Basic problem on optimal spatial cable layout

Abstract

The following basic problem on spatial optimal cable layout is considered: a vertical load, P, with only specified x, y coordinates is to be transmitted by a cable whose ends rest at supporting edges forming a right angle corner. The optimal profile and the orientation of the cable with respect to the corner are to be determined so that the cable volume takes on a miniumum value. Some experienced designers felt that the cable should be orientated such that the load is found at the mid-span, thus having a fully stressed cable (half-span solution). Moreover, a traditional Chinese practice suggests the layout of the cable to be such that its span takes on a minimum value (minimum-span solution). The paper presents the optimal-span solution and, in so doing, checks whether the above speculated or intuitive solutions are correct.