Substructuring the Building for Modal Analysis

[JoeH78]

Hi,

Could you advise me how the building is idealized for modal analysis?
In basic concepts and per the requirement of codes, storeys in buildings are assumed as, whole storey mass is being lumped at the storey level. The whole building should have a 2 translation and a 1 twisting rotation defined as DOF per storey basis, and others DoFS should be eliminated via static, dynamic etc.. condensation.

Based on that, columns and beams are assumed as frame FEM (6 DoFs per node) elements, unwanted DoFs (UDofs) are eliminated with condensation, from now on is just my prediction, shear walls are assumed as plane (triangular, quad) elements(2 DOF per node) again the UDoFs are eliminated, so how the slabs and shear-walls are actually being assumed in that process?

Regards,

 

[PicoStruc]

This 3DOF by story/diaphragm hypothesis works for building idealized with rigid diaphragm assumption. In that case you have to apply joint displacement constraint on your floor node / element for each story.

The only mistake you made are the DOF number. Because you work in 3D (3DOF by story), beam will have 6 translational DOFs and 6 Rotational DOFs for each nodes, etc...

Shell element (Membrane + Plate) are used for shear wall and slab.

If you model a RC building, don't forget to modify geometric properties for cracking state (slab can have up to 80% stiffness loss, beam 60% stiffness loss and Columns and wall about 30% stiffness loss).

 

[JoeH78]

The only mistake you made are the DOF number. Because you work in 3D (3DOF by story), beam will have 6 translational DOFs and 6 Rotational DOFs for each nodes, etc.... Shell element (Membrane + Plate) are used for shear wall and slab.

Thin or thick shell formulation ?
Here comes the paradox, Generally you know that there is not a variable to express the Z direction "twisting" in the shape function to associate with twisting effect for shell elements (triangular or quad). IMHO commercial packages implement that with some kind of stochastic expression.

If you model a RC building, don't forget to modify geometric properties for cracking state (slab can have up to 80% stiffness loss, beam 60% stiffness loss and Columns and wall about 30% stiffness loss).

Could you elaborate that a bit further?
With geometric properties do you mean modifying the inner products of stiffness and mass matrics? If so how am I supposed to do that ?

 

[PicoStruc]

For cracked section properties, check ACI 8.8 or more detailled in CSA A23.3-04 21.2.5. You migth require to modify second moment of inertia of your beam/column, and membrane coefficient. The method differ depending of the software used. For ETABS/SAP for example, check for "Properties Modifier".