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Cable Elements

Requires: Advanced Level

Cable Background

Cable elements are unique due to their large displacements and exhibit highly geometrical nonlinear behavior.  Cables do not carry shear or bending moments, only axial loads. Cables have a number of uses including suspension and cable stayed bridges, guyed poles and towers, and cable nets.  This nonlinear element is highly sensitive to initial conditions!

Limitations of Cables

Cables in VisualAnalysis assume that Y is the vertical direction, you must use this setting with cable elements.

Cable elements require self weight to function properly, therefore disabling or factoring self-weight will not have any impact on the cable elements, their actual weight is included in each service case or combination that is analyzed.

Due to the fact that they only carry axial loads, loading cables is limited to their own self-weight and concentrated vertical loads only. Concentrated loads must act at a nodal point, thus requiring the cable to be split.  Out-of-plane loading or longitudinal loads are NOT supported (even though analysis may proceed, answers will not be correct.)

We recommend that you wait to split cables until geometry is fully defined.  While VisualAnalysis does allow segments of a cable to be edited after it has been split, there is no "knowledge" of its global identity.  In other words, a cable segment could sag within the overall cable as shown below.  Obviously this does not make physical sense and should be avoided.

Convergence can be a problem with cables.  As previously mentioned, cables are geometrically nonlinear and the solution method is iterative.  It is possible to apply too large a load to a cable element and not have the analysis converge.  In this case, you simply need to apply a smaller load and re-run the analysis.  Cables are also unique in that as you load them they become stiffer and carry more.  As VisualAnalysis analyzes a cable element, it may first cut the load back until it gets a solution.  As the analysis proceeds with each iteration, it may then increment the load back up until it reaches the total applied load.  If it cannot reach the total applied load, it will give you results for the last largest load that it found a solution.

Also related to the nonlinearity of cables is the limitation that you cannot obtain mode shapes for cables or other nonlinear problems in VisualAnalysis. Remember, many principles that are valid in the linear realm are not valid in the non-linear realm (superposition, etc.).

Reporting Cables

Reporting cable results is very similar to reporting member results.  There are two main report categories for cables: Cable Elements and Cable Results.  The cable elements report includes all the typical cable element properties such as the material, end nodes, weight, catenary length, etc.  The cable results report includes the reported cable, displacements, axial force, and axial stress.  The usual reports are available which include the double-click report or you can always create a custom report using the report wizard.

Strange Deflected Cable Shapes?

An upward arc type displacement may be seen in long cables that have been split into several sub cables.  This is a visual artifact and is normal.  When you use the large displacement magnifiers like the default 0.2 factor in the Filter, the displaced shapes might look unreasonable.  Cables deflect in a nonlinear fashion and simple linear-scaling of all displacements can lead to weird cable shapes.  If you encounter this, just set the displaced shape factor back to zero to display the true displaced shape.

Using Cables

In the advanced level of VisualAnalysis, cables are treated as separate element types like members and plates.  Cables are fairly easy to specify, but difficult to model and understand (see above)!  Draw a cable between two end points and define the catenary length of the cable, which is different than the straight-line distance between the nodes.  The cable will sag under its own weight, you can adjust the amount of sag by adjusting the catenary length. 

If you define the catenary length shorter than the straight line length, you apply a pretension or prestress to the cable. The catenary length is entered on the Project Manager or the Edit Cable dialog. There is no way to specify pretension directly, you must back-calculate it from the "stretch" using Hook's law, or similar.

Modeling

Cable cross-sections can be defined using standard round shapes or selected from the shape database.  IES has added some common cable cross-sections to the database, however there are many more available from manufacturers that can be added to the database using the ShapeBuilder.  Another item to keep in mind is that Y is always considered the vertical axis for cables.  This is important as it defines the cable's sag

Loading

Cables do not carry shear or bending moments, only axial load.  Supports can only be pinned (or restrict translation) and always connect to other members "released."  Cables may only be loaded with concentrated nodal loads in the vertical direction.  Because of this, cables must be split before a concentrated load is to be applied along the span. Out-of-plane loading or longitudinal loads are NOT supported.

Splitting Cables

As mentioned previously, if a concentrated load is to be applied to a cable it is necessary to split the cable.  A cable is split using the Model | Split Cable command, much like splitting members.  The dialog box is shown below.

Essentially there are there options for splitting cables: equal segments, equal horizontal projections, and specified lengths.  For the equal segments and equal horizontal projections options, simply specify the number of desired segments.  For the specific lengths option, specify the length as measured on the cable for each segment with the exception of the last segment.  The last segment will automatically become the remaining portion of the cable length.

Results

Analysis of cable members is performed much like any other element in VisualAnalysis.  One exception and note of caution is to check the results very carefully.  After a cable analysis is performed, an Analysis Diagnostic report will immediately appear.  It may be reported that the analysis was completed successfully; however careful attention should be taken to observe the largest load for which a solution was found.  The completed analysis may not have used the full applied load.  For a further discussion on this behavior refer to the Limitations section or to the given references.

Why does it look like my cable is deflecting up when the load is acting down?

This is due to the magnification factor under the General category on the Filter tab.  The magnification factor exaggerates the graphical deflections on the model to make them easier to see.  When a sagging cable has a load applied to it, the area around the load deflects down with the load but as the "slack" is taken out of the cable, areas away from the load actually move up.  Now, if the magnification factor is set to 0.2, this is applied equally across all deflections and can make the shape look unreasonable.  The magnification should be set to zero or something very small to get accurate looking results.

Cable References

A Curved Element for the Analysis of Cable Structures by H.B. Jayaraman and W.C. Knudson.  Computers & Structures, Vol 14, No 3-4, pp. 325-333, 1981.

Some Modeling Aspects in the Nonlinear Finite Element Analysis of Cable Supported Bridges by Raid Karoumi.  Computers & Structures 71, 397-412, Copyright 1999