| Applies To | |||
| Product(s): | RAM Structural System; Ram Frame | ||
| Version(s): | Any | ||
| Area: | Analysis |
Eigen Value Error Messages
The Eigen Value (eigenvalue) error message is given when the program cannot calculate all the requested mode shapes of the building.
The most common cause is an instability in the model. It is also possible to get an instability error instead.
The first step is to analyze the Dead Load or any single gravity load case individually and correct any reported instabilities.
The error can also occur when there is an extreme inequality between the mass and stiffness at different levels. In buildings with partial levels, this is common, as there are some levels that do not have many lateral members framing to the diaphragm. Often, the mass for these levels is small, but highly eccentric in relation to the adjacent levels. Sometimes, the masses can be lumped with adjacent levels, either above or below, in order to simplify the model and allow the program to run. This can be done using the Loads - Masses command, and changing the value in the Combine cell for such levels.
A model will sometimes run with a reduced number of modes. The program default is to solve 3 modes per rigid diaphragm in the model. The first 3 modes are typically the controlling modes so running the analysis with fewer modes may be acceptable. To do this create a new load case called "Modes" of the type, Dynamic - Eigen Solution. When you click [Add] you will be prompted to select the desired number of modes (see illustration).
Sometimes these problems are caused from having highly flexible or unstable structures. If the exact modes shapes are not required, you can solve the problem by assigning the period (or frequency) for the lateral load case(s) explicitly, so that the program does not have to calculate it.
For seismic loads, this is done by setting T=Ta (or "Use Method A" in the UBC code) under the "T" heading in the load case definition (see illustration). The program will then use the approximate period of the building, and will not have to calculate the modes. If you analyze the building using the approximate period, you can observe the deflection at each level, and also review the loads and applied forces so that you can see how much load is being applied at each level.
For wind loads per IBC or ASCE, the same type of thing can be done in relation to the building frequencies. Set the frequency of the building in both directions to n=1 Hz (or some other estimated value) and also set the Gust Factor = 0.85 to avoid having wind loads which require an eigen solution (see illustration).
Please note that performing the eigen solution to calculate the period in conjunction with P-Delta can be more difficult for the program to solve. The softening of the stiffness matrix performed as part of the P-Delta analysis can even lead to an instability for the eigen solution where the second order effects are large. Likewise, solving the eigen solution for a dynamic load case with eccentricity requires 4 times as many modes compared to concentric analysis. When tension-only braces are used in a model, 50% of those members stiffness are considered in the eigen solution.
For additional information related to semi-rigid diaphragms and the eigen solution, please refer to the links below.
Ritz Vectors - Version 14.06.00 and later
In version 14.06.00, an alternate method for calculating modal results using Ritz vectors was added as a feature in RAM Frame. Ritz vectors use an approximate method that produces results that are the same or nearly the same as the Eigen analysis. Generally, Ritz vectors are faster and more reliably converge to the solution. Because Ritz vectors converge more reliably, they are another tool that can be used to resolve Eigenvalue errors.
In version 15.00 a third option for performing the Eigenvalue analysis (periods and modes) was added, Lanczos Eigenvalue solver. The new solver has some remarkable advantages over the other two solutions: the new solver is faster than other two solutions (i.e., subspace iteration and Ritz vectors solution) and it consumes significantly less memory and it is a very robust solution (the Lanczos implementation is an open source code developed by Rice University and widely used in academia and in industry).
When eigenvalue errors occur, we suggest starting with the Ritz vector option and trying the others as needed.
The Eigenvalue analysis option is selected in RAM Frame - Analysis mode - Criteria - General:
See Also
RAM Instability In Finite Element Analysis
[[RAM Frame - Dynamic Analysis FAQ]]