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Torsional stability

It is well known that a structure without any fixed point can not be analyzed. It would be as if floating in a state of weightlessness. Any load that we apply to the structure will move the structure. If the load is constant, it will speed up as per the known equation F = m · a, hence with an acceleration of F / m.

That’s why the whole structure must have a fixed point, which we call mounts, responsible for counteracting the actions applied.

Now, for a structure to be in equilibrium it is not enough that it does not move. It should also be stable against rotation. If a structure rotates, although it does not move, is not in balance.

In the case of the tensile structures, where the majority of elements can only withstand tensile loads, consideration of move does not have much importance. But as soon as rigid bars appear to bear moments, things change. Because we know that a moment produces a twist. Often we solve the problem by fixing the node to rotation and displacement. All the nodes in WinTess other than moment resisting ones on rigid bars like the ones on membrane, cables, tubes, etc. supports displacement in X, Y and Z directions.

Simple node: No moment allowed

If the node is rigid (which support moments), we see that it has more degrees of freedom: the three displacements mentioned earlier over the three rotations in X, Y, and Z.

Rigid node: Supports moments

In the following image, we see an inverted umbrella having a paradigmatic example at the base node: it must be a fixed node that neither moves nor rotates, since otherwise the umbrella is going to collapse.

Paraguas invertido

Inverted umbrella

On the other hand, in the following image the situation is very different. It is a question of a membrane with a perimeter by means of apexes and border cables. In the top part, nevertheless, there is a tube which replaced the border cable. In fact this tube is formed by a set of rigid bars, capable of supporting moments as set of these bars will behave like a beam with a distributed load creating tension on the membrane.

Membrana con un tubo rígido de borde

Membrane with a rigid tube

Ends of this tube composed of rigid bars can be fixed or articulated. If it is fixed it will not turn in any way and the node will support moments created. Its distortion and maximum moment leading us to a much smaller tube. Nevertheless the design of a fixed node for a tube is complicated and it can turn out to be expensive.

Barras rígidas que forman el tubo

Rigid bars that form the tube

As such, we do not want to fix the ends of this tube. The solution seems easy: we are going to think that the end nodes of the tube are allowed to rotate:

Rigid node which can be rotated freely at the ends

If we do this and start to calculate this this structure, we see that WinTess fails to balance. It seems that it stands still in a specific position which is not balanced. If we define much movement of the structure then it maybe able to balance. But you can now see something weird happens.

What happens?
Simply that the tube rotates around its axis and finds no impediment, since the two ends are allowed for any type of rotation. Can we solve this problem? In some cases it will be very easy and in others it will be more difficult.

WinTess allows rotation of a node in a different manner according to the axis X, Y, and Z. If the rotation axis of the tube coincides with one of these coordinate axis it will be very easy easy: simply prevent the rotation point in this direction. In our example the rigid tube is parallel to the Y-axis. Therefore if we prevent rotation of its ends in the Y-axis, the tube will not be able to turn more and find the balance quickly.

Rigid node that rotates in X and Z, but not in Y

In fact to prevent rotation at only one end is sufficient to find the balance, but during construction we need to know if two ends or only one must be restricted to rotation.

Unfortunately if the rotation axis of the torsion does not coincide with any main axis, the issue becomes much more complicated. WinTess cannot do it straight and the only solution will be to prevent all the rotations. Thus there will not be problems with the rotation to torsion, but this will come with all the advantages and disadvantages that this implies.

These torsion mechanisms (i.e., this lack of balance to torque) is often overlooked, since it seems that they do not intervene in the result. But we will notice immediately to see that the program does not converge and find the balance.

Ramon Sastre, May 2013

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