Validation of modal analysis: specifics for seismic analysis
Dynamic analysis troubleshooting > modal analysis > specifics for seismic analysis
Up to this point, the described validations are relevant for any dynamic analysis. Once that is done, some points can be refined specifically in the case of seismic analysis.
Specific checks of modal analysis for seismic analysis
This section gives more details about the number of modes that must be taken into account for seismic analysis.
Fundamental principle
As ground rule, all modes that contribute significantly to the behaviour of the seismic resisting system must be taken into account.
In the Eurocode (EN 1998-1:2004 clause 4.3.3.3.1 (2)P ):
The response of all modes of vibration contributing significantly to the global response shall be taken into account.
Alternatively, in Australia (AS 1170.4-2007 clause 7.4.2) and similarly in New Zealand (NZS 1170-5 2004 clause 6.3.3.2):
In three-dimensional analysis, where structures are modelled so that modes that are not those of the seismic-force-resisting system are considered, then all modes not part of the seismic-force-resisting system shall be ignored.
Total effective modal mass ratio
All modern seismic design codes define validity criteria on the cumulated modal mass ratio for the response spectrum method.
The rule of minimum 90% total modal mass ratio is commonly used. The Eurocode states (EN 1998.1:2004 clause 4.3.3.3.1 (3) ):
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
And additionally (EN 1998.1:2004 clause 4.3.3.3.1 (4) ):
When using a spatial model, the above conditions should be verified for each relevant direction
The Eurocode also proposes an alternative condition (EN 1998.1:2004 clause 4.3.3.3.1 (3) ):
all modes with effective modal masses greater than 5% of the total mass are taken into account.
which is a form of mode filtering and can be assimilated to the relevance criterion mentioned above in fundamental principles for Australia and New Zealand standards.
Various aspects of the modelization and modal analysis can make the 90% condition difficult to meet, such as immobilized masses and local modes.
As a summary, the following steps must be checked:
Relevance of modes
The relevance of a mode for seismic response must be assessed according two criteria:
The contribution of the mode to the behaviour of the seismic-resisting system:
This is essentially covered by the evaluation of the modal mass ratio. The contribution of a mode to the overall seismic behaviour is directly related to the value of its participation factor and modal mass ratio.
The sensitivity of the mode to the seismic action:
Typically, seismic action is acting in a frequency range from 0 to approximately 30-35 Hz. Seismic response spectra are usually defined in that frequency range. Spectral acceleration is not defined for higher frequency values and is typically considered constant and equal to the zero-period ground acceleration (aZPA). Modes with frequency value above that range should then be considered as rigid and handled through residual mode techniques rather than modal analysis. Based on that logic, considering modes with frequency value higher than 35 Hz is essentially pointless.
Alternatively, Australia standard (AS 1170.4-2007 clause 7.4.2):
all modes with periods less than 5% of the fundamental natural period of the structure (<0.05T1) may be ignored.
Next step: check total modal mass ratio