| Along with the application of a series of the cable vibration control method, the boundary conditions of the cable structures become more complex, which increases the difficulty to estimate their internal forces. Under complex boundary conditions, the traditional method will bring incalculable error and therefore is not applicable any more. It is imperative to investigate the methods of estimating internal force in cable systems under complex boundary conditions. In this paper, aiming at solving the challenging problems in the identification of cable tension of the large span cable supported bridge, we have investigated the cable tension estimation method under complex boundary conditions including fixed-fixed, intermediate support, and with anti-vibration mount boundaries.(1) Based on the general solution of the cable’s transverse vibration equation, a unified formula was derived for calculating the cable tension under a variety of boundary conditions. The formula was obtained by modifying the taut string theory formula by a correction factor Kn, and the cable tension can then be calculated using multiple frequencies. The proposed formula has the advantages of being simply formed, of high precision and error predictable. Furthermore, it can be used to calculate the bending stiffness of the cables explicitly and can be used in real application conveniently.(2) Following the means of dynamic stiffness matrix method, a frequency-dependent dynamic element displacement mode was adopted to derive the stiffness matrix and mass matrix of a precise dynamic beam element which can be used to estimate the cable tension. A program was developed to implement the dynamic beam element for cable tension estimation. Compared to cable tension estimation by a conventional beam element, it is found that the proposed cable tension estimation method has a distinct advantage on the accuracy and computational time.(3) Based on the energy variational principle, finite element analysis(FEA) was conducted to calculate the cable tension of a multiply elastic supported cable using the precise dynamic beam element proposed in this paper. Through FEA, a variety of complex boundary conditions can be simulated and their effects on the cable tension estimation can be studied, unlike the current methods which can only cope with simply supported or both-side clamped boundary conditions. Besides, it can also consider the effects of the shock absorber, steering block, usage of sheath and the multi-point elastic support boundary. The FEA results have been validated to have high precision by data from both laboratory experiment and field test.(4) A new three-dimensional two-node beam element is constructed in which the stability function was used as the lateral displacement interpolation function of the element. To consider the effect of anti-vibration mount on the cable tension identification, equivalent processing method of the mass and stiffness of the anti-vibration mount is proposed.. This equivalent processing method may simplify the finite element model of hangers system with anti-vibration mount and reflect the interaction between each component in the system, therefore the accuracy of the tension estimation can be guaranteed. A corresponding cable tension identification program was developed using Matlab. The calculated hangers’ tension was compared to the field test data of two long-span suspension bridges and the results demonstrated the good accuracy in the cable tension estimation and its workability in practical engineering of present method.(5) Beginning with equilibrium equation on micro segment of suspension, analytical expression of element stiffness matrix is obtained by solving element equilibrium differential equations. An accurate catenary element is then constructed to find the shape of the suspension cable. Based on the new concept of finding ‘force’ from ‘shape’ a program was developed to estimate the tension of all hangers in one shot. Compared with the conventional frequency method, present method is more efficient and can monitor the shape of the main suspension and the tension of the hanger synchronously. |
