09. How does AutoPIPE compute the missing mass response when the modal analysis option is selected?


Applies To  
Product(s): AutoPIPE
Version(s): ALL;
Area: Analysis
Date Logged
& Current Version		 June,2025
24.00.02.243

Problem:

How does AutoPIPE compute the missing mass response when the modal analysis option is selected in missing mass combination method? 

 

Solution:

There are two methods of calculating the static correction for the missing mass 

Zero Period Acceleration (ZPA)

Zero Period Acceleration (ZPA) represents a rigid-body response equivalent to applying a static acceleration to the entire structure.

In AutoPIPE, the ZPA response is evaluated separately from the flexible modal response. The program then envelopes the ZPA response with the modal response by selecting the maximum response value for each load direction.

This approach provides an estimate of the rigid response contribution that may not be fully represented by the extracted flexible modes.

Missing Mass Response

For a uniform response spectrum analysis, AutoPIPE computes the missing mass correction based on the method described by Ole Edvard Hansteen in the paper"On the Accuracy of Mode Superposition Analysis in Structural Dynamics" published in Earthquake Engineering and Structural Dynamics (1979).

When only a truncated set of modes is extracted during modal superposition, a portion of the structure's total mass participation may remain uncaptured. The missing mass method computes a static correction for this uncaptured contribution.

The missing force vector is calculated as:

 


Where:

The resulting missing force vector is then applied to the static equilibrium equation:


Where:

The calculated static response represents the contribution of the modes that were not extracted during the modal analysis.

 

AutoPIPE calculates the missing mass at the cutoff frequency specified in the Modal tab of the Dynamic Analysis dialog. By setting the missing mass combination dropdown to 'Modal', AutoPIPE will apply missing mass to the flexible responses using the same method that is selected in the Modal Combination dropdown.
For example, by selecting 'Modal' in the M. Mass Combination dropdown, and 'Ten Percent' in the Modal Combination dropdown, provided the Missing Mass option is checked, both flexible and rigid responses will be modally combined using the ten percent method. The example below for instance uses SRSS to combine missing mass in both analysis sets, such that both results should be exactly the same. 

As accurately stated in the help documentation:  
The rigid response (missing mass response) is treated as any other mode and combined with flexible modes according to Modal combination option chosen.

 

Question:

How is the Missing Mass Response (Rigid Response) combined with the Modal Response (Flexible Response) when the Modal and Following options are selected?


 

Answer:

When the Modal method is selected as the missing mass combination approach, the missing mass (rigid) response is integrated with the modal (flexible) response using one of the following modal combination techniques: 

      1. SRSS
      2. Grouping
      3. Ten Percent
      4. Double Sum
      5. Signed Double sum 
      6. Signed CQC
      7. Absolute CQC

See Also

Dynamic "Response Spectrum" Analysis

Bentley AutoPIPE