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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 δz, φx, φy of each node belonging to the diaphragm are independent of each other, while the rest δx, δy, φz are depended on the 3 displacements of point CT called Center of Elastic Torsion of the diaphragm. Displacements δxi, δyi, φzi at the point i of the horizontal diaphragm are expressed as:

φ zi =φz

δ xi =δxCT-yi·φz

δ yi =δyCT+xi·φz

 Figure 3.1.4-1: Diaphragmatic function of floor Figure 3.1.4-1: Diaphragmatic function of floor The displacements of a random point i of the diaphragm due to φz The displacements of a random point i of the diaphragm due to φz

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.

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