When to use or not to use the "ZPA" option when analyzing a Time History Load case in AutoPIPE?
A common rule of thumb is to capture at least 75% of the total mass. This is fairly easy to achieve for simple geometries but complex, large piping systems with many different pipe sizes and stiffnesses will result in a large number of modes (remember there is one mode for each degree of freedom in the system and each node has up to six degrees of freedom). Therefore, the analysis can get very long and increasing the refinement of the model by adding more finely distributed mass points increases the number of degrees of freedom, which may not achieve much more benefit. Also, remember that for high frequencies the accuracy of the modal analysis approach drops off and the effect of these high frequency modes is not so significant as they are normally in the rigid range with small modal mass. Eventually, it becomes impractical to keep increasing the cut off frequency and refining the model to determine the high frequency modes because it will only a marginal affect.
To help with the problem of model refinement vs mass participation we have two static correction methods
1. Missing Mass Correction
To include all the system mass in the dynamic analysis it has to have all been assigned to the modes determined by the modal analysis. If a significant
amount of mass is missing, then a correction needs to be made. By including Missing Mass in the analysis the following procedure is followed:
2. Zero Period Acceleration
In cases where the dynamic load is applied very near a support or directly at the support as in case of imposed support displacement history or axial fluid transient loads, the support reaction may be near zero or very much less than the actual reaction. The reason can be because the mode shapes involving the movement between the applied load direction and the support point were not computed as specified by the number of modes or cut-off frequency. These missing mode shapes are usually very stiff and hence associated with mode shapes in the high frequency range. In such cases, an additional static earthquake analysis should be performed and the maximum reaction from both static and dynamic analyses should be used. This can be easily done by using the ZPA option which envelops dynamic results with equivalent static results. However, the ZPA method is an approximate one and not exact. Zero Period Acceleration (ZPA) follows this procedure:
For more information on using Static Correction Methods, go to the AutoPIPE Help, Help > Contents > Contents Tab > Reference Information > Analysis Considerations > Modal Analysis > General Principle of Static Correction Methods and theory of Missing Mass and ZPA Correction.
While it is our recommended guideline to capture at least 75% of modal mass and to use static correction methods to account for the entire response of the system, any requirements would be listed in each specific project’s specifications.
Dynamic "Time History" Analysis