Practical formulas for estimation of cable tension by vibration method

The vibration method is usually used for field measurement of cable tension during the construction of cable system bridges such as an arch bridge stiffened with inclined cables or a cable-stayed bridge. Practical formulas for the vibration method are proposed herein taking the effects of flexural rigidity and sag of a cable into account. The formulas are based on the approximate solutions of high accuracy for the equation of inclined cable with flexural rigidity. Cable tensions are easily estimated by these formulas using measured natural frequencies of low-order modes. The practical formulas presented herein are applicable to various cables, regardless of length and tension as far as the vibration of first- or second-order mode is measurable. As to a very long cable that cannot be easily excited artificially, a formula is presented by using natural frequencies of high-order modes obtained from stationary microvibrations. The accuracy is confirmed through comparison of the values obtained by practical formulas with measured values and calculated values by the finite element method.