Civil Engineering Reference
In-Depth Information
In essence, the Direct Design Method is a three-step analysis procedure. The first step is the calculation of the
total design moment M
o
for a given panel. The second step involves the distribution of the total moment to the
negative and positive moment sections. The third step involves the assignment of the negative and positive
moments to the column strips and middle strips.
For uniform loading, the total design moment M
o
for a panel is calculated by the simple static moment
expression, ACI Eq. (13-4):
M
o
= q
u
˜
2
˜
n
2
/8
where q
u
is the factored combination of dead and live loads (psf), q
u
= 1.2 w
d
+ 1.6 w
˜
. The clear span
˜
n
is defined in a straightforward manner for slabs supported on columns or other supporting elements of
rectangular cross section (ACI 13.6.2.5). Circular or regular polygon shaped supports must be treated as square
supports with the same area (see ACI Fig. R13.6.2.5). The clear span starts at the face of support and must not
be taken less than 65% of the span center-to-center of supports (ACI 13.6.2.5). The span
˜
2
is simply the span
transverse to
˜
n
; however, when the panel adjacent and parallel to an edge is being considered, the distance from
edge of slab to panel centerline is used for
˜
2
in calculation of M
o
(ACI 13.6.2.4).
Division of the total panel moment M
o
into negative and positive moments, and then into column and
middle strip moments, involves direct application of moment coefficients to the total moment M
o
. The moment
coefficients are a function of span (interior or exterior) and slab support conditions (type of two-way slab
system). For design convenience, moment coefficients for typical two-way slab systems are given in Tables
4-2 through 4-6. Tables 4-2 through 4-5 apply to flat plates or flat slabs with various end support conditions.
Table 4-6 applies to two-way slabs supported on beams on all four sides. Final moments for the column strip
and middle strip are computed directly using the tabulated values. All coefficients were determined using the
appropriate distribution factors in ACI 13.6.3 through 13.6.6.
Table 4-2 Flat Plate or Flat Slab Supported Directly on Columns
End Span
Interior Span
4
5
1
2
3
End Span
Interior Span
1
Exterior
Negative
2
Positive
3
First Interior
Negative
4
Positive
5
Interior
Negative
Slab Moments
Total Moment
0.26 M
o
0.52 M
o
0.70 M
o
0.35 M
o
0.65 M
o
Column Strip
0.26 M
o
0.31 M
o
0.53 M
o
0.21 M
o
0.49 M
o
Middle Strip
0
0.21 M
o
0.17 M
o
0.14 M
o
0.16 M
o
Note: All negative moments are at face of support.
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