Static Perturbation Analysis of Inclined Shallow Elastic Cables under general 3D-loads

Abstract

Inclined, shallow, elastic cables under static 3D loads, arbitrarily distributed, are studied. Cables having natural length both larger or smaller than the distance between the supports (i.e. suspended or taut cables, respectively), are considered. Kinematically exact equations are derived, and projected onto an orthonormal basis intrinsic to the chord. A perturbation procedure is proposed, which extrapolates the solution relevant to the taut string, up to the desired order, and leads to a closed-form solution. Lower-order solutions are consistent with the hypotheses normally adopted in technical environment. Emphasis is given to the mechanical interpretation of the cable behavior. The asymptotic solution is compared to the explicit (not in closed-form) solution of the literature.

Keywords

• statics of cables
• inclined shallow cables
• suspended vs. taut cables
• elastic cables
• perturbation methods