam-string. Experimental research was conducted using a vibration technique. The specimens use solid cylindrical steel beam, having length specimens of 2 m, hinge-hinge of boundary condition, and difference variations I/L of 0.024, 0.08, 0.58, 1.53 and 10.22. Numerical analysis was simulated by using Abaqus software v 6.13. The result shows that the ratio of I/L equally lowers than 0.082 has close to the analytical string theory. The ratio of I/L greather than 0.082 has close to the beam string theory.

Natural Frequency of Tension Cable Based on Moment Inertia to Span Ratio: Determination Using Analytical, Numerical and Experimental Study