How does Non-Linear Cable Analysis differ to Linear Analysis?

Cable elements used in structural software are very useful when dealing with cable stayed bridges, suspension bridges, cable nets and guyed poles/towers. However, cables are very difficult to model and analyze because of their highly non-linear traits. When we think of cables, we imagine thin steel wires or ropes which are very flexible. This means that they often undergo large deflections. For these reasons a linear-static analysis is not appropriate and can lead to extremely inaccurate results.

Catenary Cable Elements

A good structural analysis software will include the ability to model structures using a dedicated cable element. Some software do not directly support cable elements but suggest that cables are modelled using a series of tension-only truss elements. However, in order for truss elements to be even remotely accurate in this scenario, the user is required to enter initial nodal positions to guess or estimate the deformed shape of the cable. As you could imagine, in the case of sagging and pre-tension this often becomes a painful task.

Furthermore, if an engineer attempts to model a cable element using a beam member with weak flexural stiffness (Iz and Iy) then when a transverse loading is applied, the deflection will be large without any increase in axial force. This is clearly not how cables behave. A true catenary cable element will take into account the change in geometry due to the transverse loading and "convert" this action into axial tension.

Thus a single catenary cable element will model the true behavior of a cable much more accurately and less painfully than multiple truss elements or a beam element.

Catenary Cable Deflection in SkyCiv

A single catenary cable element showing deflection due to a UDL.

Unique Attributes of Cables

Cables are special in that they only have axial stiffness that supports tension-only. This means that they have no flexural, shear or torsional capacity. Also, as cables are loaded more they tend to become stiffer and can support more.

Why does a Non-Linear Analysis suit Cables?

As stated above, cables are geometrically non-linear because they are highly elastic and flexible. Hence, large deflections are common when cables are involved. In a linear-static analysis, the equations of equilibrium are based on the undeformed geometry before loads are applied. However, if deformation is large (such as when cables exist) it is necessary to consider equilibrium in deformed states. Imagine that as loads are applied, they change direction as the structure deforms and rotates. You can see an example of this in the image below. If the beam experiences small deflection then the path of the loads will remain constant as the beam deflects. However, if the beam is deflecting and rotating significantly then the loads become diagonal rather than vertical. Cables exhibit similar behavior when they deform, and therefore a geometrically non-linear analysis is required.

Loading path under large deflection

The direction of loads changes when deflection is large making a linear-static analysis inappropriate.

The difficulty with modelling cables often arises due to convergence issues. Non-linear analyses are iterative, so the solution may diverge.

SkyCiv Structural 3D - Catenary Cables

The great news is that SkyCiv can now analyze catenary cables via non-linear analysis using large displacement theory. In v2.1 of SkyCiv Structural 3D, users will now be able to model cables using a true catenary cable element. Furthermore, users can control pre-tensioning and sagging of the cable by specifying an initial (or unstrained) cable length.

I hope this article has informed you about catenary cable analysis and why it's unique. If you have any doubts with your modelling and analysis needs our support team can assist you with this. So when you're using SkyCiv Software, please don't hesitate to contact support.

Paul Comino CTO and Co-Founder of SkyCiv
Paul Comino
CTO and Co-Founder of SkyCiv
BEng Mechanical (Hons1), BCom