Minimum weight design of cables with supports at different levels

A systematic method for determining the least-weight cable profiles for any given vertical external load system and for supports at different (or same) levels is presented and illustrated with examples. The support levels may be either prescribed or optimized as well. The method is based on the optimality conditions which are derived using the calculus of variations. Moreover, it is established that the slopes at both ends of the cable must be equal when the total structural weight is minimized with respect to both maximum tension in the cable and relative position of the supports