### Cable members

The analysis of cable members requires special treatment because of their pure axial capacity, large displacements and highly non-linear behaviour.

Cable members never actually go into compression, they simply sag or change their shape so that they are in equilibrium at all times. They have no flexural, torsional or shear capacity, and resist lateral loads by tension alone.

Cable members can be loaded with UDLs, thermal loads, prestress loads and self weight. For "Local" or "Global projected" UDLs, the total load is equal to the load per unit length multiplied by the actual (for "Local") or projected (for "Global projected") distance between the end nodes. For "Global inclined" UDLs, the total load is equal to the load per unit length multiplied by the unstrained cable length.

Cables must be loaded with at least one uniformly distributed load (self weight will do) in every load case they are analysed for. If there is no UDL on a cable, SPACE GASS will apply an artificial lateral UDL equal to one-tenth of the self-weight of the cable. While this adds a non-existent load to the model, it is not likely to affect the results significantly due to the small magnitude of the load.

Note that the procedure of converting cables without UDLs to tension-only members in SPACE GASS 9.03 and earlier versions is no longer done.

Restraining nodes connected to cables

Cable members have zero moment capacity and must be assumed to be pin-ended even if the end fixities are input as FFFFFF. This would normally cause rotational instabilities in the nodes that are connected only to cables, however SPACE GASS recognises this and automatically restrains these rotations if instabilities would occur.

Cable convergence

Convergence is often a problem for structures which contain cables because of their large deflections and highly non-linear behaviour. There are four recognized methods for obtaining convergence.

1. One load step, many iterations, no damping.

2. One load step, many iterations, deflection related damping.

3. One load step, many iterations, damping with uniform relaxation.

All four methods give the same results for the same final convergence. Methods 1 and 2 are generally the fastest but they don’t achieve convergence in all structures, especially flexible structures. Methods 3 and 4 are more likely to achieve convergence but sometimes require more iterations. For methods 3 and 4, the number of iterations required is pre-defined by the number of relaxation steps or load steps that you specify at the start of the analysis.

For each method, but methods 3 and 4 in particular, it is generally apparent after only a few iterations whether convergence is going to be achieved or not. If the convergence level is not steadily creeping upwards or has not reached about 60% or 70% by 5 or 6 iterations then it is unlikely that convergence will be achieved. If this happens, it is generally best to stop the analysis and then start it again with a different method, or change the damping, or increase the number of load steps. For example, using method 4, it is quite feasible that 50 load steps will converge where 40 load steps will not.

If you lower the convergence accuracy, the analysis may not converge sufficiently and you risk getting incorrect results. It is particularly important that you don’t lower the convergence accuracy for highly non-linear structures such as those that contain cables.

Cable prestress

The prestress load you apply to a cable is not likely to be the final axial force in the cable at the end of the analysis. This is because the axial force changes as the cable stretches or sags as its end nodes move. If you wish to achieve a particular axial force at the end of the analysis then a trial and error process is required. This involves setting an initial prestress force, performing the analysis, checking the final axial force, adjusting the prestress and repeating the process until the desired axial force is achieved. This is a common requirement in post-tensioned concrete applications where the tendons are jacked to a known tension.

In some instances, you may wish to apply a prestress load to a cable member instead of specifying a non-zero unstrained cable length. The prestress load P that is equivalent to an unstrained cable length L is given by the equation:

 where D = chord length, A = cross sectional area, E = Young’s modulus of elasticity.

! IMPORTANT NOTE !

If cable members exist in your structure, it is imperative that you specify them as "Cable" members in your SPACE GASS model. If you try to model them as "Normal" or "Tension-only" members, the results will be incorrect.