Truss and cable elements are defined by their ability to carry solely axial loads. Nonetheless, since cables have no stiffness when loaded in compression, they function only in tension. Moreover, cables are typically pre-tensioned, i.e., they carry an initial tension load, while truss elements are, typically, not pre-tensioned. This pre-tension force substantially differentiates the behavior of the two elements.
A truss and a cable of the same length (L), cross-section (A), and elasticity modulus (E), as shown in Figure 1, are subjected to a horizontal force, F. The cable is pre-tensioned by a force, T. Both the truss and the cable are anchored to the ground in both ends, and the upper end is free to move laterally. The lateral force, F, results in a horizontal displacement, δ. Therefore, based on Figure 1, we have:
As shown in Figure 1, the horizontal equilibrium is formulated as:
Therefore, the truss element is unstable under lateral loading.
Therefore, the cable element is characterized by an “effective” stiffness under lateral loading (k) which is independent of the properties (E and A), and is equal to: