A New Parabolic Cable Element And Verification

Cables are very efficient structural members used in tension structures such as cable-supported bridges, cable roofs, and guyed towers/masts etc. due to their high strength and light weight. With an increase in the span length of cable-supported structures, the accurate analysis of cables becomes more and more complicated and also important. Based on the analytical solution of cable dynamic stiffness matrix, a finite element formulation and iteration solution procedure of a new two-node parabolic cable element is proposed in this thesis for the static nonlinear analysis of cable structures. The applicability and reliability of the proposed parabolic cable finite element formulation are extensively verified through both numerical examples and experimental results. The main work and conclusions of this thesis include: 1. Starting from the derived analytical dynamic stiffness matrix of a parabolic cable and by letting the frequency be zero, the explicit expression of nonlinear static stiffness matrix for a 2-node parabolic cable element is obtained. This static cable element stiffness matrix has a high accuracy since it comes from the analytic solution of a parabolic cable. 2. The finite element formulation and corresponding increment iteration solution procedure of a proposed parabolic cable element are established. The computer program is developed. 3. Several numerical examples are presented to illustrate the accuracy, convergence and efficiency of the proposed parabolic cable finite element formulation. It is demonstrated that present results agree well with those obtained from the nonlinear theory of parabolic cable and published in previous literatures. The iteration procedure converges fast and only a limited number of cable elements are implemented. 4. A series of cable statically loaded tests have been conducted in the laboratory to further verify the proposed parabolic cable finite element formulation. It can be observed that the experimental results of cable tensions and deflections agree well with those calculated from the cable finite element formulation.