Long-span cable problems are governed by differential equations with singular perturbations as a result of the small bending stiffness compared to the cable’s self-weight. We use the method of matched asymptotic expansions for such singular problems to construct accurate analytical solutions and use these to formulate a general and geometrically exact theory of analytical form-finding for multispan cable systems. We apply the theory to two classes of problems: suspension bridge problems, in which the span shapes are given and the cable lengths need to be found; and transmission line problems, in which the cable lengths are given and the span shapes need to be found. The governing algebraic equations are conveniently developed on a per-span basis. The two types of problems require different solution approaches: in the former, spans are solved in series, while in the latter they are solved in parallel. The provided analytical expressions could be used for efficient experimentation in early design stages.
Feng et al. (Thu,) studied this question.