| Applies To | |
| Product(s): | AutoPIPE |
| Version(s): | ALL; |
| Environment: | N/A |
| Area: | |
| Original Author: | Bentley Technical Support Group |
| Date Logged & Current Version | Feb. 2017 11.00.00.22 |
Problem:
What are the Participation Factors and the Captured Modal Mass in AutoPIPE's frequency report?
What should be the minimum acceptable percentage value in all 3 axis directions?
Solution:
The participation factor is a measure of the importance of the mode in earthquake type load. The captured modal mass is another way of quantifying the importance of the mode and the two are related. The captured modal mass percentage shows how much of the response is attributed to a particular mode and also shows the mode orientation (X, Y or Z). The sum of modal masses should be 100% if all modes are counted. But since many modes are not counted, the sum is less than 100 and hence the importance of the ZPA and missing mass options for dynamic analysis. Please refer to the topic "Missing Mass and ZPA Correction" in the online help for more information.
The participation factors are calculated from the product of the mode shape, the mass matrix and a vector of ones. For mode i the participation factor is calculated as:
Participation_Factor_i= Transpose(ModeShape_i) * MassMatrix * {1}
The mode shape is mass normalized. The above equation is used three times for X, Y and Z directions.
The mass participation report illustrates how sensitive each of the piping system’s modes are to the dynamic loading. High modal participation factors indicate that the mode is easily excited by the applied dynamic forces. If subsequent displacement reports indicate high dynamic responses then the modes having high participation factors must be dampened or eliminated. Once a particular mode is targeted as being a problem, it may be viewed in the mode shape report, or graphically via the animated mode shape plots.
A common rule of thumb is to capture at least 75% of the modal mass but the missing mass correction will capture the remaining modal mass for an accurate dynamic analysis.
Question:
Do we have to make sure mass participation is 75% or higher in all 3 directions (X, Y and Z)?.
Answer:
The higher the captured modal mass, the better accuracy you would get for your results. Try increasing the number of modes and check whether your modal mass is reacting to increase in modes. Some guidelines on trying to determine whether you have sufficient modes is as shone on Wiki page here.
The usual procedure for determining how many modes are sufficient is to extract a certain number of modes and review the results; then to repeat the analysis while extracting 5 to 10 additional modes, and comparing the new results to the old. If there is a significant change between the results, a new analysis is made, again extracting 5 to 10 more modes above those that were extracted for the second analysis. This iterative process continues until the results taper off, becoming asymptotic. If results continue to be significantly different for different cut-off frequency, this would indicate that a particular loading on a specific piping layout has higher frequencies.
Again, It is important to capture a significant amount of mass in all directions. For a complex models, anyone's guess which direction will be significant dynamically. Thus the mode shape and mass participation results provides an indication on number of modes / frequency set point required.
The important part is that you capture all the modes when carrying out dynamic loading, or apply the maximum load statically using the ZPA.
Remember, ZPA is very conservative. If a model has captured most of the mass, this would suggest that the dynamic approach will be OK, and ZPA is not needed. However, if one prefers conservative results, include ZPA. This is an Engineering decision outside of Bentley's scope.
See Also
Options to increase the participation factors