Structural Concrete - Hassoun

682 Chapter 17 Design of Two-Way Slabs
Figure 17.37
Critical sections for column moment, equivalent frame method.
face of the column, bracket, or capital. This region may be considered as a thickened section
of the floor slab. To account for the large depth of the column and its reduced effective width
in contact with the slab beam, the ACI Code, Section 8.11.3.1, specifies that the moment of
inertia of the slab beam between the center of the column and the face of the support is to
be assumed equal to that of the slab beam at the face of the column divided by the quantity
(1 − c 2 /l 2 ) 2 ,wherec 2 is the column width in the transverse direction and l 2 is the width of the
slab beam. The area of the gross section can be used to calculate the moment of inertia of the
slab beam.
4. Column moment of inertia: The ACI Code, Section 8.11.4.1, states that the moment of inertia
of the column is to be assumed infinite from the top of the slab to the bottom of the column
capital or slab beams (Fig. 17.37).
5. Column stiffness, K ec , is defined by
1
= ∑ 1 + 1 (Eq. 17.17)
K ec Kc K t
where ΣK c is the sum of the stiffness of the upper and lower columns at their ends,
K t = ∑ 9E cs C
(Eq. 17.19)
l 2 (1 − C 2 ∕l 2 ) 3
C = ∑ ( 1 − 0.63 x )( x 3 )
y
(Eq. 17.20)
y 3
6. Column moments: In frame analysis, moments determined for the equivalent columns at the
upper end of the column below the slab and at the lower end of the column above the slab
must be used in the design of a column.
7. Negative moments at the supports: The ACI Code, Section 8.11.6, states that for an interior
column, the factored negative moment is to be taken at the face of the column or capital but
at a distance not greater than 0.1175l 1 from the center of the column. For an exterior column,
the factored negative moment is to be taken at a section located at half the distance between