Cable Movements Under Two-Dimensional Loads

A numerical method is presented for the determination of the deflected shape of a suspended cable subjected to a general two-dimensional system of gradually applied, concentrated loads. Cable sag is treated. The equations of static equilibrium for the various load points and cable segments between load points are solved in terms of geometrical compatibility requirements by systematic, successive approximations. Other effects, such as temperature change, yielding of the supports, slipping of the cable at the supports, and uniformly distributed loads along parts of the span, are included. Two classes of suspended cable problems are considered: Loads attached at specified points along the cable, and the vertical and horizontal movements of the cable under these loads are determined; and the horizontal location of the final positions of the load points is specified, and the deflections of the load points and the location of their points of attachment in the unstressed condition of the cable are directly determined. The use of the method is demonstrated in three examples.