"GRDSLAB" Program

Doc"GRDSLAB" --- CONCRETE SLAB ON GRADE ANALYSISProgram Description:"GRDSLAB" is a spreadsheet program written in MS-Excel for the purpose of analysis of concrete slabs ongrade. Specifically, a concrete slab on grade may be subjected to concentrated post or wheel loading. Thenfor the given parameters, the slab flexural, bearing, and shear stresses are checked, the estimated crack width isdetermined, the minimum required distribution reinforcing is determined, and the bearing stress on the dowelsat construction joints is checked. Also, design charts from the Portland Cement Association (PCA) are includedto provide an additional method for determining/checking required slab thickness for flexure. The ability toanalyze the capacity of a slab on grade subjected to continuous wall (line-type) load as well as stationary,uniformly distributed live loads is also provided. Loading data for fork trucks and AASHTO trucks is included.This program is a workbook consisting of ten (10) worksheets, described as follows:Worksheet NameDescriptionDocThis documentation sheetSlab on GradeConcrete Slab on Grade Analysis for Concentrated Post or Wheel LoadingPCA Fig. 3-Wheel LoadPCA Figure 3 - Design Chart for Single Wheel LoadsPCA Fig. 7a-Post LoadPCA Figure 7a - Design Chart for Post Loads (k = 50 pci)PCA Fig. 7b-Post LoadPCA Figure 7b - Design Chart for Post Loads (k = 100 pci)PCA Fig. 7c-Post LoadPCA Figure 7c - Design Chart for Post Loads (k = 200 pci)Wall LoadConcrete Slab on Grade Analysis for Wall LoadUnif. LoadConcrete Slab on Grade Analysis for Stationary Uniform Live LoadsFork Truck DataFork Truck Axle Load, Wheel Load, and Spacing DataAASHTO Truck DataAASHTO Truck Axle Load, Wheel Load, and Spacing DataProgram Assumptions and Limitations:1. This program is based on the following references:a. "Load Testing of Instrumented Pavement Sections - Improved Techniques for Appling the Finite ElementMethod to Strain Prediction in PCC Pavement Structures" - by University of Minnesota, Department of CivilEngineering (submitted to MN/DOT, March 24, 2002)b. "Principles of Pavement Design" - by E.J. Yoder and M.W. Witczak (John Wiley & Sons, 1975)c. "Design of Concrete Structures" - by Winter, Urquhart, O'Rourke, and Nilson" - (McGraw-Hill, 1962)d. "Design of Slabs-on-Ground" - ACI 360R-10 - by American Concrete Institute (2010)e. "Dowel Bar Optimization: Phases I and II - Final Report" - by Max L. Porter (Iowa State University, 2001)f. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) - by Robert G. Packard(Portland Cement Association, 1976)g. "Concrete Floor Slabs on Grade Subjected to Heavy Loads"Army Technical Manual TM 5-809-12, Air Force Manual AFM 88-3, Chapter 15 (1987)h. "Stresses and Strains in Rigid Pavements" (Lecture Notes 3) - by Charles Nunoo, Ph.D., P.E.(Florida International University, Miami FL - Fall 2002)2. The "Slab on Grade" worksheet assumes a structurally unreinforced slab, ACI-360 "Type B", reinforced onlyfor shrinkage and temperature. An interior load condition is assumed for flexural analysis. That is, theconcentrated post or wheel load is assumed to be well away from a "free" slab edge or corner. The originaltheory and equations by H.M. Westergaard (1926) as modified by Reference (a) in item #1 above are used forthe flexural stress analysis. Some of the more significant simplifying assumptions made in the Westergaardanalysis model are as follows:a. Slab acts as a homogenous, isotropic elastic solid in equilibrium, with no discontinuities.b. Slab is of uniform thickness, and the neutral axis is at