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1Design of SlabsDesign of Slabs--onon--GroundGround(ACI 360R(ACI
360R--06)06)
T. Bart Quimby, P.E., Ph.D.T. Bart Quimby, P.E., Ph.D.
UAA Professor of Civil UAA Professor of Civil
EngineeringEngineering
22 July 201022 July 2010
DefinitionDefinition
ACI 360RACI 360R--06 1.1: A slab, supported by 06 1.1: A slab,
supported by ground, whose main purpose is to support ground, whose
main purpose is to support the applied loads by bearing on the the
applied loads by bearing on the ground.ground.
This does not include footings or mat This does not include
footings or mat foundations which should be designed foundations
which should be designed using ACI 318.using ACI 318.
IntroductionIntroduction
Slabs on grade are similar to PAVEMENTS Slabs on grade are
similar to PAVEMENTS and not generally structural elementsand not
generally structural elements
Pavements pass loads through compression to Pavements pass loads
through compression to the supporting soilthe supporting soil
As long as the soils deformations are low, As long as the soils
deformations are low, there is negligible bending in the slabthere
is negligible bending in the slab
Slabs on grade are deemed to be Slabs on grade are deemed to be
successful if there is little or no crackingsuccessful if there is
little or no cracking
Slab TypesSlab Types(ACI 360R(ACI 360R--05 2)05 2)
Unreinforced slabsUnreinforced slabs
Also know as Also know as Plain Plain SlabsSlabs
Slabs reinforced to Slabs reinforced to limit crack widthslimit
crack widths
Mild steel reinforcing Mild steel reinforcing in upper third of
slabin upper third of slab
Fiber reinforcementFiber reinforcement
Slabs reinforced to Slabs reinforced to prevent cracking due
prevent cracking due to shrinkage and to shrinkage and temperature
restraint temperature restraint and applied loadsand applied
loads
Shrinkage Shrinkage compensating concretecompensating
concrete
PostPost--tensioningtensioning
Structural SlabsStructural Slabs
Use ACI 318Use ACI 318
Simplified MechanicsSimplified Mechanics
Apply load to top of slab
Since the slab is stiffer than the soil the load is distributed
over a larger
area of soil
A thicker slab is stiffer and distributes the load over a
larger area of soil
The thicker the slab the lower the induced bending stresses and
thus less structural cracking
Types of CracksTypes of Cracks
StructuralStructural Structural cracks are the result of
Structural cracks are the result of subgradesubgradesettlement
and/or stiffness discontinuitysettlement and/or stiffness
discontinuity
Often occur when a slab is over loadedOften occur when a slab is
over loaded
ShrinkageShrinkage Shrinkage cracks occur soon after a floor
slab Shrinkage cracks occur soon after a floor slab DRIES and will
not increase in length, width DRIES and will not increase in
length, width or number after the drying process is or number after
the drying process is completed.completed.
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2Causes of Structural CrackingCauses of Structural Cracking
Virtually all structural cracks are the result of Virtually all
structural cracks are the result of subgradesubgrade failure (See
ACI 360Rfailure (See ACI 360R--06 3)06 3)
The failure may result from one or more of the The failure may
result from one or more of the following conditionsfollowing
conditions The The subgradesubgrade is improperly designed or
preparedis improperly designed or prepared The slab thickness is
too thin for applied loads and The slab thickness is too thin for
applied loads and the stiffness of the the stiffness of the
subgradesubgrade
The concrete does not have sufficient strengthThe concrete does
not have sufficient strength
It is necessary to determine the stiffness of the It is
necessary to determine the stiffness of the subgradesubgrade and
the magnitude of the expected and the magnitude of the expected
loads so that the proper slab thickness can be loads so that the
proper slab thickness can be determineddetermined
Structural CracksStructural Cracks
Cracks form when the Moment exceeds the Cracking Moment
Thickness Design of Slabs on GradeThickness Design of Slabs on
Grade
Slabs on grade are, to a limited extent, Slabs on grade are, to
a limited extent, beams on elastic foundations. The softer beams on
elastic foundations. The softer the supporting soil and/or the
larger the the supporting soil and/or the larger the load, the
stronger and stiffer the slab load, the stronger and stiffer the
slab must be to spread the load over more of must be to spread the
load over more of the supporting soil the supporting soil (See ACI
360R(See ACI 360R--06 1.4)06 1.4) Slab Slab stiffnessstiffness is a
function of slab is a function of slab thicknessthickness
Slab Slab cracking strengthcracking strength is a function of is
a function of concrete strengthconcrete strength and and slab
thicknessslab thickness
Thickness Design ProceduresThickness Design Procedures
Portland Portland Cement Cement Association Association (ACI
