Structural Concrete - Hassoun

17.6 Minimum Slab Thickness to Control Deflection 621
3. For α fm ≤ 0.2,
where
h = minimum slab thickness without interior beams (Table 17.1) (17.3)
l n = clear span in long direction measured face to face of columns (or face to face of beams for
slabs with beams)
β = ratio of the long to the short clear spans
α fm = average value of α for all beams on the sides of a panel
α f = ratio of flexural stiffness of a beam section E cb I b to flexural stiffness of the slab E cs I s ,
bounded laterally by the centerlines of the panels on each side of the beam
where
α f = E cbI b
E cs I s
(17.4)
E cb , E cs = moduli of elasticity of concrete in beam and slab, respectively
I b = gross moment of inertia of beam section about centroidal axis (beam section includes a slab
length on each side of beam equal to projection of beam above or below slab, whichever is
greater, but not more than four times slab thickness)
I s = moment of inertia of gross section of slab
However, the thickness of any slab shall not be less than the following:
1. For slabs with α fm ≤ 2.0 then thickness ≥ 5.0 in. (125 mm)
2. For slabs with α fm > 2.0 then thickness ≥ 3.5 in. (90 mm)
If no beams are used, as in the case of flat plates, then α f = 0andα fm = 0. The ACI Code
equations for calculating slab thickness, h, take into account the effect of the span length, the panel
shape, the steel reinforcement yield stress, f y , and the flexural stiffness of beams. When very stiff
beams are used, Eq. 17.1 may give a small slab thickness, and Eq. 17.2 may control. For flat plates
and flat slabs, when no interior beams are used, the minimum slab thickness may be determined
directly from Table 8.3.1.1 of the ACI Code, which is shown here as Table 17.1.
Table 17.1
Minimum Thickness of Slabs Without Interior Beams
Without Drop Panels a
Exterior Panels
With Drop Panels a
Exterior Panels
Yield
Stress f y
psi (1) b
Without
Edge
Beams
With
Edge
Beams
Interior
Panels
Without
Edge
Beams
With
Edge
Beams c
Interior
Panels
40,000
60,000
l n
33
l n
30
l n
36
l n
33
l n
36
l n
33
a For values of reinforcement, yield stress between 40,000 and 60,000 psi minimum thickness shall be obtained by linear
interpolation.
b Drop panel is defined in ACI Sections 13.3.7 and 13.2.5.
c Slabs with beams between columns along exterior edges. The value of α f
for the edge beam shall be not less than 0.8.
l n
36
l n
33
l n
40
l n
36
l n
40
l n
36