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Design 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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Causes 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, f’day strength, f’cc = 7,000 psi= 7,000 psi�� Concrete flexural strength, MR ~ 7.5sqrt(f’Concrete flexural strength, MR ~ 7.5sqrt(f’cc) ~ 640 ) ~ 640 psipsi

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PCI 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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Reducing 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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Restraint by Restraint by FeaturesFeatures

Cracks from

Structural Restraint

Locating “Cracks”Locating “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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Construction JointsConstruction Joints Particular ExampleParticular Example

Cracking 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, in22/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�� µµ = Friction factor (1 to 2.5)= Friction factor (1 to 2.5)

W

fAL

StrengthfAL

WFriction

ss

allowabless

µ

µ

2

2

=

===

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 ¼ slab Joint should extend at least ¼ 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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Controlling 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 ¾” inch clear cover for slabs protected Top cover ¾” 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�� µµ = 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: �� Req’dReq’d AAss = 0.0781 in= 0.0781 in22//ftwftw

�� Spacing Spacing CalcsCalcs::�� #3 bar: s #3 bar: s << (.11 in(.11 in22/bar)(12”/ft)/(.0781 in/bar)(12”/ft)/(.0781 in22/ft) = 16.9 /ft) = 16.9 inin

�� #4 bar: s #4 bar: s << 30.7 in 30.7 in

�� 6x6 W4.0xW4.0 wire mesh gives A6x6 W4.0xW4.0 wire mesh gives Ass = 0.080 in= 0.080 in22//ftwftw..

�� ACI 318 7.6 limits spacing to min(3h, 18”)ACI 318 7.6 limits spacing to min(3h, 18”)

�� Decision: Use #3 bars 15” O.C. each way. Place Decision: Use #3 bars 15” O.C. each way. Place with a clear cover of 1” below top of slab.with a clear cover of 1” below top of slab.

Cracking ExamplesCracking Examples