Structural Concrete - Hassoun

17.8 Analysis of Two-Way Slabs by the Direct Design Method 631
Figure 17.11 Critical sections for negative design moments. A-A, section for negative
moment at exterior support with bracket.
same as those in a fixed-end beam subjected to uniform loading, where the negative moment at the
support is twice the positive moment at midspan. In Fig. 17.12, if l 1 > l 2 , then the distribution of
moments in the long and short directions is as follows:
M 0l =(q u l 2 ) l2 n1
8
M pl = 0.35M 0l
M nl = 0.65M 0l
M 0s =(q u l 1 ) l2 n2
M
8 ps = 0.35M 0s M ns = 0.65M 0s
If the magnitudes of the negative moments on opposite sides of an interior support are different
because of unequal span lengths, the ACI Code specifies that the larger moment should be
considered to calculate the required reinforcement.
In an exterior panel, the slab load is applied to the exterior column from one side only, causing
an unbalanced moment and a rotation at the exterior joint. Consequently, there will be an increase
in the positive moment at midspan and in the negative moment at the first interior support. The
magnitude of the rotation of the exterior joint determines the increase in the moments at midspan
and at the interior support. For example, if the exterior edge is a simple support, as in the case of a
slab resting on a wall (Fig. 17.13), the slab moment at the face of the wall there is 0, the positive
moment at midspan can be taken as M p = 0.63M 0 , and the negative moment at the interior support
is M n = 0.75M 0 . These values satisfy the static equilibrium equation
M 0 = M p + 1 2 M n = 0.63M 0 + 1 2 (0.75M 0)