mid-depth.c. All forces act normal to the surface (shear and friction forces are assumed to be negligible).d. Deformation within the elements, normal to slab surface, are considered.e. Shear deformation is negligible.f. Slab is considered infinite for center loading and semi-infinite for edge loading.g. Load at interior and corner of slab distributed uniformly of a circular contact area.h. Full contact (support) between the slab and foundation.3. Other basic assumptions used in the flexural analysis of the "Slab on Grade" worksheet are as follows:a. Slab viewed as a plate on a liquid foundation with full subgrade contact (subgrade modeled as a seriesof independent springs - also known as "Winkler" foundation.)b. Modulus of subgrade reaction ("k") is used to represent the subgrade.c. Slab is considered as unreinforced concrete beam, so that any contribution made to flexural strength bythe inclusion of distribution reinforcement is neglected.d. Combination of flexural and direct tensile stresses will result in transverse and longitudinal cracks.e. Supporting subbase and/or subgrade act as elastic material, regaining position after application of load.4. The "Slab on Grade" worksheet allows the user to account for the effect of an additional post or wheel load.The increase in stress, 'i', due to a 2nd wheel (or post) load expressed as a percentage of stress for a singlewheel (or post) load and is to be input by the user. Refer to the input comment box for recommendations.5. All four (4) worksheets pertaining to the PCA Figures 3, 7a, 7b, and 7c from Reference (f) in item #1 above arebased on interior load condition and other similar assumptions used in the "Slab on Grade" worksheet.Other assumed values used in the development of the Figures 3, 7a, 7b, and 7c are as follows:a. Modulus of elasticity for concrete, Ec = 4,000,000 psi.b. Poisson's Ratio for concrete, m = 0.15.6. In the four (4) worksheets pertaining to the PCA Figures 3, 7a, 7b, and 7c, the user must manually determine(read) the required slab thickness from the design chart and must manually input that thickness in theappropriate cell at the bottom of the page. An iteration or two may be required, as when the slab thicknessis input, it may/may not change the effective contact area. Note: the user may unprotect the worksheet (nopassword is required) and access the Drawing Toolbar (select: View, Toolbars, and Drawing) to manuallydraw in (superimpose) the lines on the chart which are used to determine the required slab thickness.7. This program contains numerous comment boxes which contain a wide variety of information includingexplanations of input or output items, equations used, data tables, etc. (Note: presence of a comment boxis denoted by a red triangle in the upper right-hand corner of a cell. Merely move the mouse pointer to thedesired cell to view the contents of that particular "comment box".)

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+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)) (for semi-circle) (Reference 1)Note: there will be a few situations where certain combinations of the Concentrated=181.25psi= 0.572*P/t^2*(4*LOG(Lr/b)+0.359) (Reference 2)Load, P, Subgrade Modulus, k, and Contact Area, Ac, result in a #N/A error messageResults:Typical Construction Joint for Load Transfer=175.71psi= 0.572*P/t^2*(LOG(t^3)-4*LOG(b)-LOG(k)+5.77) (References 3 & 4)and thus no solution for the minimum slab thickness, t(min), for one or more of the=225.29psi= 0.803*P/t^2*(4*LOG(Lr/a)+0.666*(a/Lr)-0.034) (for circle)equations listed above. For those