1. Flexible Cables Cables can be loaded similar to beams, but they tend to deform under these loads. We will look at two different types of loads and the corresponding shapes of the cables. To begin let us examine some general properties of flexible cables. Flexible cables have a load distributed throughout their length. Similar to a beam the load can be expressed as a single resultant positioned at the centroid of the load. This is not always the most convenient description of a cable since the cable is not a rigid structure and can deform under load. To address this we will relate the load to the shape of the cable. To do so we will look at an infinitesimal section of the cable. Begin by examining the external forces on the cable:

2. Using small angle approximation (cos d 1, sin d d ): Using 1 st order approximation: Let us start by examining the y-direction: Now let us look at the x-direction: Using small angle approximation, and 1 st order approximation:

3. If we examine the results we notice that: If the differentiation of a function results in zero that function must be constant, therefore: Now substitute back into our expression from y: This relationship can be used to determine an expression relating y to x, for any load, in order to determine the shape of the cable.