Civil Engineering Reference
In-Depth Information
Slabs with Interior Beams
To determine the minimum thickness of slabs with beams spanning between their sup-
ports on all sides, Section 9.5.3.3 of the Code must be followed. Involved in the expres-
sions presented there are span lengths, panel shapes, flexural stiffness of beams if they are
used, steel yield stresses, and so on. In these equations the following terms are used:
n
the clear span in the long direction, measured face to face, of
(a) columns for slabs without beams and (b) beams for slabs with beams
the ratio of the long to the short clear span
m
the average value of the ratios of beam- to- slab stiffness on all
sides of a panel
The minimum thickness of slabs or other two-way construction may be obtained by
substituting into the equations to follow, which are given in Section 9.5.3.3 of the Code.
In the equations, the quantity
is used to take into account the effect of the shape of the
panel on its deflection, while the effect of beams (if any) is represented by
m
. If there are
no beams present (as is the case for flat slabs),
m
will equal 0.
1.
For
0.2, the minimum thicknesses are obtained as they were for slabs with-
out interior beams spanning between their supports.
2.
For 0.2
m
m
2.0, the thickness may not be less than 5 in. or
f
y
200,000
n
0.8
h
(ACI Equation 9-12)
36
5
(
m
0.2)
3.
For
m
2.0, the thickness may not be less than 3.5 in. or
f
y
200,000
n
0.8
h
(ACI Equation 9-13)
36
9
where
n
and
f
y
are in inches and psi, respectively.
For panels with discontinuous edges, the Code (9.5.3.3d) requires that edge beams be
used, which have a minimum stiffness ratio
equal to 0.8, or else that the minimum slab
thicknesses, as determined by ACI Equations 9-12 and 9-13, must be increased by 10%.
The designer may use slabs of lesser thicknesses than those required by the ACI
Code as described in the preceding paragraphs if deflections are computed and found to
be equal to or less than the limiting values given in Table 9.5(b) of the ACI Code (Table
6.1 in this text).
Should the various rules for minimum thickness be followed but the resulting slab be
insufficient to provide the shear capacity required for the particular column size, column
capitals will probably be required. Beams running between the columns may be used for
some slabs where partitions or heavy equipment loads are placed near column lines. A
very common case of this type occurs where exterior beams are used when the exterior
walls are supported directly by the slab. Another situation where beams may be used oc-
curs where there is concern about the magnitude of slab vibrations. Example 16.2 illus-
trates the application of the minimum slab thickness rules for a two-way slab with beams.
