Procedure for Dynamic Analysis of 3D Buildings

Dynamic analysis of 3D building frames is computationally demanding, especially for multi-story and multi-bay frames. By applying Guyon reduction and rigid constraints, the analysis is highly efficient.

Reduction Workflow

Full 3D frame DOFs  (As Static Analysis) →  Guyan condensation to translational DOFs (Lateral mass only) →  rigid diaphragm transformation  →  3 DOF per floor

Stage	Main operation	Resulting coordinates
Full model	Assemble K and M using all frame DOFs	Nodal translations and rotations
Guyan reduction	Eliminate massless rotational DOFs by static equilibrium	Translations at column/floor nodes
Rigid diaphragm	Relate floor translations to diaphragm master DOFs	Ux, Uy, Θz per floor

Fig. Typical 3D Building Frame Model

(Green = Translational DOF, Red = Rotational DOF, Blue = Master DOF at Diaphragm CM)

References:

Guyon (1965) Reduction of stiffness and mass matrices. AIAA J 3(2):380