Structural Concrete - Hassoun

630 Chapter 17 Design of Two-Way Slabs
17.8.2 Total Factored Static Moment
If a simply supported beam carries a uniformly distributed load w K/ft, then the maximum positive
bending moment occurs at midspan and equals M 0 = q u l 2 1 ∕8, where l 1 is the span length. If the beam
is fixed at both ends or continuous with equal negative moments at both ends, then the total moment
M 0 = M p (positive moment at midspan) + M n (negative moment at support) = q u l 2 ∕8 (Fig. 17.10).
1
Now if the beam AB carries the load W from a slab that has a width l 2 perpendicular to l 1 , then
W = q u l 2 , and the total moment is
M 0 = (q ul 2 )l 2 1
8
where q u is the load intensity in K/ft 2 . In this expression, the actual moment occurs when l 1 equals
the clear span between supports A and B. If the clear span is denoted by l n , then
M 0 = q ul 2 ln
2 (ACI Code, Eq. 8.10.3.2) (17.11)
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The clear span, l n , is measured face to face of supports in the direction in which moments are
considered but not less than 0.65 times the span length from center to center of supports. The face
of the support where the negative moments should be calculated is illustrated in Fig. 17.11. The
length l 2 is measured in a direction perpendicular to l n and equals the direction between center to
center of supports (width of slab). The total moment M 0 calculated in the long direction will be
referred to here as M 0l
and that in the short direction, as M 0s
.
Once the total moment, M 0 , is calculated in one direction, it is divided into a positive moment,
M p , and a negative moment, M n , such that M 0 = M p + M n (Fig. 17.10). Then each moment, M p and
M n , is distributed across the width of the slab between the column and middle strips, as is explained
shortly.
17.8.3 Longitudinal Distribution of Moments in Slabs
In a typical interior panel, the total static moment, M 0 , is divided into two moments, the positive
moment, M p ,atmidspan,equalto0.35M 0 ,andthenegativemoment,M n , at each support, equal
to 0.65M 0 , as shown in Fig. 17.12. These values of moment are based on the assumption that the
interior panel is continuous in both directions, with approximately equal spans and loads, so that
the interior joints have no significant rotation. Moreover, the moment values are approximately the
Figure 17.10
Bending moment in a fixed-end beam.