A METHOD FOR THE ANALYSIS OF INTERNALLY REDUNDANT STRUCTURAL CABLE ARRAYS

A method is presented for determining the tensions in, and equilibrium configuration of, internally redundant structural cable arrays. The method has applications to suspension bridges, structural nets, and moorings. Cable stretch is included in the formulation, and arbitrary strain-tension relations are permitted. An iterative solution that does not require the calculation of slopes or derivatives is generated for varying the unknown redundant reactions. Global convergence of the iteration to the correct reactions (and, consequently, to the correct equilibrium configuration of the array) from any set of initially guessed reactions is insured. The rapidity of this convergence is demonstrated by several numerical examples. Although the basic solution assumes external loads that are independent of the array configuration, a combination of the method with the mathematical technique of successive approximations allows configuration dependent loadings to also be treated. This combined technique, extremely useful in the analysis of mooring systems, is described.