Cumulative Modal Mass Reference

Definition

Cumulative modal mass participation is the running sum of effective modal masses, expressed as a percentage of the total mass in each direction. It indicates how much of the structural mass has been captured by the extracted modes. The threshold for adequacy is set by the applicable standard, typically 90%.

Computation

For each direction, the cumulative modal mass at mode N is: Cumulative = sum(Meff_n for n=1 to N) / M_total * 100%. The effective modal mass for each mode is computed from the participation factor and generalised mass. The total mass M_total is the sum of all translational mass in the direction of interest.

Thresholds and missing mass

• If cumulative mass participation reaches 90% in all directions, the modal extraction is typically considered adequate
• If the threshold is not met, either more modes must be extracted or missing mass correction applied
• Missing mass = M_total - sum(Meff_n for all extracted modes)
• The missing mass response is computed using the rigid (zero-period) spectral acceleration
• Some standards accept less than 90% if missing mass correction is applied; others require 90% regardless