Validation of modal analysis: total modal mass ratio

Dynamic analysis troubleshooting > modal analysis > total modal mass ratio

 

Check the total modal mass ratio

Standard validation criteria

Most seismic design codes define validity criteria on the cumulated modal mass ratio for the response spectrum method. Typically, the Eurocode states in EC-EN 1998-1 clause 4.3.3.3.1 that

(2)P The response of all modes of vibration contributing significantly to the global response shall be taken into account. (3) The requirements specified in paragraph (2)P may be deemed to be satisfied if either of the following can be demonstrated: the sum of the effective modal masses for the modes taken into account amounts to at least 90% of the total mass of the structure; all modes with effective modal masses greater than 5% of the total mass are taken into account.

In most seismic design codes, only the 90% rule is mentioned.

Total modal mass ratio in SCIA Engineer

As of SCIA Engineer 19.0 patch 1, seismic load case settings include a mode filtering feature, which allows to automatically use only the most significant mode shapes. Modes that are not necessary to meet the total modal mass ratio criteria are filtered out (see mode filtering section in " Defining a seismic load case").

The total modal mass ratio can be found in two places in SCIA Engineer results:

• In the eigenfrequencies calculation protocol, at the bottom of each modal mass ratio column; the modal mass ratios are given separately for each global direction and for rotation around each global axis
  
• In the linear calculation protocol, at the bottom of the summary table of each seismic load case (as of SCIA Engineer 19.0 patch 1);  only one set of values is given, corresponding to the direction of the applied seismic action, defined by the direction factors in the seismic load case settings (column Wi/Wtot); when mode filtering is used, modes are sorted in decreasing order of modal mass ratio value
  
  

Meeting relative modal mass criteria

It is not uncommon, that the 90% condition is not met at first when running the modal analysis. This can happen for various reasons:

• immobilized masses, such as an overall foundation slab or a very rigid basement, can cause a significant part of the mass of the structure to remain immobile under seismic excitation. The modes associated to such masses typically have very high frequencies, which are out of the usual range of seismic action, and their mode shape has often little real physical meaning.
• local modes can appear in flexible elements at relatively low frequencies, increasing the number of modes necessary to achieve the required 90%. Those can be either insignificant modes, exhibiting purely local behaviour on secondary members, resulting in very low relative modal mass that are irrelevant for seismic analysis. Or they can ba significant modes that represent only part of the overall seismic behaviour - for instance a frame structure without diaphragms where beams of different lengths will have different fundamental frequencies.

Depending on the reason for the lack of relative modal mass, the solution can be either increasing the number of computed modes or modifying the model and calculation parameters to remove unwanted modes from the results.

 

Next step: check for immobilized masses