Cable Systems with Elastic Supporting Elements

Abstract

A system of cables supported by linear elastic springs and subjected to a concentrated static load is investigated. A method to determine tensions in individual cables and the location in space of the system under load is presented. The cables are assumed to be massless and inextensible. Friction is ignored in the formulation. The method is based on satisfying compatibility and equilibrium conditions for the cables and intercable connections, respectively. A system of coupled, nonlinear algebraic equations is solved numerically using the Newton-Raphson algorithm. A good initial guess for the unknown quantities, based on the physics of the problem, is provided. The method is applicable to intermediate support cable logging systems. In these systems, suspended cables supported by existing trees (intermediate supports) are used to transport freshly cut logs over sensitive terrain. A model of an example intermediate-support cable logging system is analyzed by the proposed approach, and the resulting behavior is discussed.