Design of
Unreinforced
Slabs-on-Ground
Made Easy
BY WAYNE W. WALKER AND JERRY A. HOLLAND
I
n our previous article “The First
Commandment for Floor Slabs:
Thou Shalt Not Curl Nor
Crack...(Hopefully)” (Concrete
International, January 1999), we
discussed some important concepts
concerning the design of slabs-onground such as curling, linear
shrinkage, joint spacing, and serviceability issues. In this article we have
used those concepts and others,
plus a unique computer analysis, to
develop design aids for slabs-onground that are unreinforced or have
a small amount of reinforcing that is
not included in the structural
capacity.
We have used these design aids
for many years to design numerous
successful industrial slabs. Design
graphs presented here for joint
spacings, uniform loads, rack loads,
and lift truck loads help make the
design of unreinforced slabs much
simpler and easier; furthermore, these
design aids usually provide more
economical slabs than those designed
by more traditional methods.
What should the joint
spacing be?
There are a variety of slab design
options a designer can choose from
based on the project requirements.
These options can be separated into
two broad categories: slab designs
that are based on the slab not
cracking (uncracked option) and
slab designs based on the slab
cracking but remaining serviceable
(cracked option). Typically, the
uncracked slab design option would
be a design using the concrete
flexural tensile strength to resist the
loads, and the cracked option would
be a slab reinforced to limit the
cracks to an acceptable width. This
article addresses slabs designed not
to crack between joints, and an
upcoming article in CI will address
slabs designed to crack but remain
serviceable.
To minimize the size and number
of cracks in an unreinforced slab, it
is important to use the proper joint
spacing to minimize the curling
stresses, which are usually much
larger than linear shrinkage stresses.
The authors have observed numerous
industrial slabs having a calculated
curling stress of 200 psi (1.4 MPa) or
less that have performed well. Based
on a theoretical model that predicts
our field-measured values, we
derived equations using curvilinear
regression that provide joint
Concrete international
/ MAY 2001 37
Fig. 1: Recommended joint spacing for unreinforced slabs
curling and cracking. Application of
the joint spacing criteria shown
(solid lines) in Fig. 1 has resulted in
many successful slabs that have
remained much flatter and with far
fewer cracks than typically seen.
For joint spacings approaching 15 ft
(4.6 m) or longer, with medium to high
shrinkage potential concrete and
heavy vehicular traffic, the slab
designer should consider using
dowels in the joints since the joints
may no longer have adequate shear
transfer by aggregate interlock. For
aggregate interlock to be effective
long-term, the joint spacing should
theoretically be extremely close
together (5 to 10 ft [1.5 to 3.0 m] for
anything but low-shrinkage concrete),
but in actuality, joints tend to open a
little less than the theoretical prediction because of the restraints. If the
designer cannot be sure of positive,
long-term shear transfer at the joints
through aggregate interlock, dowels
should be used.
It may be more economical to keep
the joint spacing at 15 ft (4.6 m) for the
thicker slabs and eliminate the dowels
in the contraction joints; however,
there will be more linear feet of joints
to maintain. One other consideration
concerning close joint spacing and
joint maintenance is that, although
there may be more joints, joint
movement is less (both horizontally
and vertically), which means there is
less joint maintenance required per
unit length of joint. These options
should be discussed with the owner.
Fig. 2: Concentrated load on a slab-on-ground
Design for top or
bottom cracking?
spacing data to maintain curling stress at approximately 200 psi (1.4 MPa).
Figure 1 shows the graph for this equation for two types of concrete: a
concrete with typical shrinkage values and a concrete with low shrinkage
values.
Figure 1 also shows the joint spacing criteria of 36 and 24 times the slab
thickness which has been referenced in the past. Using the commonly
specified joint spacing of 36 times the slab thickness may cause a high
curling stress, especially for the thicker slabs. Using a joint spacing of 36
times the slab thickness, along with some of the newer concrete materials
that have higher shrinkage potential, has caused many slabs to exhibit
For a single concentrated load on a
slab, the first cracks that will develop
will be in the bottom of the slab in a
radial direction, as shown in Fig. 2. As
the load continues to increase, the
next crack will be in the top of the slab
in a partially or completely circumferential direction, as also shown in Fig.
