You’ve just finished building your ETABS structural model. It may be a huge multi-level high-rise building or a simple low-rise structure. Either way, you have spent time and effort building your future structure as a three dimensional representation and its ready to run for the very first time. With the click of a button you run the analysis and the anticipation is palpable. The analysis finishes and there is a warning… “structure is unstable or ill-conditioned”, your heart sinks, does this mean your structure will collapse? You were so careful with your meshing and snapping too. What should you do next?…

The error “structure is unstable or ill-conditioned” is a warning that is produced by ETABS after the structure has been analysed. The warning is generally caused by a member which produces a loss of accuracy of 11 digits or more during the analysis. An excessive loss of digits beyond 11 is regarded as too inaccurate for analysis purposes and should be investigated and rectified by the designer.

If you receive the error message in ETABS “structure is unstable or ill-conditioned”, you should not proceed any further. Do not use any results which that model has produced. In all likelihood the results may be be orders or magnitude wrong. This is true for all results including deflection, stress, forces and base reactions. You should absolutely fix this error before moving to the next step in your analysis. So how do we fix this? Lets take a closer look…

The structure is unstable or ill-conditioned!! Check the structure carefully for:

– Inadequate support conditions, or
– One or more internal mechanisms, or
– Zero or negative stiffness properties, or
– Extremely large stiffness properties, or
– Buckling due to P-Delta or geometry nonlinearity, or
– A frequency shift (if any) onto a natural frequency

ETABS Software – Maybe for your latest model you’ve just analysed

First I’m going to give you the quick answer so you can go away and critique your own model and fix your issue as fast as possible. Then I’m going to go through a real example on a project I’m working on to show you a step by step process of how I solve this issue myself.

Steps for fixing the “structure is unstable or ill-conditioned” warning message:

1. Make sure you are running the Standard Solver within ETABS as this produces the most detailed instability data
2. Open the error/warning log (found in the same folder location as the ETABS *.edb file)
3. Identify the locations which have a loss of accuracy of 11 digits or more
4. Navigate to these locations within your model using the x, y and z coordinates provided.
5. Thoroughly inspect the location for abnormalities in the modelling including elements not snapped together and irregular mesh.
6. Once all locations have been rectified, re-run the analysis using the standard solver to ensure all instabilities have been fixed.

Running the Correct Analysis for Identifying Locations where Structure is Unstable or Ill-Conditioned.

If you have encountered this message and you did not use the “Standard Solver” for your analysis, the very first thing you need to do is re-run your analysis using the “Standard Solver” immediately (if you already used the Standard Solver and know the difference between the solvers, skip to the next section, if not, continue reading)…

in ETABS, there are three different solver options. These are found by navigating to…

Analyze >> Advanced SAPFire Options…

The three possible options with an explanation for each is as follows…

Multi-threaded Solver (Don’t use this one)

This is the fastest solver out of all the options. It uses multiple cores in your machines GPU to solve the analysis and also uses a large amount of RAM. This is the reason why the multi-threaded solver runs so fast, but this comes at a cost… It gives almost no instability information. This means that if your receiving the error that your structure is unstable or ill-defined, it will be like trying to find a needle in a haystack as to where the issue is!!! This solver is best used when you have already ran your model a few times and are confident that it is stable and free from major issues or warnings.

For more information about “how to check if your ETABS model is correct” and outputting logical answers, take a look at THIS article.

Advanced Solver (Don’t use this one)

The advanced solver uses multiple cores in your GPU to solve the analysis similarly to the multi-threaded solver. Its a little easier on the RAM however so it takes a little longer to run. It does provide a little more information on instabilities and errors in your model, however still not that useable, especially if your error is “structure is unstable or ill-conditioned”.

Standard Solver (!! Use this one !!)

The standard solver is the one you are after for resolution of instabilities. It does however take the longest time to run. The trade off though is that you receive a lot more information and exact locations of the instability. This makes it much easier to fix your model and move on to the next stage of your design.

Reading the Error and Warning Log in ETABS once the Analysis is Finished.

Now that we have ran the standard solver, we now need to locate the position of our instabilities (or instabilities depending on how bad your model is!!).

For this you need to access the error and warning log after ETABS has finished analysing your building. The error log is found in the same location as your model file (*.ebd file) for the model you’ve just analysed.

Once open, scroll down to the section that starts with…

** Warning***

NUMERICAL PROBLEMS ENCOUNTERED DURING EQUATION SOLUTION:

ETABS – Maybe for the latest model you’ve just analysed

A list of the inaccuracies and “loss of digits then follows. It may look a little bit like this…

Lets take a look at what each column represents…

Column	Explanation
Type	The type of element with the loss of accuracy associated with it. For example joint.
Label	The unique label name for this element in question
DOF	The degree of freedom for the error (UX, UY, UZ or RX, RY, RZ etc.)
X-Coord	The x-coordinate where the loss of accuracy exists
Y-Coord	The y-coordinate where the loss of accuracy exists
Z-Coord	The z-coordinate where the loss of accuracy exists
Problem	The issue with the element in question (for example, most commonly “Lost accuracy”)
Value**	The value of the error (for example number of digits lost)

For the “structure is unstable or ill-conditioned” error, the “value” column is the first important piece of information (hence the double asterisk). Lets take a look at this one first…

When you press the run button in ETABS its analysis calculates the stiffness matrix and other calculations on your building with an accuracy of 16 digits. When poor modelling practice is used, or when the analysis involves systems of significantly different stiffness, digits of accuracy can be “lost”.

