Civil Engineering Reference
In-Depth Information
For practical design, only direct shear (uniformly distributed around the perimeter b
o
) occurs around interior
slab-column supports where no (or insignificant) moment is to be transferred from the slab to the column.
Significant moments may have to be carried when unbalanced gravity loads on either side of an interior column
or horizontal loading due to wind must be transferred from the slab to the column. At exterior slab-column
supports, the total exterior slab moment from gravity loads (plus any wind moments) must be transferred
directly to the column.
Transfer of unbalanced moment between a slab and a column takes place by a combination of flexure (ACI
13.5.3) and eccentricity of shear (ACI 11.11.7). Shear due to moment transfer is assumed to act on a critical
section at a distance d/2 from the face of the column, the same critical section around the column as that used
for direct shear transfer [Fig. 4-12(b)]. The portion of the moment transferred by flexure is assumed to be
transferred over a width of slab equal to the transverse column width
c
2
, plus 1.5 times the slab or drop panel
thickness (1.5h) on each side of the column. Concentration of negative reinforcement is to be used to resist
moment on this effective slab width. The combined shear stress due to direct shear and moment transfer often
governs the design, especially at the exterior slab-columns supports.
The portions of the total moment to be transferred by eccentricity of shear and by flexure are given by ACI Eqs.
(11-37) and (13-1), respectively. For square interior or corner columns, 40% of the moments is considered
transferred by eccentricity of the shear (
γ
v
M
u
= 0.40 M
u
), and 60% by flexure (
γ
f
M
u
= 0.60 M
u
), where M
u
is
the transfer moment at the centroid of the critical section. The moment M
u
at an exterior slab-column
support will generally not be computed at the centroid of the critical transfer section in the frame analysis.
In the Direct Design Method, moments are computed at the face of the support. Considering the approximate
nature of the procedure used to evaluate the stress distribution due to moment transfer, it seems unwarranted to
consider a change in moment to the transfer centroid; use of the moment values at the faces of the supports
would usually be accurate enough.
The factored shear stress on the critical transfer section is the sum of the direct shear and the shear caused by
moment transfer,
v
u
= V
u
/A
c
+
γ
v
M
u
c/J
or
v
u
= V
u
/A
c
-
γ
v
M
u
'
/J
Computation of the combined shear stress involves the following properties of the critical transfer section:
A
c
= area of critical section, in.
2
c or
'
= distance from centroid of critical section to the face of section where stress
is being computed, in.
J
c
= property of critical section analogous to polar moment of inertia, in.
4
The above properties are given in terms of formulas in Tables 4-7 through 4-10 (located at the end of this
chapter) for the four cases that can arise with a rectangular column section: interior column (Table 4-7), edge
column with bending parallel to the edge (Table 4-8), edge column with bending perpendicular to the edge
(Table 4-9), and corner column (Table 4-10). Numerical values of the above parameters for various
combinations of square column sizes and slab thicknesses are also given in these tables. Properties of the
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