Seismic loading: Mass in the seismic analysis

The mass can be taken in two ways in the seismic analysis.

In case Use residual mode is OFF, then only the participating mass from the computed modes is taken into account in the seismic spectral analysis.

In case Use residual mode is ON, then the missing mass is taken in the seismic analysis as an extra pseudo-mode which represents the weight of the missing mass. The modal result of this mode is computed by a static equivalent load case.

Remark: The used method is displayed in the linear calculation protocol.

Residual mode: Add rigid behaviour as an additional pseudo-mode

This compensating technique may be used in case the required modal mass ratio cannot be met. However, it is based on the assumption, that the missing modal mass is due to so-called rigid modes, which typical have a frequency that is too high to be set in motion by seismic action. If flexible modes are missing and therefore compensated by that technique, the results can become very inaccurate.

Modes that are within the typical frequency range of seismic action (i.e. 0-33 Hz) should be taken into account. Some codes specify, that at least 70% of the modal mass ratio must be covered by computed modes. The rest may be covered, for instance, by a residual mode analysis.

The aim of the method is to evaluate the missing mass as an extra mode, which is computed as an equivalent static load case. The static load represents the weight of the missing mass under the zero period acceleration. Modal superposition is then carried out normally according to the selected rule SRSS, CQC or MAX.

The missing mass is computed in each node as difference between total mass and effective mass.

(5.23)

k - is direction

i - is node

j - is mode

M_ef,k,i - is effective mass, direction k, node i

Missing mass can now be written as

(5.24)

A static load case of weight is computed, which is handled in the same way as a “real” mode.

For each direction k, selected in the seismic load case settings, the amplitude of static load is computed as:

(5.25)

Sa_k,ZPA is the value of acceleration for the rigid mode, a.k.a. Zero Period Acceleration

^MissM_k,i is the missing mass in direction k, node i

Afterwards, the extra mode is combined according to the SRSS rule.

Remarks

• In case of CQC superposition, it is assumed that there is no correlation between the residual mode and the other modes (i.e. SRSS is applied for the residual mode).
• The direction of the static equivalent loads is the same as the direction selected by user in the spectrum direction.
• If the seismic load is defined in 2 or 3 global directions, then the static equivalent mass in the residual mode is computed in the global 2 or 3 defined directions with respect to the directions defined in the input.
• The value of ZPA is taken as the last value of the selected response spectrum (i.e. highest frequency defined in the spectrum). It is of the responsibility of the user to define the spectrum accordingly.