# Missing Mass & Residual Rigid Response
A modal analysis takes account of how the mass is mobilised in a dynamic
analysis. However only a relatively small number of modes are
calculated, so not all of the mass if mobilised. Provided the modes up
to a high enough frequency are calculated the remaining response can be
considered as an essentially static response. There are procedures for
establish the missing mass and taking this into account through a static
analysis. One is given by the U.S Nuclear Regulatory Commission
For a given excitation direction
The missing mass is then
Given the ground zero period acceleration (ZPA) The missing response can be treated as a static load case
A set of static loads corresponding to the different directions can then be established.
# Gupta Method
The Gupta method is a way of including the residual rigid response along
with the response spectrum analysis. This defines a rigid response
coefficient,
The coefficient α is defined by Gupta as
where