Building mass is distributed throughout an actual structure. In Eigenvalue analysis of such buildings, it is usually assumed that mass distribution can be idealized as lumped at the nodes of a discretized structure. Furthermore, it is generally assumed that building mass is mostly concentrated at story levels and hence usually no mass is considered between stories.

For a 3D model, the mass lumped at a node is associated with only three translational degrees of freedom, X, Y and Z (these degrees of freedom are referred to as dynamic degrees of freedom). Rotational mass inertias at each individual node can be ignored since they have negligible influence on the overall dynamic properties of building type structures (Chopra, A. K., 2001)

Regarding displacements and rotations (deformation characteristics), six degrees of freedom (three translational and three rotational) are defined at each node. They are needed for an accurate stiffness representation. Note the distinction between "dynamic degrees of freedom" which has a reference to the mass, and "Deformation degrees of freedom" which has a reference to the stiffness.

To this end, one can notice that the number of dynamic degrees of freedom may not always match the deformation degrees of freedom in an analytical model. Hence, there are degrees of freedom with no mass defined at all and they can be statically condensed out from the solution since they have no influence on dynamic properties.

Further simplification can be carried out if one assumes that the diaphragm is rigid (i.e., in-plane stiffness of the diaphragm is infinitely stiff). This is a reasonable assumption for most buildings and it significantly reduces the number of degrees of freedom. The diaphragm behavior can be represented with only three degrees of freedom: translation in X and Y direction and rotation around Z-direction. Building lateral stiffness is then expressed in terms of these 3 degrees of freedom (usually using master\slave constraint equations). Similarly, one can also convert a distributed (spatial) network of nodal masses (Refer to (a) in preceding figure and (a) in the following figure) to a lumped mass system at the diaphragm mass center ( (b) in the following figure). Note that vertical mass components can be also ignored if no vertical acceleration is considered in analysis.

The user is provided an option in General Criteria dialog that the user can also include nodal mass components in Z-direction as well. This is only applicable for semirigid diaphragms. If the option is selected, the Periods and Modes report is updated: Z-direction (vertical) values have been added to Modal Participation Factors, Modal Direction Factors, and Modal Effective Mass Factors.

It should be noted that the configuration shown in (a) in the following figure is equivalent to the configuration shown in (b) of the same figure as far as dynamic properties (periods and model shapes) of the structure in concerned. One can use the parallel axis theorem (I_mi= m_i d_i², m_i and d_i are the i^th node mass value and distance from the node to the mass center, respectively) to calculate an equivalent rotational mass inertia of the diaphragm (i.e., 3^rd degree of freedom in (b) ).

In RAM Frame, the mass distribution shown in (a) in the preceding figure is used if the diaphragm is specified as semirigid while the mass distribution shown in (b) in the following figure is used if the diaphragm is specified as rigid.

The rotational inertia of mass is basically represented with the 3rd degree of freedom in Figure 126b. The same effect is actually captured with the distributed nodal masses (i.e., mass particles) as shown in Figure 126a. In other words, spatial distribution of mass defined at each node suffices for capturing all essential dynamic properties (including Eigen modes related to rotational inertias or twisting modes of buildings).