—Design for slabs on expansive soils

360R-42 ACI COMMITTEE REPORT
(SI)
Center lift design moment in the short direction (flexural
strength requirement of the section across the short direc-
tion) is given by Eq. (9-16):
For L
L
/L
S
 
≥ 1.1,
(in.-lb) (9-16)
(SI)
For L
L
/L
S
 < 1.1,
M
S
= M
L 
(9-17)
Edge lift design moment in the long direction (flexural
strength requirement of the section across the long direction)
is given by Eq. (9-18)
(in.-lb) (9-18)
(SI)
Equation (9-19) gives edge lift design moment in short
direction (flexural strength requirement of the section across
the short direction):
For L
L
/L
S
 
≥ 1.1,
(in.-lb) (9-19)
(SI)
For L
L
/L
S
 < 1.1,
M
S
= M
L 
(9-20)
Concrete flexural stresses produced by the applied service
moments can be calculated with the following
(9-21)
The resultant concrete flexural stresses f must be limited to f
t
in tension and f
c
in compression.
9.8.2 Differential deflection—Allowable and expected
deflections can be determined from actual section properties.
The relative stiffness distance 
β for both long and short
direction can be calculated using Eq. (9-22)
(in.-lb) (9-22)
(SI)
Differential deflection distance—Either L or 6
β, whichever is
shorter, should be used in determining allowable deflections.
Equation (9-23) can be used to obtain allowable differential
deflections for center lift, long and short directions
(in.-lb) (9-23)
(SI)
Allowable differential deflection for edge lift, long and
short directions, is given by Eq. (9-24)
(in.-lb) (9-24)
(SI)
C
Δ
may be selected from the following table, which presents
sample C
Δ
values for various types of superstructures.
Expected differential deflection without prestressing,
center lift, long and short directions, can be calculated from
Eq. (9-25)
(in.-lb) (9-25)
(SI)
Expected differential deflection without prestressing, edge
lift, long and short directions, can be calculated from 
Eq. (9-26)
C
8
P
8940
–
3720
---------------------
–
102
y
m
–
76.2
--------------------
0
≥
=
M
s
58
e
m
+
60
------------------ M
L
=
M
s
17.7
e
m
+
18.3
---------------------- M
L
=
M
L
S
( )
0.10
he
m
(
)
0.78
y
m
( )
0.66
7.2 L
( )
0.0065
P
( )
0.04
--------------------------------------------------------
=
M
L
S
( )
0.10
he
m
(
)
0.78
y
m
( )
0.66
54 L
( )
0.0065
P
( )
0.04
--------------------------------------------------------
=
M
s
h
0.35
19
e
m
+
57.75
------------------ M
L
=
M
s
0.322h
0.35
5.79
e
m
+
17.6
---------------------- M
L
=
f
P
r
A
-----
M
L S
,
S
t b
,
-----------
P
r
e
S
t b
,
--------
±
±
=
Sample values of C
Δ
Material
Center lift
Edge lift
Wood frame
240
480
Stucco or plaster
360
720
Brick veneer
480
960
Concrete masonry units
960
1920
Prefab roof trusses
1000
2000
β
1
12
------
E
c
I
E
s
--------
4
=
β
1
1000
------------
E
c
I
E
s
--------
4
=
Δ
allow
12 L or 6
β
(
)
C
Δ
-----------------------------
=
Δ
allow
1000 L or 6
β
(
)
C
Δ
-----------------------------------
=
Δ
allow
12 L or 6
β
(
)
C
Δ
-----------------------------
=
Δ
allow
1000 L or 6
β
(
)
C
Δ
-----------------------------------
=
Δ
o
y
m
L
(
)
0.205
S
( )
1.059
P
( )
0.523
e
m
( )
1.296
380 h
( )
1.214
---------------------------------------------------------------------------------
=
Δ
o
9.0 y
m
L
(
)
0.205
S
( )
1.059
P
( )
0.523
e
m
( )
1.296
h
( )
1.214
-----------------------------------------------------------------------------------------
=

