     # Analysis of Concrete Slabs on Grade

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### Text of Analysis of Concrete Slabs on Grade

"GRDSLAB" Program

Slab on GradeCONCRETE SLAB ON GRADE ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Interior Concentrated Post or Wheel LoadingAssuming Slab is Reinforced for Shrinkage and Temperature Only3000Check Slab Flexural Stress:(assuming unreinforced slab with interior load condition)Job Name:Subject:3500a =6.770in.a = SQRT(Ac/p)Job Number:Originator:Checker:4000Ec =3834254psiEc = 33*wc^1.5*SQRT(f 'c)4500MR =569.21psiMR = 9*SQRT(f 'c)Input Data:5000Mr =6.07ft-kipsMr = MR*(12*t^2/6)/12000 (per 1' = 12" width)Note: Formulas and results shown in "Red" represent other5500m =0.15m = 0.15 (assumed for concrete)variations of "modified" Westergaard stress equations.Minimum Required Slab Thickness for Single Interior Load:Slab Thickness, t =8.000in.6000Lr =35.968in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25t(min) =6.25in.Set Fb(allow) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Ref. 1)Concrete Strength, f 'c =4000psi40000b =6.319in.b = SQRT(1.6*a^2+t^2)-0.675*t , for a < 1.724*tReferences for slab (pavement) stress equations:Conc. Unit Weight, wc =150pcfTop/Slab500001 Load: fb1(actual) =121.22psifb1(actual) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Reference 1)1. "Load Testing of Instumented Pavement Sections" - by University of Minnesota, Dept. of Civil Eng. (submitted to MN/DOT, March 24, 2002)Note: The interior load condition isReinforcing Yield, fy =60000psi60000=121.17psi= 0.316*P/t^2*(4*LOG(Lr/b)+1.069) (Reference 2)2. "Principles of Pavement Design" - by E.J. Yoder and M.W. Witczak (John Wiley & Sons, 1975)assumed in this worksheet. However, theSubgrade Modulus, k =100pci65000=118.10psi= 0.316*P/t^2*(LOG(t^3)-4*LOG(b)-LOG(k)+6.48) (References 3 & 4)3. "Design of Concrete Structures" - by Winter, Urquhart, O'Rourke, and Nilson" - (McGraw-Hill, 1962)thicknesses for corner and edge condtionsConcentrated Load, P =6000.00lbs.700002 Loads: fb2(actual) =N.A.psifb2(actual) = N.A.4. "Design of Slabs-on-Ground" - ACI 360R-10 - by American Concrete Institute (2010)are shown below for comparison only.Contact Area, Ac =144.00in.^275000Fb(allow) =189.74psiFb(allow) = MR/FSFactor of Safety, FS =3.0080000Minimum Required Slab Thickness for Single Corner Load:Dowel Bar Dia., db =0.750in.Concrete Slab on Grade0.750(assuming unreinforced slab with corner load condition)t(min) =7.00in.Set Fb(allow) = 3*P/t^2*(1-(1.772*a/Lr)^(0.72)) (Ref. 1)Dowel Bar Spacing, s =12.000in.1.000fb1(actual) =153.68psifb1(actual) = 3*P/t^2*(1-(1.772*a/Lr)^(0.72)) (Reference 1)Minimum Required Slab Thickness for Single Edge Load (circular area):Const. Joint Width, z =0.2500in.Lubricate this endStop slab reinf. (As) at jointMin. of1.250=154.13psi= 3*P/t^2*(1-(SQRT(2)*a/Lr)^(0.6)) (References 2, 3 & 4)t(min) =9.00in.Set Fb(allow) = 3*(1+m)*P/(p*(3+m)*t^2)*(LN(Ec*t^3/(100*k*a^4))+1.84-4*m/3+(1-m)/2+1.18*(1+2*m)*a/Lr) (Ref. 1)Joint Spacing, L =20.000ft.of all Dowels1/8"-1/4" x t/4 formed jointt/3 or 2"Minimum Required Slab Thickness for Single Edge Load (semi-circular area):Temperature Range, DT =50.00deg.(assuming unreinforced slab with edge load condition)t(min) =10.00in.Set Fb(allow) = 3*(1+m)*P/(p*(3+m)*t^2)*(LN(Ec*t^3/(100*k*a^4))+3.84-4*m/3+(1+2*m)*a/(2*Lr)) (Ref. 1)Increase for 2nd Load, i =0.00%fb1(actual) =225.22psifb1(actual) = 3*(1+m)*P/(p*(3+m)*t^2)*(LN(Ec*t^3/(100*k*a^4))+1.84-4*m/3+(1-m)/2+1.18*(1+2*m)*a/Lr) (for circle) (Reference 1)fb1(actual) =271.26psifb1(actual) = 3*(1+

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