360R(ACI 360R--06 6.2.1)06 6.2.1)
Wire Wire Reinforcing Reinforcing Institute Institute (ACI
360R(ACI 360R--06 6.2.2)06 6.2.2)
Corp. of Corp. of Engineers Engineers (ACI 360R(ACI 360R--06
6.2.3)06 6.2.3) ACI 360R-06 6.2 also gives some equations
for loads at corners and edges
PCI MethodPCI Method(Concrete Floors on Ground, 2008)(Concrete
Floors on Ground, 2008)
Good for INTERIOR loadings onlyGood for INTERIOR loadings
only
A series of charts for various loading A series of charts for
various loading conditions (wheels, racks, posts, etc)conditions
(wheels, racks, posts, etc)
Example of slab thickness determination Example of slab
thickness determination for a wheeled vehicle:for a wheeled
vehicle: Data for lift truckData for lift truck
Axle load = 25 kAxle load = 25 k
Wheel spacing = 37 inWheel spacing = 37 in
Number of wheels = 2Number of wheels = 2
Tire inflation pressure = 110 psiTire inflation pressure = 110
psi
PCI Example ContinuedPCI Example Continued
Contact area = wheel load/inflation Contact area = wheel
load/inflation pressure pressure Contact area = (25,000 lb / 2
wheels) / 110 Contact area = (25,000 lb / 2 wheels) / 110 psi = 114
inpsi = 114 in22
Subgrade and Concrete DataSubgrade and Concrete Data Subgrade
Modulus, k = 100 pciSubgrade Modulus, k = 100 pci
Concrete 28Concrete 28--day strength, fday strength, fcc = 7,000
psi= 7,000 psi Concrete flexural strength, MR ~ 7.5sqrt(fConcrete
flexural strength, MR ~ 7.5sqrt(fcc) ~ 640 ) ~ 640 psipsi
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3PCI Example ContinuedPCI Example Continued
Use a factor of safety of 2.0Use a factor of safety of 2.0
Choice depends of number of stress Choice depends of number of
stress repetitions permittedrepetitions permitted
Concrete working stress = MR/FSConcrete working stress = MR/FS
WS = MR/FS = 640 psi / 2 = 320 psiWS = MR/FS = 640 psi / 2 = 320
psi
Slab stress per 1,000 lb of axial loadSlab stress per 1,000 lb
of axial load WS / axle load, kips = 320/25 = 12.8 psi per WS /
axle load, kips = 320/25 = 12.8 psi per 1,000 lbs.1,000 lbs.
PCI Example ContinuedPCI Example Continued
Slab Stress per 1,000 lb of axle
load
Effective Contact
Area
Wheel SpacingSubgrade Modulus
Use 8 Slab
PCI Chart for RacksPCI Chart for Racks
Need to match Need to match criteria for the criteria for the
chartchart
Read the Read the instructions for instructions for each
chart!each chart!
Basic ParametersBasic Parametersused in thickness
determinationused in thickness determination
The basic parameters needed to determine slab The basic
parameters needed to determine slab thickness arethickness are
LoadLoad
MagnitudeMagnitude
Distribution/Contact AreaDistribution/Contact Area
Proximity to other loadsProximity to other loads
MoreMore
Slab StiffnessSlab Stiffness
This is normally taken as function of the concrete tensile This
is normally taken as function of the concrete tensile
strengthstrength
Soil StiffnessSoil Stiffness
Causes of Shrinkage CrackingCauses of Shrinkage Cracking
Shrinkage cracking occurs due to the Shrinkage cracking occurs
due to the normal volumetric changes associated normal volumetric
changes associated with dryingwith drying
Normal concrete can only stretch about Normal concrete can only
stretch about 0.0020.002 inches per foot without rupturinginches
per foot without rupturing
Normal shrinkage is about Normal shrinkage is about 0.0060.006
((++25%) 25%) inches per footinches per foot
If the slab is restrained against movement If the slab is
restrained against movement then cracking is inevitablethen
cracking is inevitable
Minimizing Shrinkage CrackingMinimizing Shrinkage Cracking
Shrinkage cracking can be Shrinkage cracking can be
minimizedminimized byby Reducing the shrinkage characteristics of
the Reducing the shrinkage characteristics of the concrete
mixconcrete mix
Reducing restraint on the slabReducing restraint on the slab
Shrinkage cracking can be Shrinkage cracking can be
controlledcontrolled byby Encouraging cracks to appear at
Encouraging cracks to appear at predetermined
locationspredetermined locations
The use of reinforcing steelThe use of reinforcing steel
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4Reducing Shrinkage Characteristics Reducing Shrinkage
Characteristics of the Concrete Mixof the Concrete Mix
Reduce the volume of water in the mixReduce the volume of water
in the mix The challenge is to limit the amount of water The
challenge is to limit the amount of water in the mix while
maintaining workability and in the mix while maintaining
workability and finishability without excessive use of water
finishability without excessive use of water reducersreducers
Use coarser ground cementUse coarser ground cement
Use the largest sized aggregate permitted Use the largest sized
aggregate permitted by designby design
Use shrinkage compensating concreteUse shrinkage compensating
concrete
Reducing Shrinkage Characteristics Reducing Shrinkage
Characteristics of the Concrete Mix (Cont.)of the Concrete Mix
(Cont.)
