Determination of the axial force on stay cables accounting for their bending stiffness and rotational end restraints by free vibration tests

Determination of the axial force in terms of its natural frequencies may be significantly influenced by the bending stiffness of the cable and the rotational elastic restraints at the ends, depending on the geometrical and mechanical parameters of the cable and its supports and restraints, particularly in cement-grouted parallel-bundle wire cables. The paper presents an explicit analytical expression for the natural frequencies taking into account both the bending stiffness of the cable and the rotational restraint at the ends that may be used to determine the axial force. While the bending stiffness of the cable and the axial force are selected as variables to attain an optimal match between analytical and experimental data, the rotational stiffness at the ends is treated as a known parameter in that process. The degree of rotational restraint at the ends cannot be accurately inferred from the sequence of the experimentally determined natural frequencies, since this parameter does not appreciably affect the progression of their values. Techniques are discussed that allow approximate determination of the rotational stiffness at the ends for the most common arrangements of anchors and cables with, and without, intermediate supports provided by deviators located near the ends. The axial force and the bending stiffness of the cable are both simultaneously adjusted by matching the natural frequencies of the analytical model with the experimental values. The proposed approach leads to a reduction of the error in the estimation of the axial force for short cables with relatively high bending stiffness such as those typical of cement-grouted parallel-bundle wire cables often used as cable stays for bridges until the early 1990s.