Stability

Instabilities occur whenever a node can deflect or rotate without limit.  Put another way; a node is unstable if there is nothing to restrain it.

With that one statement you can understand and resolve any instability problem. Instabilities are easy to understand and easy to fix. The next section explains what RISA-3D does with instabilities. The following sections provide some simple examples of instabilities and their resolution.

For additional advice on this topic, please see the RISA Tips & Tricks webpage at risa.com/post/support. Type in Search keywords: Instabilities.

Instability Procedure

Because many instabilities are inconsequential to the results yet they prevent a solution RISA-3D locks them as they are discovered and proceeds with the solution. This locking is a boundary condition that removes the degree of freedom from the solution.  A reaction (if any) is not calculated and that is one of the dangers of ignoring instabilities. See Testing Instabilities to learn how to test if an instability is affecting the results.

At the end of the solution you will be notified that nodes have been locked and that you may view the affected nodes in a model view.  These locks will also be reported in the Reactions spreadsheet.

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Instability Causes

Common causes of instabilities are briefly mentioned here and then highlighted in the following examples.

Member End Releases – Boundary Conditions

Overuse of member end releases and/or boundary conditions is by far the most common cause of instability as shown in the examples below.  The solution is to either remove a member end release or change a boundary condition so that the node is restrained. At least one member or boundary needs to be fixed to each node to prevent instability. If you think of a node as the end of a member and specify no release for that member end this member still will not experience moment at the end if all other elements are left unfixed.

Unconnected Elements

Nodes that are not connected into the model cause instabilities.  This is much more common in models without Physical Members as can be seen below. The solution may be to merge the model with the model merge feature.

Flexible Elements

Members or plates with relatively small properties such as a long member with a moment of inertia of 1.0 in⁴ can cause instabilities. This is usually not a problem unless the members are not used properly.

Instability Examples

These simple examples are provided to directly address the common scenarios that occur in structural modeling. You will notice a recurring theme so once you understand one or two of them you will have a handle on the causes and resolutions for most instabilities, including those in more complex models.

Remember the golden rule as you look at each example:  A node is unstable if there is nothing to restrain it.

Cantilever Beam/Column

If a member end release is specified at the free end of a cantilever the node becomes unstable because it is free to rotate without any resistance.

Cause:  Specifying a member release at the free end of a cantilever member.

Resolution:  Remove the member end release.

If the member is not released from the node then the member provides resistance to the node so that it cannot rotate without limit. The member end moves and rotates and the node goes along for the ride. There will be no moment at the free end of the member since there is nothing there to pass moment.

Column at a Support

If a pinned column base is modeled with a pinned boundary condition AND a member end release at the base of the column the node becomes unstable because it is free to rotate without any resistance.

Cause:  Specifying a pinned boundary condition AND a member release.

Resolution:  Either remove the member end release or specify a fixed boundary condition.  Do not do both unless you want a fixed column base that resists moment.

If the member is not released from the node then the member provides resistance to the node so that it cannot rotate without limit. The member end rotates and the node goes along for the ride. There will be no moment at the base of the member since the pinned boundary cannot resist moment.

If instead the boundary is specified as fixed then the boundary provides resistance to the node so that it cannot rotate. The member end release allows it to rotate while the node does not. There will be no moment at the base of the member since the fixed boundary cannot pass moment through the member end release.

Simply Supported Beam

If a pinned beam end is modeled with a pinned boundary condition AND a member end release the node becomes unstable because it is free to rotate without any resistance.

Cause:  Specifying a pinned boundary condition AND a member release.

Resolution:  Either remove the member end release or specify a fixed boundary condition. Do not do both unless you want a fixed member end that resists moment.

If the member is not released from the node then the member provides resistance to the node so that it cannot rotate without limit. The member end rotates and the node goes along for the ride. There will be no moment at the end of the member since the pinned boundary cannot resist moment.

If instead the boundary is specified as fixed then the boundary provides resistance to the node so that it cannot rotate. The member end release allows it to rotate while the node does not. There will be no moment at the end of the member since the fixed boundary cannot pass moment through the member end release.

Beam-Column Connection

If a pinned beam/column connection is modeled with a released column end AND a released beam end the node becomes unstable because it is free to rotate without any resistance.

Cause:  Specifying a released column end AND a released beam end.

Resolution:  Either remove the column end release or the beam end release. Do not do both unless you want a fixed connection that resists moment.

If the column is not released from the node then the column provides resistance to the node so that it cannot rotate without limit. There will be no moment at the connection since the beam end release cannot pass moment.

Simple Truss

If a truss panel point is modeled with releases at the ends of EVERY member connecting to that point the node becomes unstable because it is free to rotate without any resistance.

Cause:  Specifying all members with released ends.

Resolution:  Either remove one end release or add a rotational boundary condition at each node. Do not do both.

If one member end is not released from each node then the member provides resistance to the node so that it cannot rotate without limit.  There will be no moment at the member end since the remaining members have end releases and cannot pass moment.

You can also solve the problem with a rotational boundary condition at each node. Using the ALL code you can restrain each node for rotation and proceed to use end releases at all members.

2D Models

If you are solving a 2D model defined in the XY plane and you're only interested in the planar action, you could enter "ALL" and put an "F" (for Fixed) for Z translation, X Rotation and Y Rotation. See the following figure:

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There is a 2D Mode button which can quickly add Fixed boundary conditions to all nodes in the Z translation:

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Unconnected Elements

If a node, member or plate is not connected to the model then there will be instability. With the use of Physical Members this is rare in a model that only consists of beam elements however those that have plates or finite members can be defined in a way that they are not connected.

Cause:  Unconnected elements.  The portal frame is not connected to the plate elements because the bottoms of the columns do not fall on plate corners. The plates are stable however the portal frame is not.

Resolution:  For beam models, run the Model Merge feature. For plate models redefine the mesh so that plates are connected at their corners. Model merge will not solve problems caused by lack of plate continuity.

3D Models

For three-dimensional models, torsional instabilities are not uncommon. A "torsional" instability is where a member, or a series of members, is free to spin about its centerline (local x) axis. This diagram illustrates such a situation:

The member M3 as a whole is unstable because there is nothing to restrain it from spinning in torsion. At nodes N1 and N2 the columns and beams framing into the member (members M1, M2, M8, M9) are pinned. The same can be said of Members M7 and M10 framing into the member ends. Therefore, there is nothing in the model that will restrict the torsional rotation of the M1 beam. 

Another example of a potential local instability is X-bracing with a center node and loaded with self-weight. X-bracing has almost no out-of-plane stiffness, so even a little bit of out-of-plane load applied at the center node could cause an instability. (The out-of-plane load could come from a P-Delta analysis, lateral load, etc.)  A diaphragm with very weak out-of-plane properties modeled with plate elements can also be a source of potential local instability.

Testing Instabilities

Although some can be ignored, keep in mind that not all instabilities are necessarily inconsequential. Look at the following model:

This is an example of a single bent frame that is laterally unstable.  To obtain a solution the lateral direction would be locked and a solution obtained, though not a correct one. The warning message may be annoying if you know the instabilities being locked are of no consequence, but there won't be any surprises.

The best way to test whether an instability is inconsequential or not is to apply a Reaction to the node in the unstable degree of freedom.  Then re-run the model and examine the reactions. If the Reaction that is restraining the instability is showing a non-zero force or moment, then you have a problem with the model that must be corrected for you to get valid results. If the Reaction that is restraining the instability is showing a ZERO force or moment, then the instability is inconsequential to the results.