Equilibrium solutions and existence for traveling, arbitrarily sagged elastic cables

The exact, closed-form, three-dimensional solutions for the steady motion o f traveling, sagged, elastic cables under arbitrarily distributed and conce ntrated loading are developed in this paper. Three components of displaceme nt describing two equilibrium states of an extensible traveling elastic cab le are derived. These exact solutions apply to straight and sagged cables t raveling under their own weight and uniformly distributed loading. The exac t solutions are also used to investigate the steady motion of three-dimensi onal traveling cables under the uniformly distributed and concentrated load ing. Traveling elastic cables with large sag can be modeled approximately t hrough the inextensible cable model when both the loading and the translati on speed are very small. A slightly sagged cable must be modeled as extensi ble, rather than inextensible, even though both the loading and transport s peed are very small. These solutions can be applied to multi-span cable str uctures. [S0021-8936(00)02601-5].