Optimal Shape of Cables

Abstract

This paper is concerned with the optimal shape of cables subject to external loads only. Design-dependent loads (e.g. selfweight) are assumed to be negligibly small. Consequently, the cable axis is given by the funicular for the prescribed loads. However, the equilibrium condition still admits an infinite number of solutions, each of which is associated with a different value of horizontal support reaction. Using calculus of variations, a necessary optimality condition for minimum volume (or weight) is derived which eliminates all other possible solutions except for the optimal case. On the basis of this optimality condition, a general procedure is developed to construct the optimal shape of the cables and it is applied to some examples for illustrative purposes.