Building Design and Construction Handbook - Merritt - Ventech!

9.88 SECTION NINE
column of a flat plate system where the unbalanced moment, M u, resulting from
gravity loads on the slab, must be transferred to the column. The unbalanced moment
is transferred by flexure and by eccentricity of shear.
Part of the unbalanced moment, � ƒM u, must be transferred by flexure within an
effective slab width equal to the column width plus 1.5h on side of the column,
i.e., a width of (c 2 � 1.5h) where c 2 is the edge-column width transverse to the
direction in which moments are being determined and h is the overall thickness of
the slab. The remaining part of the unbalanced moment, � ƒM u, must be transferred
by eccentricity of shear about the centroid of the critical section which is located
at distance of d/2 from the column where d is the effective depth of the slab. (As
noted in the following discussion, the code supersedes the requirement of designing
for � vM u by prescribing the magnitude of the gravity load moment to be transferred
by eccentricity of shear.) The fractions � ƒ and � v are calculated
1
� � (9.78)
ƒ
1 � (2/3) �b /b
1 2
� � (1 � � ) (9.79)
v ƒ
where b 1 � width of critical section measured in the direction in which moments
are being determined
b 2 � width of critical section measured in the direction perpendicular to b 1
For a square edge column and square panels, approximately 60% of the unbalanced
moment will be transferred by flexure within the slab width (c 2 � 3h) centered
on the column centerline. The result is that about 60% of the total top reinforcement
required in the column strip must be concentrated within the slab width
(c 2 � 3h) at the edge column. The designer must ensure that the top reinforcing
bars selected can be physically fitted into the width (c 2 � 3h) within allowable bar
spacings, and clearly show the bar spacings and details on the design drawings.
For transfer of gravity load moment from the slab to the edge column by eccentricity
of shear, the Code prescribes � v(0.3 M o) as the magnitude of the moment
to be transferred, rather than � vM u, where M o is calculated by Eq. (9.72).
For preliminary design, with square columns flush at edges of the flat plate, a
rapid estimate of the shear capacity to allow for effects of combined shear due to
gravity loads and to moment transfer can be made by using uniform vertical load
w u only, with nominal strength for factored load as follows:
For edge column, total shear V u � 0.5w uL 2L 1 and shear strength V c � 2 b od
�ƒ� c
For first interior column, V u � 1.15w uL 2L 1 and shear strength V c � b od
4�ƒ� c
where � specified concrete compressive strength, psi.
ƒ� c
Use of this calculation in establishing a preliminary design is a short cut, which
will often avoid the need for repeating steps 1 through 5 in Art. 9.59.1, because it
gives a close approximation for final design.
The minimum cantilever edge span of a flat plate so that all columns can be
considered interior columns and the direct-design method can be used without tedious
stiffness calculations is 4 ⁄15 of the length of the interior span (Fig. 9.29). This
result is obtained by equating the minimum cantilever moment at the exterior column
to the minimum negative-factored moment at the interior column.