cases, the user would then manually iterate theCheck Slab Flexural Stress:(assuming unreinforced slab with interior load condition)=173.47psi= 0.803*P/t^2*(4*LOG(Lr/a)+0.282*(a/Lr)-0.650) (for semi-circle)input slab thickness to determine the minimum value if desired.Effective Load Radius, a =6.770in.a = SQRT(Ac/p)Modulus of Elasticity, Ec =3834254psiEc = 33*wc^1.5*SQRT(f 'c)Check Slab Bearing Stress:(assuming working stress)Check Slab Bearing Stress:(for edge or corner load)Modulus of Rupture, MR =569.21psiMR = 9*SQRT(f 'c) (Slab tensile strength in flexure)fp(actual) =41.67psifp(actual) = P/Acfp(actual) =41.67psifp(actual) = P/AcCracking Moment, Mr =6.07ft-k/ft.Mr = MR*(12*t^2/6)/12000 (per 1' = 12" width)Fp(allow) =2390.68psiFp(allow) = 4.2*MRFp(allow) =1195.34psiFp(allow) = 2.1*MRNote: For additional in depth analysis please refer to "BOEF.xls"Poisson's Ratio, m =0.15m = 0.15 (assumed for concrete)(Beam On Elastic Foundation) spreadsheet workbook.Radius of Stiffness, Lr =35.968in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25Check Slab Punching Shear Stress:(assuming working stress and interior load)Check Slab Punching Shear Stress: (for edge load)Check Slab Punching Shear Stress: (for corner load)Equivalent Radius, b =6.319in.b = SQRT(1.6*a^2+t^2)-0.675*t , for a < 1.724*tbo =48.000in.bo = 4*SQRT(Ac) (assumed load perimeter)bo =48.000in.bo = 4*SQRT(Ac) (assumed load perimeter)bo =48.000in.bo = 4*SQRT(Ac) (assumed load perimeter)For 1 Load: fb1(actual) =121.22psifb1(actual) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Ref. 1)fv(actual) =9.38psifv(actual) = P/(t*(bo+4*t))fv(actual) =14.42psifv(actual) = P/(t*(0.75*bo+2*t))fv(actual) =23.44psifv(actual) = P/(t*(0.5*bo+t))For 2 Loads: fb2(actual) =N.A.psifb2(actual) =N.A.Fv(allow) =153.69psiFv(allow) = 0.27*MRFv(allow) =153.69psiFv(allow) = 0.27*MRFv(allow) =153.69psiFv(allow) = 0.27*MRFb(allow) =189.74psiFb(allow) = MR/FSFb(allow) >= fb(actual), O.K.Note: Effect of a 2nd load was not considered.Shrinkage and Temperature Reinf.:(assuming subgrade drag method)Check Slab Bearing Stress:(assuming working stress and interior load)(Ref. 4)F =1.50F = 1.5 (assumed friction factor between subgrade and slab)Check Slab Bearing Stress for Edge or Corner Load:(Ref. 4)fp(actual) =41.67psifp(actual) = P/AcW =100.00psfW = wc*(t/12)fp(actual) =41.67psifp(actual) = P/AcFp(allow) =2390.68psiFp(allow) = 4.2*MRFp(allow) >= fp(actual), O.K.fs =45000psifs = 0.75*fyFp(allow) =1195.34psiFp(allow) = 2.1*MRAs =0.033in.^2/ft.As = F*L*W/(2*fs)Check Slab Punching Shear Stress:(assuming working stress and interior load)(Ref. 4)Check Slab Punching Shear Stress for Edge Load:(Ref. 4)bo =48.000in.bo = 4*SQRT(Ac) (assumed load perimeter)Slab Reinforcing:(assuming temperature method)bo =48.000in.bo = 4*SQRT(Ac) (assumed load perimeter)fv(actual) =9.38psifv(actual) = P/(t*(bo+4*t))fr =189.74psifr = MR/FSfv(actual) =14.42psifv(actual) = P/(t*(0.75*bo+2*t))Fv(allow) =153.69psiFv(allow) = 0.27*MRFv(allow) >= fv(actual), O.K.fs =45000psifs = 0.75*fyFv(allow) =153.69psiFv(allow) = 0.27*MRa =0.0000055a = 5.5x10^(-6) (assumed thermal expansion coefficient)Shrinkage and Temperature Reinforcing:(assuming subgrade drag method)(Ref. 3)Es =29000000psiEs = 29x10^6 (modulus of elasticity for steel)Check Slab Punching Shear Stress for Corner Load:(Ref. 4)Friction Factor, F =1.50F = 1.5 (assumed friction factor between subgrade and slab)As =0.246in.