360R-06 Design of Slabs-on-Ground

R-36 ACI COMMITTEE REPORT

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Design of Slabs-on-Ground

CHAPTER 9—DESIGN OF POST-TENSIONED SLABS-ON-GROUND 9.1—Notation

360R-36 ACI COMMITTEE REPORT
surface abrasion resistance with the use of a wear-resistant
aggregate. At times, more ductile materials, such as graded
iron, are employed in bonded overlays to improve the abrasion
resistance and impact resistance of the floor surface.
Joints in a deferred topping slab should accommodate
shrinkage strains by matching the base slab joints. The base
slab joints should be carefully coordinated with the topping
slab joints and continued through the topping, or a crack will
develop. Further, base slabs that contain cracks that move
due to slab motion will often reflect cracks into the topping.
Therefore, these cracks should be repaired. If the base slab
contains shrinkage-compensating concrete, the portland-
cement concrete bonded topping should be applied at least
10 days after the base slab is placed. This allows the base slab
to display volume change characteristics similar to portland-
cement concrete, as both the topping and the base slab shorten
simultaneously. For bonded toppings, joints in addition to
those matching joints in the base slab do not serve a purpose.
A bonded topping of shrinkage-compensating concrete
should not be attempted as an overlay on a portland-cement
concrete base slab. The base slab restraint will negate the
expansion action of the topping, leading to cracking or
possibly delamination.
CHAPTER 9—DESIGN OF POST-TENSIONED
SLABS-ON-GROUND
9.1—Notation
A = area of gross concrete cross section, in.
2
(mm
2
)
A
b
= bearing area beneath tendon anchor, in.
2
(mm
2
)
A
b
′ = maximum area of portion of supporting surface that
is geometrically similar to and concentric with
loaded area, in.
2
(mm
2
)
A
bm
= total area of beam concrete, in.
2
(mm
2
)
A
c
= activity ratio of clay
A
o
= coefficient in
Eq. (9-11)
A
ps
= area of prestressing steel, in.
2
(mm
2
)
A
sl
= total area of slab concrete, in.
2
(mm
2
)
B
= constant used in
Eq. (9-11)
B
w
= assumed slab width, in. (mm)
b
= width of individual stiffening beam, in. (mm)
C = constant used in
Eq. (9-11)
C
Δ
= coefficient used to establish allowable differential
deflection used in
Eq. (9-23)
CGC = geometric centroid of gross concrete section
CGS = center of gravity of prestressing force
C
p
= coefficient in
Eq. (9-41)
for slab stress due to partition
load—function of k
s
CR
= prestress loss due to creep of concrete, kips (kN)
c
= distance between CGC and extreme cross-section
fibers, in. (mm)
E
c
= long-term or creep modulus of elasticity of
concrete, psi (MPa)
ES
= prestress loss due to elastic shortening of concrete,
kips (kN)
E
s
= modulus of elasticity of soil, psi (MPa)
e
= eccentricity of post-tensioning force (perpendicular
distance between CGS and CGC), in. (mm)
e
m
= edge moisture variation distance, ft (m)
e
n
= base of natural (Naperian) logarithms
f
= flexural concrete stress (tension or compression),
ksi (kN/mm
2
)
f
B
= section modulus factor for bottom fiber
f
bp
= allowable bearing stress under tendon anchorages,
psi (MPa)
f
c
= allowable concrete compressive flexural stress, psi
(MPa)
f
c
′
= 28-day concrete compressive strength, psi (MPa)
f
ci
′
= concrete compressive strength at time of stressing
tendons, psi (MPa)
f
cr
= concrete modulus of rupture, flexural tension stress
that produces first cracking, psi (MPa)
f
p
= minimum average residual prestress compressive
stress, psi (MPa)
f
pi

= allowable tendon stress immediately after stressing,
psi (MPa)
f
pj
= allowable tendon stress due to tendon jacking force,
psi (MPa)
f
pu
= specified maximum tendon tensile stress, psi (MPa);
f
py
= specified yield strength of prestressing steel, psi
(MPa)
f
T
= section modulus factor for top fiber
f
t
= allowable concrete flexural tension stress, psi (MPa)
g
= moment of inertia factor
H
= thickness of uniform thickness foundation, in. (mm)
h
= total depth of stiffening beam, measured from top
surface of slab to bottom of beam (formerly d,
changed for consistency with ACI 318), in. (mm)
I
= gross concrete moment of inertia, in.
4
(mm
4
)
k
= depth-to-neutral axis ratio; also abbreviation for
kips
k
s
= soil subgrade modulus, lb/in.
3
(N/mm
3
)
L
= total slab length (or total length of design rectangle)
in direction being considered (short or long),
perpendicular to W, ft (m)
L
L
= long length of design rectangle, ft (m)
L
S
= short length of design rectangle, ft (m)
M
cs
= applied service moment in slab on compressible
soil, ft-kips/ft (kNm/m)
M
L
= maximum applied service load moment in long
direction (causing bending stresses on short cross
section) from either center lift or edge lift swelling
condition, ft-kips/ft (kNm/m)
M
max
= maximum moment in slab under load-bearing

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