Diaphragmatic function

In general, when there is eccentric loading at a floor, e.g. imposed by the horizontal seismic action, the rigidity of the slab on its plane forces all the in-plane points (therefore all column heads[*]NoteThe term column' refers to columns as well as to shear walls. on the slab) to move the same way.

The 3 displacements δ_z, φ_x, φ_y of each node belonging to the diaphragm are independent of each other, while the rest δ_x, δ_y, φ_z are depended on the 3 displacements of point C_T called Center of Elastic Torsion of the diaphragm. Displacements δ_xi, δ_yi, φ_zi at the point i of the horizontal diaphragm are expressed as:

φ _zi =φ_z

δ _xi =δ_xCT-y_i·φ_z

δ _yi =δ_yCT+x_i·φ_z

In a floor diaphragm of 20 main and 14 slave nodes, the number of the unknown displacements (degrees of freedom) is equal to 20x3+3=63.