Structural Concrete - Hassoun

620 Chapter 17 Design of Two-Way Slabs
periphery of the columns will have maximum negative bending moments. Considering a strip along
AFB, the strip bends like a continuous beam (Fig. 17.5b), having negative moments at A and B and
positive bending moment at F. This strip extends between the two columns A and B and continues
on both sides of the panel, forming a column strip.
Similarly, a strip along EOG will have negative bending moments at E and G and a positive
moment at O, forming a middle strip. A third strip along DHC will behave similarly to strip AFB.
Therefore, the panel can be divided into three strips, one in the middle along EOG, referred to as the
middle strip, and one on each side, along AFB and DHC, referred to as column strips (Fig. 17.5a).
Each of the three strips behaves as a continuous beam. In a similar way, the panel is divided into
three strips in the other direction, one middle strip along FOH and two column strips along AED
and BGC, respectively (Fig. 17.5e).
Referring to Fig. 17.5a, it can be seen that the middle strips are supported on the column
strips, which in turn transfer the loads onto the columns, A, B, C,andD in this panel. Therefore, the
column strips carry more load than the middle strips. Consequently, the positive bending moment in
each column strip (at E, F, G,andH) is greater than the positive bending moment at O in the middle
strip. Also, the negative moments at the columns A, B, C,andD in the column strips are greater than
the negative moments at E, F, G, andH in the middle strips. The portions of the design moments
assigned to each critical section of the column and middle strips are discussed in Section 17.8.
The extent of each of the column and middle strips in a panel is defined by the ACI Code,
Sections 8.4.1.5 and 8.4.1.6. The column strip is defined by a slab width on each side of the column
centerline, x in Fig. 17.5, equal to one-fourth the smaller of the panel dimensions l 1 and l 2 , including
beams if they are present, where
l 1 = span length, center to center of supports, in the direction moments are being determined
l 2 = span length, center to center of supports, in the direction perpendicular to l 1
The portion of the panel between two column strips defines the middle strip.
17.6 MINIMUM SLAB THICKNESS TO CONTROL DEFLECTION
The ACI Code, Sections 8.3.1.1 and 8.3.1.2, specifies a minimum slab thickness in two-way slabs
to control deflection. The magnitude of a slab’s deflection depends on many variables, including the
flexural stiffness of the slab, which in turn is a function of the slab thickness, h. Byincreasingthe
slab thickness, the flexural stiffness of the slab is increased, and consequently the slab deflection is
reduced [13]. Because the calculation of deflections in two-way slabs is complicated and to avoid
excessive deflections, the ACI Code limits the thickness of these slabs by adopting the following
three empirical limitations, which are based on experimental research. If these limitations are not
met, it will be necessary to compute deflections.
1. For 0.2 2.0,
h = l n(0.8 + f y ∕200,000)
36 + 9β
but not less than 3.5 in.
(f y in psi) h = l n(0.8 + f y ∕1400)
36 + 5β(α fm − 0.2)
(f y in psi) h = l n(0.8 + f y ∕1400)
36 + 9β
(f y in MPa) (17.1)
(f y in MPa) (17.2)