Cables are very important members in long-span bridges such as cable-stayed bridges and suspension bridges. So it is a very important and a essential part of maintenance of bridge to evaluate the tension of cables. But most theory on evaluation of cable tension does not consider the inclination of cable and additional tension due to cable vibration, hence we can apply these results to limited cases.
In this paper, new formula for evaluating the tension of cables is studied to improve the existing formula by introducing the inclination and additional tension of cable. Exact solution for static cable problem is solved to derive new tension formula, and it is proved that symmetry and anti-symmetry of cables are broken in the existence of inclination of cables. The dynamic equation of motion of cable is studied on base of exact static solution and dynamic displacement of cable is derived on the assumption that the sag of cable is negligible and the dynamic displacement is much smaller than static one.
In case of inclined cables, there is no criterion for judging the symmetry and the anti-symmetry of mode shapes, so proposed method does not divide the modes into symmetric modes and anti-symmetric modes, hence, considers the additional tension in both symmetric and anti-symmetric modes.
The proposed method gives the better result than the result of existing methods. The error of existing method by Irvine(1981) is about 10%, but that of proposed method is only 0.04%. Moreover, the variance of results in proposed method is much smaller than Irvine's method, because Irvine's formula does not give accurate values in calculating tensions with lower frequencies.