2. The cracks in the bottom of the slab
obviously cannot be seen and normally do not cause any serviceability
problems. The cracks in the top of the
38
MAY 2001
/ Concrete international
“Using a joint spacing of 36 times the slab thickness, along with some of the newer
concrete materials that have higher shrinkage potential, has caused many slabs to
exhibit curling and cracking. Application of the joint spacing criteria shown (solid lines)
in Fig. 1 has resulted in many successful slabs that have remained much flatter and
with far fewer cracks than typically seen.”
slab can be seen, cause serviceability
problems, and raise aesthetic concerns. Thus, the design aids are based
on minimization of the top cracks,
except for conditions where lift trucks
produce highly repetitive loads. (See
the section on lift truck capacity.)
The authors have developed a
unique computer program that allows
the slab to crack on the bottom and
therefore lets the negative moment
(moment that causes tension stress
in the top) increase. As can be seen in
Fig. 3, the negative moment for the
cracked slab model is about half of
the traditional moment (which
assumes the slab is uncracked) that
is typically used to design slabs. In
other words, once the slab has
cracked on the bottom, the second
load path has much more capacity.
This increase in capacity explains
why we have observed, on many
occasions, slabs that have supported
much higher concentrated loads than
that predicted by traditional analysis.
In such cases it is thought that the
slab with the high concentrated loads
has cracked on the bottom (not
visible) and the slab has increased
capacity on the second load path. The
slab’s actual capacity to support
concentrated loads will most likely be
greater than twice the capacity
calculated by a traditional analysis
and would depend on the number of
bottom radial cracks.
Flexural stresses occur in slabson-ground when either the uniform
storage loads are not continuous
(such as at aisle ways), the soil
support beneath the slab is not
uniform, or both. At aisle ways,
the maximum tension stress in the
top of the slab will occur when the
uniform loads are located at the
critical aisle width, as shown in
Fig. 4. Aisle widths that are less
than or greater than the critical aisle
width will have less flexural tension
stress in the top.
Drag stress due to
linear shrinkage
Drag stresses (due to linear
shrinkage and frictional restraints)
that will occur for the joint spacings
shown in Fig. 1 will be small if the
slab is placed on a low friction base
with small, gradual undulations. If
the undulations in the base become
large and/or with abrupt changes, the
drag stresses can easily become
significant, and stress concentrations
can develop that can lead to cracking.
Therefore, it is important that the
base under a slab be constructed as
smooth and planar as practicably
possible (to help minimize the drag
stress due to the linear shrinkage)
and maintain a uniform thickness.
Fig. 3: Moments for a 6 in. (150 mm) thick slab-on-ground
with a 10,000 lb (45 kN) concentrated load
Fig. 4: Uniform loading on a slab-on-ground
Concrete international
/ MAY 2001 39
What allowable flexural stress
should be used?
Fig. 5: Rack plan
Fig. 6: Stresses perpendicular to the aisle for a 6 in. (150 mm)
thick slab-on-ground that has cracked on the bottom of the slab
at the rack base plate locations (red color indicates high tension
stress in the top of the slab)
Modulus of subgrade reaction
Design graphs for two values of modulus of subgrade
reaction (K) are given for uniform loads and rack loads.
The 30 pci (9000 kN/m3) value is for a soft soil with a
wide area loading that will be subjected to some longterm consolidation. The 80 pci (22,000 kN/m3) value is
for a firm soil with a wide area loading with minimal longterm consolidation. The modulus of subgrade reaction
used for lift trucks is 100 pci (30,000 kN/m3), which is
typical for many soils with temporary loads applied over
small areas.
40
MAY 2001
/ Concrete international
Design graphs are based on the allowable concrete
flexural tension stress to give the designer flexibility in
selecting the method in which the concrete modulus of
rupture is determined and which factor of safety should
be used. There are several published empirical equations that give the modulus of rupture based on the
concrete compressive strength. Equations based on
these data have considerable scatter because the
modulus of rupture is sensitive to other concrete design
mixture parameters and components, such as the
aggregate shape and texture. For similar compressive
strengths, the authors have seen modulus of rupture
values vary from less than 450 psi (3.1 MPa) to more
than 750 psi (5.2 MPa).
