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Pinned vs. Torsionally-Fixed End Conditions

By default, beam elements transfer bending and torsional moments at their nodes. To prevent the transfer of moments at a node, the end fixities of an element can be adjusted.

If an element’s fixity is changed to be a pinned, no rotational moments are transferred through the element. One could picture this as a ball joint. In addition, the torsionally-fixed end condition is the same as a pinned connection, except that rotation about the element’s longitudinal axis is prevented.

Consider the simple beam layout example in Figure 1:

Figure 1: Simple beam configuration.

Note that both supports prevent rotation and translation for X,Y, and Z directions. Figure 2 represents a scenario where the end conditions are defined as torsionally-fixed (xy pinned), and the supports fully fixed. Given this boundary conditions, the analysis can be performed successfully, and the output corresponds to the expected outcome, illustrated in Figure 3.

Figure 2: Beam configuration with torsionally-fixed end conditions and XYZxyz-supports.

Figure 3: Moment diagram for torsionally-fixed end conditions.

If, however, the end conditions are changed to pinned (xyz pin), the analysis fails with an error message indicating instability in the structure. Since the element is pinned at both ends, the torsional moments caused by the applied force cannot be transferred through the beam and subsequently the beam rotates about its own longitudinal axis.

Figure 4: Beam configuration with pinned end conditions with instability error message.

The scenario represented in Figure 1 can also be replicated by changing the support conditions to XYZz-supports, which restrains overall translation and prevents rotation about the global Z-axis. Furthermore, the end fixities of the primary beam must be defined as fixed. Once more, the structure can be solved and produce results in accordance with our expectations, as shown in Figure 6.

Figure 5: Beam configuration with fixed end conditions and XYZz-supports.

Figure 6: Moment diagram for torsionally-fixed end conditions.

Similarly, the scenario represented in Figure 2, can once again be reproduced by changing the support conditions to XYZ-supports and completely fixing the beam ends for all degrees of freedom. Once more, the model fails to analyze successfully because the beam is not fixed against torsion at the supports and thus cause instability in the model.

Figure 7: Beam configuration with fixed end conditions and XYZ-supports.

The Sumo help file gives the following suggestion:

Unless you have a ball-joint at a certain point, it is usually beneficial for the model’s stability to use torsional pins (type ‘T’ or ‘xy’) instead of full pins (type ‘P’ or ‘xyz’). In practice, even the simplest of connections typically allow some torsional restraint, adding some justification to doing this.