Column Stiffness For Flat Plate

The slab spans are not, even if a flat plate is supported on very stiff columns, really fixed at the column. The slab strip framing directly into the column is fixed over the column width, but the parallel strips farthest from the column are restrained only by the next slab span and practically none at all by the column itself. The torsional restraint that the slab could transfer laterally to this strip is nearly negligible. With a heavy transverse beam there could be more restraint, but on the average across the slab the restraint is still less than directly at the column. This is a way of saying that as far as the slab is concerned the slab restraint averages less than the column stiffness suggests. Only a transverse beam infinitely stiff in torsion between the columns could make this difference negligible.

Reduced column effectiveness is a major concept in the code treatment of the equivalent frame analysis. The commentary 13.7.4 uses the term "the equivalent column" and describes its behavior in terms of flexibilities (the inverse of stiffness). For the complete exterior column(above and below), the specified flexibility is

Where ∑K_c represents the sum of the stiffness of column above and below the joint and k_t represents the sum of the torsional stiffness of the slab or beam on each side of column.