Estimation of Cable Tension Force Independent of Complex Boundary Conditions

The presence of unknown complex boundary conditions usually imposes difficulties in estimating the cable forces in cable-stayed bridges when using conventional model-based force identification methodologies. Therefore, there exists a need for new methodologies that can overcome these challenges while achieving acceptable force identification accuracy. This paper presents an innovative method to estimate the forces within stay cables with complex boundary conditions. The proposed approach transforms the cable force estimation problem from the common procedure of constructing and solving the equation of motion of the cable to a simpler problem of finding the zero-amplitude points of its mode shapes. Ultimately, the presented methodology yields accurate cable force estimations regardless of the complexity of the boundary conditions. An equivalent segmental model whose length is given by the distance between these points is used next to find an estimate of the cable tension force. A stay cable under axial force and constrained by end rotational springs is employed to analytically investigate the force identification accuracy of the proposed method. It is observed that with mode orders lower than 18, the proposed method achieves a maximum relative error less than 5% regardless of the end-restraint condition. Therefore, the proposed method has great potential for practical application because of its theoretical simplicity, accuracy, and feasibility.