Modal response spectrum analysis mass participation can’t reach 90%

Problem description #

The 90% mass participation in modal response spectrum analysis cannot be reached even using hundreds of mode shapes.

Reason #

Excessive detailing of the structures and the ancillary (associated) structural elements can easily lead to the predominant part of the vibration shapes containing only that part of the structure, which has minor importance for the whole analysis. The mass of which in relation to the whole building is small, i.e. not even close to 90% of the mass fraction will “fill up” the vibration shapes, and other parts of the model with the significant mass participation will not be considered.

This problem is very usual if significantly different mass/stiffness parts are present in the model (steel/timber parts and concrete parts), or a part of the model (e.g. basement) is embedded in the ground.

Solution #

The method of solution should be adjusted by taking into consideration the parameters of the actual model, but general rules are:

  • Simplify the model by deleting those secondary structures which are irrelevant to the seismic design of the whole structure, and their mass is insignificant compared to the whole structure
  • Raise the number of requested mode shapes
  • Consider masses only above the basement level (please note that we have to consider dynamic earth pressure on the basement walls!)
  • Use the cracked stiffness of the concrete members (the reduced stiffness helps to decrease the required number of mode shapes)
  • Delete the mesh of the columns (they are not relevant for the global seismic design)