DESIGN OF SLABS-ON-GROUND 360R-43
(in.-lb) (9-26)
(SI)
Additional slab deflection is produced by prestressing if the
prestressing force is applied at any point other than the CGS
(in.-lb) (9-27)
(SI)
9.8.3 Shear—Expected service shear per foot (meter) of
structure: center lift condition, short direction, can be
calculated from Eq. (9-28)
(in.-lb) (9-28)
(SI)
Center lift condition, long direction, can be calculated
from Eq. (9-29)
(in.-lb) (9-29)
(SI)
Edge lift condition, long and short direction, can be calcu-
lated from Eq. (9-30)
(in.-lb) (9-30)
(SI)
9.8.3.1 Applied service load shear stress v—Only the
beams are considered in calculating the cross-sectional area
resisting shear force in a ribbed slab:
Ribbed foundations 
(9-31)
Uniform thickness foundations
(in.-lb) (9-32)
(SI)
Compare v to v
c
. If v exceeds v
c
, shear reinforcement in
accordance with ACI 318 should be provided. Possible
alternatives to shear reinforcement include:
• Increasing the beam depth;
• Increasing the beam width; and
• Increasing the number of beams (decreasing the beam
spacing).
9.8.4 Uniform thickness conversion—Once the ribbed
foundation has been designed to satisfy moment, shear, and
differential deflection requirements, it may be converted to
an equivalent uniform thickness foundation with thickness
H, if desired. The following equation for H should be used
for the conversion
(in.-lb) (9-33)
(SI)
9.8.5 Other applications of design procedure—This
design procedure has other practical slab-on-ground applica-
tions besides construction on expansive clays, discussed as
follows:
9.8.5.1 Design of nonprestressed slabs-on-ground—
Equations (9-11)
, 
(9-16)
, 
(9-18)
, 
(9-19)
, 
(9-22)
, 
(9-23)
, 
(9-25)
,
(9-26), and (9-28) through (9-30) predict the values of
bending moment, shear, and differential deflection expected
to occur using a given set of soil and structural parameters.
These design values may be calculated for slabs reinforced
with unstressed and stressed reinforcement. Once these
design parameters are known, design of either type of slab
can proceed. This report does not provide design procedures
for non-post-tensioned slabs-on-ground. To conform to the
same deflection criteria, however, non-post-tensioned slabs
designed on the basis of cracked sections will need signifi-
cantly deeper beam stems than post-tensioned slabs.
9.8.5.2 Design of slabs subject to frost heave—Applied
moments, shears, and deflections due to frost heave can be
approximated by substituting anticipated frost heave for
expected swell of an expansive clay. The value of e
m
for frost
heave should be estimated from values comparable to those
for expansive soils.
9.8.6 Calculation of stress in slabs due to load-bearing
partitions—The equation for the allowable tensile stress in a
slab beneath a bearing partition may be derived from beam-
on-elastic foundation theory. The maximum moment
directly under a point load, P (kips [kN]), in such a beam is
Δ
o
L
( )
0.35
S
( )
0.88
e
m
( )
0.74
y
m
( )
0.76
15.9 h
( )
0.85
P
( )
0.01
--------------------------------------------------------------------
=
Δ
o
22.8 L
( )
0.35
S
( )
0.88
e
m
( )
0.74
y
m
( )
0.76
h
( )
0.85
P
( )
0.01
-------------------------------------------------------------------------------
=
Δ
p
P
e
e
β
2
2E
c
I
--------------
=
Δ
p
P
e
e
β
2
2E
c
I
-------------- 10
6
(
)
=
V
S
1
1350
------------ L
( )
0.19
S
( )
0.45
h
( )
0.20
P
( )
0.54
y
m
( )
0.04
e
m
( )
0.97
[
]
=
V
S
1
126
--------- L
( )
0.19
S
( )
0.45
h
( )
0.20
P
( )
0.54
y
m
( )
0.04
e
m
( )
0.97
[
]
=
V
S
1
1940
------------ L
( )
0.09
S
( )
0.71
h
( )
0.43
P
( )
0.44
y
m
( )
0.16
e
m
( )
0.93
[
]
=
V
S
1
373
--------- L
( )
0.09
S
( )
0.71
h
( )
0.43
P
( )
0.44
y
m
( )
0.16
e
m
( )
0.93
[
]
=
V
S
V
L
L
( )
0.07
h
( )
0.4
P
( )
0.03
e
m
( )
0.16
y
m
( )
0.67
3.0 S
( )
0.015
-------------------------------------------------------------------------------
=
=
V
S
V
L
L
( )
0.07
h
( )
0.4
P
( )
0.03
e
m
( )
0.16
y
m
( )
0.67
5.5 S
( )
0.015
-------------------------------------------------------------------------------
=
=
v
VW
nhb
---------
=
v
V
12H
----------
=
v
V
1000H
----------------
=
H
I
W
-----
3
=
H
12I
1000W
-----------------
3
=

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