Some loss of accuracy is normal and common for most computational software packages. However when the loss of accuracy becomes excessive, this can indicate that something is wrong with your structure or the modelling is incorrect.

Here is a summary for the range of digits lost in your analysis:

• Less than 6 Digits Lost: The analysis is reasonably accurate. So much so that ETABS will not report on a loss of digits of 6 or less.
• Between 6 and 11 Digits Lost: This can start to indicate an issue at various locations in your model. However most of the time they are of little concern, especially if the value is in the 6 or 7 range. Value closer to 11 should be highly scrutinised, however all values should be looked at with a keen eye (use engineering judgement!). If you are unsure your model is correct, take a look at THIS article which gives you some handy tips on how to ensure that you can rely upon the answers your ETABS model is producing.
• Over 11 Digits Lost: This is regarded as excessive loss of accuracy to the point where the results produced are likely erroneous. It is these locations which you should be most interested in and track down what is causing the issue. It is these locations causing the “structure is unstable or ill-conditioned” warning within ETABS.

The process now is to pinpoint the location of each excessive loss of accuracy using the x, y and z coordinate information in the warning log. Simply navigate visually to the location and then inspect the region thoroughly for anything that looks odd. This may include:

• Meshing which doesn’t make sense, too small or too irregular
• A member which is a mechanism. For example a cantilever beam with an end release where it should be fixed.
• Pins at mid-span on members (this commonly occurs for columns which are spanning double or triple height).
• Members aren’t properly snapped to one another therefore not structurally connected in the eyes of ETABS.

The possible causes are really quite varied. Because of this, lets go through an example I encountered recently on a model I was performing a design check on…

Example “Structure is Unstable or Ill-conditioned “Scenario

Lets look at an example project I’m currently looking at. Its located in Brisbane Australia. The general specs of the building is 24 storey height, office building, relatively small floor plates (770m²) with an eccentric core. Here is an ETABS snapshot of the typical office floor plate (3D perspective view of an isolated single floor plate)…

I’ve now run the analysis and I’m getting the dreaded “structure is unstable or ill-conditioned”. Here is the warning and also the location of accuracy loss more than 11 digits…

Here I have three instances of excessive accuracy loss but only two locations. The bottom two instances appear to occur at the same joint however are giving errors for two different degrees of freedom, UX and UZ. Lets take a look at this location first. Here is that joint isolated in the model viewer…

I’ve turned joint labels on here to pinpoint the exact location. The joint in question is number 642. There doesn’t’ appear to be anything sinister going on. The joint corresponds with a joint in the frame member spanning up and down the screen. There is no end release at this joint so the member should be stable. However this joint is actually redundant for the purposes of the beam. To try and solve the instability error, I will remove this joint which is apparently not required. Here is what it now looks like…

The joint is now gone. After re-running the model, this instability warning is now gone as well.

Lets take a look at the next warning location. It is at the corner of the eccentric core…

Here we can see that the two walls at the corner of this core are not joined adequately. There are two ways to tell this, firstly the wall hasn’t automatically squared off at the corner acknowledging that the two walls join, also there are overlapping joint name labels, this indicates that there are two joints in very close proximity to each other.

Turning the unique joint names on in your model view is a great way to see snapping errors such as this. It wasn’t exactly clear why these walls weren’t touching, in all other levels at this location the snapping of the walls worked fine. I was able to fix this issue by re-drawing the wall running in the left-right direction for thsi level only. Here is what it looked like after the fix…

Now here is the really interesting part and the best evidence as to why you shouldn’t let the “structure is unstable or ill-conditioned” error stay in your model. Here is a comparison of the overall core reactions at the base of the building for dead load only…

Result	Vertical P (kN)	Moment M2 (kNm)	Moment M3 (kNm)
With Instability Errors	-97,229	52,671	45,724
Without Instability Errors	-89,666	68,713	34,802
Comparison Difference (%)	7.7%	23%	24%

These differences in results are hardly small and can result in significant errors in wall thickness, reinforcement and foundation assumptions in the model and potentially for the built structure! This is the reason why you should always check your work and perform all necessary QA procedures which involves allowing other Structural Engineers to spot check your work also.

Additional Reading

If you found this article useful and enjoy using ETABS as part of your day-to-day Structural Engineering life, you may also find these articles interesting:

• HOW TO CHECK IF YOUR ETABS MODEL IS CORRECT – Sheer Force Engineering
• SHELL VS MEMBRANE, WHICH ONE TO USE IN ETABS – Sheer Force Engineering
• MODELLING CRACKED SHEAR WALL BEHAVIOUR IN ETABS – Sheer Force Engineering
• ETABS oAPI/API TUTORIAL: HOW TO CRACK AUTOMATION SPEED SECRETS USING VBA AND EXCEL – Sheer Force Engineering
• HOW TO SET UP GRIDS IN ETABS – Sheer Force Engineering