Method for estimating tension of two Nielsen–Lohse bridge cables with intersection clamp connection and unknown boundary conditions

Abstract

Nielsen–Lohse bridges are tied arch bridges with inclined cables that cross each other and connect through intersection clamps. Estimating the tension acting on the cables is essential for maintenance. Currently, methods for estimating the tension of a single cable using natural frequencies are applied to each cable after removing the intersection clamps. However, the removal and re-installation of intersection clamps is time-consuming and laborious. To improve the efficiency of tension estimation, the authors previously proposed a method for simultaneously estimating the tension of two cables with an attached intersection clamp. However, the previous method has the drawback of considering simple support at both ends, even though the actual boundary is not a perfect simple support. The objective of this study is to develop a new method for estimating the tension of two cables with unknown boundary conditions. The cable is assumed to be supported by a rotational spring at both ends. The newly proposed method estimates the tension, bending stiffness, and rotational stiffness of two cables from the natural frequencies without requiring the removal of the intersection clamp. The proposed method can handle arbitrary boundary conditions such as simple support or fixed support. In the case of fixed support, the rotational spring constant becomes infinity. To avoid infinity in the computation, normalization was employed in the derivation of the estimation formula. The validity of the proposed method was verified by numerical simulations and field experiments on an actual Nielsen–Lohse bridge. In the field experiment, the tension of all eight cables was accurately estimated and the estimation error was less than 10%. Even when accelerometers were installed on only one of the two cables at a height near the girder, the tension of both cables was estimated with good accuracy. The proposed method improves the efficiency of tension estimation work, because the tension of two cables can be estimated simultaneously and with good accuracy by measuring the acceleration of only one cable at a height near the girder.