Page 206 - Civil Engineering Formulas

142 CHAPTER FIVE

FLAT-SLAB CONSTRUCTION

Slabs supported directly on columns, without beams or girders, are classified as
flat slabs. Generally, the columns flare out at the top in capitals (Fig. 5.3).
However, only the portion of the inverted truncated cone thus formed that lies
inside a 90° vertex angle is considered effective in resisting stress. Sometimes,
the capital for an exterior column is a bracket on the inner face.
The slab may be solid, hollow, or waffle. A waffle slab usually is the most
economical type for long spans, although formwork may be more expensive
than for a solid slab. A waffle slab omits much of the concrete that would be in
tension and thus is not considered effective in resisting stresses. To control
deflection, the ACI Code establishes minimum thicknesses for slabs, as indicated
by the following equation:

l n(0.8 f y /200,000) l n(0.8 f y /200,000)
h (5.99)
36 5 [ m 0.12(1 1/ )] 36 9

where h slab thickness, in (mm)
l length of clear span in long direction, in (mm)
n
f yield strength of reinforcement, ksi (MPa)
y
ratio of clear span in long direction to clear span in the short direction
average value of for all beams on the edges of a panel
m
ratio of flexural stiffness E I of beam section to flexural stiffness
cb b
E I of width of slab bounded laterally by centerline of adjacent
cs s
panel, if any, on each side of beam
E modulus of elasticity of beam concrete
cb
E modulus of elasticity of slab concrete
cs
I moment of inertia about centroidal axis of gross section of beam,
b
including that portion of slab on each side of beam that extends a
distance equal to the projection of the beam above or below the
slab, whichever is greater, but not more than four times slab thick-
4
4
ness, in (mm )
I moment of inertia about centroidal axis of gross section of slab
s
3
4
4
h /12 times slab width specified in definition of , in (mm )
Slab thickness h, however, need not be larger than (l /36) (0.8 f /200,000).
n y
FLAT-PLATE CONSTRUCTION
Flat slabs with constant thickness between supports are called flat plates. Gen-
erally, capitals are omitted from the columns.
Exact analysis or design of flat slabs or flat plates is very complex. It is com-
mon practice to use approximate methods. The ACI Code presents two such
methods: direct design and equivalent frame.