Use proper curing Use proper curing techniquestechniques
Proper curing keeps water Proper curing keeps water
in the concrete until it has in the concrete until it has
achieved sufficient tensile achieved sufficient tensile strength
before shrinkage strength before shrinkage
occursoccurs
Proper curing allows drying Proper curing allows drying
to occur more evenly to occur more evenly through the slab
thicknessthrough the slab thickness
CurlingCurling
Differential shrinkage due to drying can result in curling of
the slab edges, resulting in an induced moment in the slab.
When the moment equals the cracking moment a crack forms,
redistributing the stress
Sources of RestraintSources of Restraint
Friction between the slab and the groundFriction between the
slab and the ground
As the slab shrinks, the friction resists the As the slab
shrinks, the friction resists the motion, causing tension in the
slabmotion, causing tension in the slab
Bearing on other features (walls, Bearing on other features
(walls, foundation, drain pipes, columns, etc)foundation, drain
pipes, columns, etc)
Attachment to other featuresAttachment to other features
Friction RestraintFriction Restraint
Axial Stress Diagram
Tensile Capacity
Shrinkage CracksShrinkage Cracks
Axial Stress Diagram
Tensile Capacity
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5Restraint by Restraint by FeaturesFeatures
Cracks from
Structural Restraint
Locating CracksLocating Cracks
Control and construction joints are places Control and
construction joints are places of intentional weakness. They are
placed of intentional weakness. They are placed close enough
together to keep tensile close enough together to keep tensile
stresses in the slab below the tensile stresses in the slab below
the tensile rupture strength of the concreterupture strength of the
concrete
Control JointsControl Joints
The purpose of these joints is to predetermine The purpose of
these joints is to predetermine the location of cracks for esthetic
and the location of cracks for esthetic and performance purposes.
performance purposes. ACI 302.1R, pg 6ACI 302.1R, pg 6
Unless the design provides for the specific Unless the design
provides for the specific supplemental reinforcing across the
joint, the supplemental reinforcing across the joint, the resulting
induced crack may offer no structural resulting induced crack may
offer no structural advantage over a randomly occuring shrinkage
advantage over a randomly occuring shrinkage crack. crack. ACI
302.1R, pg 6ACI 302.1R, pg 6
Construction JointsConstruction Joints
These joints are placed in a slab where These joints are placed
in a slab where the concreting operations are concluded the
concreting operations are concluded for the day, generally in
conformity with a for the day, generally in conformity with a
predetermined joint layout. If at any time predetermined joint
layout. If at any time concreting is interrupted long enough for
concreting is interrupted long enough for the placed concrete to
harden, a the placed concrete to harden, a construction joint
should be used. construction joint should be used. ACI ACI 302.1R
pg 6302.1R pg 6
Control Control Joint Joint DetailsDetails
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6Construction JointsConstruction Joints Particular
ExampleParticular ExampleCracking of Slab w/o Vertical Cracking of
Slab w/o Vertical
Transfer at JointsTransfer at Joints
Joint SpacingJoint Spacing
Unreinforced SlabsUnreinforced Slabs
30 times each inch of slab thickness (ACI 30 times each inch of
slab thickness (ACI 360R360R--06 4.8). Smaller aggregate size,
higher 06 4.8). Smaller aggregate size, higher water contents, and
local experience may water contents, and local experience may
dictate use of closer jointsdictate use of closer joints
Reinforced SlabsReinforced Slabs
Use a Use a subgradesubgrade drag equation to compute drag
equation to compute joint spacingjoint spacing
Drag EquationDrag Equation