Due to the variability of the modulus of rupture values
for different concrete mixture designs, when we are not
familiar with the local concrete materials, we require
flexural beam tests prior to construction of large, critical
slabs. When beam tests are specified, compression
cylinders typically are made of the same concrete to
correlate between the flexural and the compressive
strengths. After the relationship is found to be consistent,
only compression cylinders are tested. Flexural beam
tests are highly sensitive to sampling, storage, transportation, and testing; thus, only highly qualified testing
companies and certified technicians should be used.
The factors of safety used range from 1.25 to 2.0. Lower
factors of safety can be applied when there are the following conditions: good quality control of the concrete mixture
design; dependable geotechnical information with proper
base control; adequate field testing; good construction
supervision; well-known applied loads; and required
flexural beam tests. Higher factors of safety are used where
there is less information on the conditions mentioned
above or highly repetitive dynamic loads that would cause
fatigue of the concrete, such as frequent lift truck traffic.
Rack load
considerations
The rack plan dimensions used for the design aid are as
shown in Fig. 5. This type of rack is commonly used for
double-deep pallet storage. The analysis used was as noted
above for concentrated loads, allowing the slab bottom to
crack under the post. As can be seen in the moment
contours in Fig. 6 for a center rack post load of 10,000 lbf
(45 kN) (note: no curling or drag stresses are added to the
moment contours for this graph), the high moments occur
away from the post loads, unlike traditional analysis based
on uncracked section properties that predict the maximum
stress directly under the post load. Also, a traditional
analysis for these soil values and rack plan dimensions
would provide a higher rack post load capacity than for a
single post load, thereby indicating the surrounding rack
Fig. 7: Slab thickness required for 3000 lb (13 kN) and 4000 lb
(18 kN) capacity lift trucks
Fig. 9: Allowable rack post loads
post loads act to reduce the positive moment under the
center rack post.
Since the surrounding rack posts may not be loaded
to their full capacity, the single post load capacity would
be the controlling factor for traditional analysis. For
typical slab thicknesses and soil properties, this difference in load capacity would range between 10 to 20%.
The maximum post load is controlled by one of the
following: allowable flexural stress; base plate bearing
stress; punching shear; or beam shear.
Lift truck considerations
Fig. 8: Allowable uniform loads
Typical lift trucks with rated capacities of 3000 lbf (13 kN)
and 4000 lbf (18 kN) and solid tires were chosen because
these are the most commonly used. The analytical model
used for the design aid (Fig. 7) is based on no cracking on
the slab bottom in order to ensure that fatigue is not a
significant issue. However, for lift truck loading with a low to
moderate number of load repetitions, the slab could be
designed for bottom cracking but no top cracking (similar
to the rack loading above).
Concrete international
/ MAY 2001 41
Conclusions
There are many variables that
should be considered in the design
of slabs-on-ground. Here we have
provided a sophisticated computer
analysis program developed to
address these variables with graphs
(Fig. 7, 8, and 9) that will make
designing unreinforced and lightly
reinforced slabs easier and provide
more economy for various slab
applications. Many slabs have been
designed and successfully constructed using these design aids, but
readers are cautioned to make sure
they understand all contributing
design factors before using these
design aids or seek technical assistance from appropriately competent
designers. Look for an upcoming
article in Concrete International on
the design of reinforced slabs based
on crack width control.
Selected for reader interest by the editors.
er is a senior structural engineer at
ACI Member Wa y ne W. Walk
alker
Lockwood Greene Engineers, Atlanta, Ga. He has been a speaker
at ACI seminars and is a member of ACI Committee 360, Design of
Concrete Slabs on Ground. He has also published other papers
and has developed many computer programs to analyze and
design slabs on grade.
Jerr
Jerryy A
A.. Ho
Holl l and
and,, FACI, is a structural engineering consultant
with Lockwood Greene Engineers and Architects in Atlanta, Ga.
He has 33 years of experience in design, construction, and
troubleshooting concrete materials and structures. Holland is
past chairman of ACI Committee 360, Design of Slabs on
Ground, and is currently a member of that committee; as well as
223, Shrinkage-Compensating Concrete; 301, Specifications for
Concrete; 302, Construction of Concrete Floors; and 350,
Environmental Engineering Concrete Structures.
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42
MAY 2001
/ Concrete international