Cable#
Cables are flexible nodes. They can be used to model ropes, chains, elastic bands, slings, grommets, anchor lines, crane wires or anything else that has a length and an axial stiffness.
Cables can have a mass, but do not have to.
Cables can have a diameter, but do not have to.
Cables are added between Connections (either Points or Circles). This means that a cable can only be created when its endpoints are already in the model.
Add a cable by selecting the points/circles that it needs to connect and then press “+ Cable”:
Force calculation#
As a minimum a cable has a length and a stiffness. The length of the cable is the length at rest or material length \( L_0 \). This is the length of the cable when no force is acting on it.
The force in the cable (tension) is calculated from its stretched length and its stiffness. The stretched length is calculated from the actual geometry of the model: in the positions of the Points.
To continue the example we add some watches to the cable node to view its actual length and tension. We then change the position of the second point (Point 2) to x=10, y=0 and z=0.
The resulting actual length of the cable is 10m. We then change the (material) length of the cable to 5m. The force can now be calculated using hooke’s law where \(k = EA / L_0\):
\( F = k \cdot x = ({ EA \over L_0} ) \Delta L \)
\(\Delta L = L_{stretched} - L_0 = 10 - 5 = 5 \)
\( F = ({ 10kN \over 5m }) \cdot 5m = 10 kN\)
Adding intermediate connections#
The geometry of a cable is not limited to two points. Intermediate connections can be added and circles can be used instead of points.
One of the ways to do this is by dragging and dropping the nodes to the cable’s connections. This can be done from the node tree as well from the model.
Another way to add them is via the “node picker”.
The order of connections can be changed using drag and drop. Connections can be removed using the delete key or the button.
The direction in which a cable runs over a circle is determined by the axis direction of the circle and the direction of the cable. It can be reversed by checking the box in front of the name of the circle.
Force#
The force in the cable is calculated in the same way as for a cable between two points. This means that the tension in the cable is constant over the length of the cable.
Diameter#
A cable can be given a diameter. The affects the actual length of the cable as this is calculated for the centerline.
This only affects the connections between cables and Circles (or round-bars). Points will always be located on the centerline of a cable. If you need a cable that runs over a point then use a circle with a diameter of zero.
Mass#
Mass (weight) of a cable can be specified as mass per length. Here length refers to the unstretched or material length of the cable (the cable does not gain weight when it is stretched). For convenience it is also possible to provide the total mass of the cable however this value will change if the material length of the cable is changed.
Elastic catenary#
When a non-zero mass is given, the cable forces will be calculated using the elastic catenary equation instead of hooke’s law (hooke’s law is part of the elastic catenary equation).
Mass and intermediate connections#
Combining mass and intermediate connection is a bit troublesome because there is no unique solution. Consider the following example with one continuous cable with weight running over a point in the middle. This situation is unstable: without friction in the middle the cable may shift to either side.
DAVE works around this as follows:
distribute the cable material over the cable section based on a massless cable.
then glue the cable to the connections
finally apply weight
The result may be a discontinuity in the cable tension at the connections. This is reported as “friction” and can also be obtained from the “segment end tensions”:
Note also that when catenaries are used the actual length is still based on the taut (massless) geometry.
The good news is: for rigging applications where the tension in a cable (sling, grommet) is typically much larger than the force due to the mass of the cable this approach is very accurate.