Where:Where: L = distance between joints, ftL = distance between
joints, ft AAss = Area of steel per foot width of slab, in= Area of
steel per foot width of slab, in
22/ftw/ftw ffss = Allowable steel stress (20,000 psi or 24,000
psi)= Allowable steel stress (20,000 psi or 24,000 psi) W = Dead
weight of slab, psfW = Dead weight of slab, psf = Friction factor
(1 to 2.5)= Friction factor (1 to 2.5)
WfAL
StrengthfALWFriction
ss
allowabless
22
=
===
Important Concepts for Joint Important Concepts for Joint
DetailsDetails
Only reinforcement across the joint is to Only reinforcement
across the joint is to be used for vertical load transfer only. be
used for vertical load transfer only. Use plain bars and coat to
prevent bond to Use plain bars and coat to prevent bond to
concreteconcrete
Joint should extend at least slab Joint should extend at least
slab thickness through the slabthickness through the slab
Vertical load transfer across construction Vertical load
transfer across construction joints can be accomplished with plain
bars joints can be accomplished with plain bars or properly
designed keyed joints.or properly designed keyed joints.
No Vertical Load Transfer
Joints have vertical transfer but allow in plane
shrinkage movement
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7Controlling Shrinkage Cracking with Controlling Shrinkage
Cracking with Reinforcing SteelReinforcing Steel
Reinforcement serves to restrain the shrinkage, Reinforcement
serves to restrain the shrinkage, effectively subdividing the slab
and hence effectively subdividing the slab and hence distributing
the crack area more evenly. This distributing the crack area more
evenly. This produces smaller and more numerous cracks produces
smaller and more numerous cracks than would occur in an
unreinforced slab of the than would occur in an unreinforced slab
of the same dimensions. The actual crack area same dimensions. The
actual crack area remains essentially the same.remains essentially
the same.
Fricks, T.J. Cracking in Floor Slabs, reprinted in ACI Fricks,
T.J. Cracking in Floor Slabs, reprinted in ACI SCMSCM--25 (92), pg
122.25 (92), pg 122.
Reinforcing SteelReinforcing Steel
Smaller bar sizes are better choices than large Smaller bar
sizes are better choices than large diametersdiameters
This steel should be positioned oneThis steel should be
positioned one--fourth the fourth the slab thickness below the top
surface up to 2.0 in slab thickness below the top surface up to 2.0
in maximum. ACI 302.1R, pg 5maximum. ACI 302.1R, pg 5
Minimum cover of the steel is controlled by ACI Minimum cover of
the steel is controlled by ACI 318 7.7. 318 7.7. Top cover inch
clear cover for slabs protected Top cover inch clear cover for
slabs protected from the weather, 1.1/2 for #5 or smaller bars and
from the weather, 1.1/2 for #5 or smaller bars and 2 for larger
bars exposed to weather2 for larger bars exposed to weather
3 clear between bars and the ground.3 clear between bars and the
ground.
Is Is Reinforcement Reinforcement Needed?Needed?
Concrete Floors on Ground
By Portland Cement Association
Second Edition
Sample Slab Reinforcing CalculationSample Slab Reinforcing
Calculation
Determine the reinforcing steel requirement for Determine the
reinforcing steel requirement for an outdoor, 5 thick concrete slab
with control an outdoor, 5 thick concrete slab with control joints
spaced 25 ft apart. The slab is cast on a joints spaced 25 ft
apart. The slab is cast on a compacted gravelly soil surface. Use
40 ksi compacted gravelly soil surface. Use 40 ksi rebarrebar
VariablesVariables ffss = 20,000 psi= 20,000 psi = 2.0 (assume
that gravel surface has some = 2.0 (assume that gravel surface has
some interlock with the slab)interlock with the slab)
L = 25 ftL = 25 ft W = 5 (150 pcf / 12) = 62.5 psfW = 5 (150 pcf
/ 12) = 62.5 psf
Calculation ContinuedCalculation Continued
From drag equation: From drag equation: ReqdReqd AAss = 0.0781
in= 0.0781 in
22//ftwftw
Spacing Spacing CalcsCalcs:: #3 bar: s #3 bar: s