^2/ft.As = fr*(12)*t/(2*(fs-DT*a*Es))bo =48.000in.bo = 4*SQRT(Ac) (assumed load perimeter)Slab Weight, W =100.00psfW = wc*(t/12)fv(actual) =23.44psifv(actual) = P/(t*(0.5*bo+t))Reinf. Allow. Stress, fs =45000psifs = 0.75*fySlab Reinforcing:(assuming concrete-to-steel ratio method)Fv(allow) =153.69psiFv(allow) = 0.27*MRAs =0.033in.^2/ft.As = F*L*W/(2*fs)fr =189.74psifr = MR/FS(continued)fs =45000psifs = 0.75*fyAs =0.405in.^2/ft.As = fr*(12)*t/fsSuggested Rationale for Use in Determining Stress Increase Factor for Adjacent 2nd Load,"i":Determine Estimated Crack Width:(assuming no use of stabilized or granular subbase)Slab Reinforcing:(assuming confirmed capacity method)(Note: Both methods presented below are based on the concept of overlapping areas.)Slab-base Frict. Adjust., C =1.00C = 1.0 (assumed value for no subbase)As =0.122in.^2/ft.As = 14.5*SQRT(f 'c)*t/fyS = 6'Thermal Expansion, a =0.0000055in./in./dega = 5.5x10^(-6) (assumed thermal expansion coefficient)As =1.002in.^2/ft.As = 4.4*MR*t/(fy/FS)Shrinkage Coefficient, e =0.00035in./in.e = 3.5x10^(-4) (assumed coefficient of shrinkage)As =0.351in.^2/ft.As = ((MR/FS*12*t^2/6)/(1.44*t/2))/12000Lr = 2.997'Est. Crack Width, DL =0.1500in.DL = C*L*12*(a*DT+e)(Ref. 5)S = 6'Check Bearing Stress on Dowels at Construction Joints with Load Transfer:(Ref. 2)Slab Reinforcing:(assuming crack restraint method)Lr = 2.997'D =0.00052in./in.D = 1/8"/20' = 0.00052 = assumed shrinkage = P*L/(A*Ecm)A =96.00in.^2A = 12*tEcm =1500000psiEcm = 1.5x10^6L =1.000in.L = 1.0 assumedAs =1.248in.^2/ft.As = P/fy = (A*Ecm/L)*D/fy = 9360*t/fyDetermine Crack Width:(assuming no use of stabilized or granular subbase)2*Lr-S = N.A.C =1.0C = 1.0 (assumed value for no subbase)a =0.0000055a = 5.5x10^(-6) (assumed thermal expansion coefficient)2*Lr-S = N.A.e =0.00035in./in.e = assumed coefficient of shrinkageDL =0.1500in.DL = C*L*12*(a*DT+e)Assumed Load Transfer Distribution for Dowels at Construction JointCheck Bearing Stress on Dowels at Construction Joints with Load Transfer:Le =35.968in.Le = 1.0*Lr = applicable dist. each side of critical dowelLe =35.968in.Le = 1.0*Lr = applicable distance each side of critical dowelEffective Dowels, Ne =3.00barsNe = 1.0+2*S(1-d(n-1)*s/Le) (where: n = dowel #)Determine Stress Increase Factor for 2nd Load:Determine Stress Increase Factor for 2nd Load:Joint Load, Pt =3000.00lbs.Pt = 0.50*P (assumed load transferred across joint)Table for Determining the Total Number of Dowel Bars Effective in Transfer of Concentrated Load at Construction JointLoad Spacing, S =6.000ft.Load Spacing, S =6.000ft.Critical Dowel Load, Pc =1000.60lbs.Pc = Pt/NeDowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Dowel #Radius of Stiffness, Lr =2.997ft.Radius of Stiffness, Lr =2.997ft.Mod. of Dowel Suppt., kc =1500000psikc = 1.5x10^6 (assumed for concrete)1230000000000000000000000Overlapped Area, Ao =N.A.ft.^2Overlapped Area, Ao =N.A.ft.^2Mod. of Elasticity, Eb =29000000psiEb = 29x10^6 (assumed for steel dowels)1.0000.6660.3330.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000Area for 1 Load, A1 =N.A.ft.^2Area for 1 Load, A1 =N.A.ft.^2Inertia/Dowel Bar, Ib =0.0155in.^4Ib = p*db^4/64Increase for 2nd Load, i =0.00%Increase for 2nd Load, i =0.00%Relative Bar Stiffness, b =0.889b = (kc*db/(4*Eb*Ib))^(1/4)Ne =2.998barsNe = 1+2*S(1-d(i-1)*s/Le) (i = dowel #)For 2 Loads: fb2(actual) =N.A.psiFor 2 Loads: fb2(actual) =N.A.psifd(actual) =2635.47psifd(actual) = kc*(Pc*(2+b*z)/(4*b^3*Eb*Ib))Pt =3000.00lbs.Pt = 0.50*P (assumed load transferred across joint)Fd(allow) =4333.33psiFd(allow) = (4-db)/3*f 'cFd(allow) >= fd(actual), O.K.Pc =1000.60lbs.Pc = Pt/Newhere:where:kc =1500000psikc = 1.5x10^6 (assumed for concrete)Ao = (2*Lr-S)/2*(Lr-S/2)/Lr*(1), for S < 2*LrAo = Lr^2*(2*ACOS(S/(2*Lr))-SIN(2*ACOS(S/(2*Lr)))), for S < 2*LrEb =29000000psiEb = 29x10^6 (assumed for steel dowels)A1 = (2*Lr)/2*(1)A1 = p*Lr^2References:Ib =0.0155in.