Practical Formulae for Estimating Cable Tension with Unknown Rotational Restraints by the Frequency Method

To calculate the tension in cables with different boundary conditions, the relationship between cables with fixed-fixed and hinged-hinged boundary conditions in terms of the frequency was determined according to frequency characteristic equations of cables with the two boundary conditions. In this way, a simple calculation formula for tension with fixed-fixed boundary conditions was deduced. Similarly, a calculation formula for the tension in cables with a fixed-hinged boundary condition was proposed using the method. Results show that the proposed formulae, with high computational accuracy and wide ranges of application, can be used to calculate the cable tension under a dimensionless parameter (xi) not lower than 6.9, so it is convenient to apply the formulae to calculate tension in practice. Meanwhile, changes in the frequency ratios of cables with different boundary conditions than those with a hinged-hinged boundary condition were analyzed. Results show that when xi is not lower than 25, the frequency ratios of cables of various orders tend to be the same. The boundary coefficient(lambda) was introduced. Given the cable stiffness, the tension and boundary coefficient(lambda) can be calculated through linear regression. The method considers influences of unknown rotational end-restraints of cables and accurately calculates the cable tension. By using simulation examples and engineering examples, the method was verified to be accurate in calculating the cable tension, thus providing a novel, practical method for estimating tension in cables, booms, and anchor-span strands of suspension bridges.