 # G.8.2.1 Linearized Cable Members

Cable members may be specified by using the MEMBER CABLE command. While specifying cable members, the initial tension in the cable must be provided. The following paragraph explains how cable stiffness is calculated.

The increase in length of a loaded cable is a combination of two effects. The first component is the elastic stretch, and is governed by the familiar spring relationship:

 F = Kx

where
 Kelastic = EA/L

The second component of the lengthening is due to a change in geometry (as a cable is pulled taut, sag is reduced). This relationship can be described by

F = Kx

but here,

$K s a g = 12 T 3 w 2 L 3 ( 1 cos 2 ⁡ α )$
where
 w = weight per unit length of cable T = tension in cable α = angel that the axis of the cable makes with a horizontal plane (= 0, cable is horizontal; = 90, cable is vertical)

Therefore, the "stiffness" of a cable depends on the initial installed tension (or sag). These two effects may be combined as follows:

$K c o m b = 1 ( 1 / K s a g + 1 / K e l a s t i c ) = ( E A / L ) ( 1 + w 2 L 2 E A ( cos 2 ⁡ α ) 12 T 3 )$
Note: When T = ∞ (infinity), Kcomb = EA/L and that when T = 0, Kcomb = 0. It should also be noted that as the tension increases (sag decreases) the combined stiffness approaches that of the pure elastic situation.

The following points need to be considered when using the cable member in STAAD :

1. The linear cable member is only a truss member whose properties accommodate the sag factor and initial tension. The behavior of the cable member is identical to that of the truss member. That is, it can carry axial loads only. As a result, the fundamental rules involved in modeling truss members have to be followed when modeling cable members.

For example, when two cable members meet at a common joint, if there is not a support or a 3rd member connected to that joint, it is a point of potential instability.

2. Due to the reasons specified in 1) above, applying a transverse load on a cable member is not advisable. The load will be converted to two concentrated loads at the two ends of the cable and the true deflection pattern of the cable will never be realized.

3. A tension only cable member offers no resistance to a compressive force applied at its ends. When the end joints of the member are subjected to a compressive force, they "give in" thereby causing the cable to sag. Under these circumstances, the cable member has zero stiffness and this situation has to be accounted for in the stiffness matrix and the displacements have to be recalculated. But in STAAD.Pro, merely declaring the member to be a cable member does not guarantee that this behavior will be accounted for. It is also important that you declare the member to be a tension only member by using the MEMBER TENSION command, after the CABLE command. This will ensure that the program will test the nature of the force in the member after the analysis and if it is compressive, the member is switched off and the stiffness matrix re-calculated.

4. Due to potential instability problems explained in item 1 above, you should also avoid modeling a catenary by breaking it down into a number of straight line segments. The cable member in STAAD.Pro cannot be used to simulate the behavior of a catenary.

By catenary, we are referring to those structural components which have a curved profile and develop axial forces due their self weight. This behavior is in reality a nonlinear behavior where the axial force is caused because of either a change in the profile of the member or induced by large displacements, neither of which are valid assumptions in an elastic analysis. A typical example of a catenary is the main U shaped cable used in suspension bridges.

5. The increase of stiffness of the cable as the tension in it increases under applied loading is updated after each iteration if the cable members are also declared to be MEMBER TENSION. However, iteration stops when all tension members are in tension or slack; not when the cable tension converges.