^4Ib = p*db^4/64i = Ao/A1i = Ao/A11. "Load Testing of Instrumented Pavement Sections - Improved Techniques for Appling the Finite Elementb =0.889b = (kc*db/(4*Eb*Ib))^(1/4)Method to Strain Prediction in PCC Pavement Structures" - by University of Minnesota, Depart. of Civilfd(actual) =2635.47psifd(actual) = kc*(Pc*(2+b*z)/(4*b^3*Eb*Ib))Engineering (submitted to MN/DOT, March 24, 2002)Fd(allow) =4333.33psiFd(allow) = ((4-db)/3)*f 'cExample:Comparison of slab bending stress values per Method 1, Method 2, and BOEF.xls (Beam on Elastic2. "Dowel Bar Optimization: Phases I and II - Final Report" - by Max L. Porter (Iowa State University, 2001)Foundation Analysis spreadsheet) for 8" thick slab, f'c = 4000 psi, Ec = 3834 ksi., k = 100 pci,3. "Guide to Design of Slabs-on-Ground" - ACI 360R-10 - by American Concrete Institute (2010)P1 & P2 = 6000 lbs./each, and Ac = 144 in.^24. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) - by Robert G. PackardDetermine Minimum Slab Thickness for Flexure: (iterative solutions for t(min))(Portland Cement Association, 1976)Iteration #Eqn. for fbiEqn. for fbcEqn. for fbecEqn. for fbesctiLoad WidthLoad WidthLoad WidthLoad Width5. "Stresses and Strains in Rigid Pavements" (Lecture Notes 3) - by Charles Nunoo, Ph.D., P.E.1-2203.397286.29-3444.68-5083.521.00= 0 (Point)= 0 (Point)= 0.50 ft.= 0.50 ft.(Florida International University, Miami FL - Fall 2002)2-1694.742908.18-2749.11-3961.261.25LoadMethod 1Method 2BOEF.xlsBOEF.xlsBOEF.xlsBOEF.xls3-1319.151150.44-2221.58-3142.901.50SpacingB = .75*2*LrB = .70*2*LrB = .75*2*LrB = .70*2*LrComments:4-1043.20369.74-1822.14-2542.581.75SStress, fbStress, fbStress, fbStress, fbStress, fbStress, fb5-836.724.91-1515.10-2092.612.00(ft.)(psi)(psi)(psi)(psi)(psi)(psi)6-678.78-166.41-1274.77-1747.512.251.002052172132282102257-555.41-242.07-1083.28-1477.162.501.501892041912051872008-457.23-268.63-928.25-1261.372.752.001751921721851671799-377.78-269.54-800.91-1086.263.002.5016218015716815016110-312.55-257.13-694.96-942.113.253.0015116914415513814711-258.31-238.10-605.82-821.943.503.5014215813414412713612-212.68-216.14-530.04-720.633.754.0013514812613611912713-174.48-193.30-465.04-634.364.004.5012913912112911312114-142.82-170.73-408.84-560.274.255.0012513111712510911715-115.21-149.04-359.88-496.114.505.5012212511412210711416-90.98-128.52-316.95-440.164.756.0012112111312110511317-69.59-109.31-279.07-391.055.00P1 (only)12112113414412613518-50.59-91.44-245.48-347.685.2519-33.64-74.86-215.52-309.195.50Notes:1. For "BOEF.xls" spreadsheet analysis, L = 20 ft., B = Assumed Slab Strip Width (see table20-18.45-59.53-188.69-274.855.75above) ft., and concentrated loads P1 & P2 were assumed to be placed symmetrically21-4.77-45.35-164.56-244.076.00about the center of the span length, "L".227.59-32.24-142.76-216.386.252. For this example, in the "BOEF.xls" spreadsheet, the Load Width was first assumed = 02318.80-20.12-123.00-191.356.50for true "point" loads of 6000 lbs. each, and then assumed = 0.50 ft. using distributed2429.00-8.91-105.03-168.666.75loads = 12000 lbs./ft. each, based on that given Load Width per load.2538.311.48-88.63-148.017.003. "P1 (only)" denotes only 1 isolated concentrated load is considered.2646.8411.10-73.62-129.177.254. From comparison of results above, the use of effective slab strip widths, "B", of between2754.6620.04-59.85-111.937.5070% to 75% of 2 times the radius of stiffness in the "BOEF.xls" spreadsheet produces2861.8728.34-47.18-96.097.75results which compare reasonably well to those obtained by either Methods 1 or 2.2968.5136.06-35.49-81.538.003074.6643.26-24.68-68.098.253180.3549.97-14.66-55.668.503285.6356.24-5.36-44.148.753390.5562.103.29-33.459.003495.1367.5911.35-23.509.253599.4072.7418.88-14.239.5036103.4077.5725.92-5.589.7537107.1482.1232.522.5210.0038110.6586.3938.7110.1010.2539113.9490.4144.5317.2210.5040117.0394.2150.0023.9010.7541119.9597.7955.1530.1911.0042122.69101.1860.0236.1211.2543125.28104.3864.6141.7111.5044127.73107.4168.9646.9811.7545130.04110.2973.0751.9712.0046132.23113.0176.9656.6912.2547134.31115.6080.6661.1712.5048136.27118.0684.1765.4112.7549138.14120.4087.5169.4413.0050139.91122.6290.6873.2713.2551141.60124.7493.7076.9213.5052143.20126.7696.5980.3913.7553144.73128.6999.3383.6914.0054146.18130.53101.9686.8414.2555147.57132.29104.4689.8514.5056148.89133.97106.8692.7314.7557150.16135.58109.1595.4715.0058151.36137.12111.3498.1015.2559152.52138.59113.45100.6215.5060153.62140.01115.46103.0315.7561154.68141.36117.40105.3416.0062155.69142.66119.25107.5516.2563156.67143.91121.03109.6816.5064157.60145.11122.75111.7216.7565158.49146.26124.40113.6817.0066159.35147.37125.98115.5717.2567160.17148.43127.51117.3817.5068160.96149.46128.98119.1317.7569161.73150.44130.39120.8118.0070162.46151.40131.76122.4318.2571163.16152.31133.07123.9918.5072163.84153.20134.34125.5018.7573164.50154.05135.57126.9519.0074165.13154.88136.75128.3519.2575165.73155.67137.90129.7019.5076166.32156.44139.01131.0119.7577166.88157.18140.08132.2820.0078167.43157.90141.11133.5020.2579167.95158.59142.11134.6820.5080168.46159.27143.08135.8320.7581168.96159.91144.02136.9421.0082169.43160.54144.93138.0121.2583169.89161.15145.82139.0521.5084170.33161.74146.67140.0621.7585170.76162.32147.50141.0322.0086171.18162.87148.31141.9822.2587171.58163.41149.09142.9022.5088171.97163.93149.85143.7922.7589172.35164.44150.59144.6623.0090172.72164.93151.30145.5023.2591173.07165.41152.00146.3123.5092173.42165.87152.67147.1123.7593173.75166.32153.33147.8824.0094174.08166.76153.97148.6324.2595174.39167.18154.59149.3624.5096174.70167.60155.20150.0624.7597175.00168.00155.79150.7525.0098175.28168.39156.36151.4325.2599175.56168.77156.92152.0825.50100175.84169.14157.47152.7225.75101176.10169.50158.00153.3426.00102176.36169.85158.51153.9426.25103176.61170.19159.02154.5326.50104176.85170.53159.51155.1026.75105177.09170.85159.99155.6627.00106177.32171.17160.46156.2127.25107177.55171.48160.91156.7427.50108177.77171.78161.36157.2627.75109177.98172.07161.79157.7628.00110178.19172.36162.22158.2628.25111178.39172.64162.63158.7428.50112178.59172.91163.04159.2128.75113178.78173.18163.43159.6729.00114178.96173.44163.82160.1229.25115179.15173.69164.20160.5629.50116179.33173.94164.57160.9929.75117179.50174.18164.93161.4130.00118179.67174.42165.28161.8230.25119179.83174.65165.63162.2230.50120180.00174.87165.96162.6130.75121180.15175.09166.29163.0031.00122180.31175.31166.62163.3731.25123180.46175.52166.93163.7431.50124180.61175.73167.24164.1031.75125180.75175.93167.55164.4532.00126180.89176.13167.84164.7932.25127181.03176.32168.13165.1332.50128181.16176.51168.42165.4632.75129181.29176.70168.70165.7833.00130181.42176.88168.97166.1033.25131181.54177.05169.24166.4133.50132181.67177.23169.50166.7133.75133181.79177.40169.76167.0134.00134181.90177.57170.01167.3034.25135182.02177.73170.26167.5934.50136182.13177.89170.50167.8734.75137182.24178.05170.74168.1435.00138182.35178.20170.97168.4135.25139182.45178.35171.20168.6835.50140182.56178.50171.43168.9435.75141182.66178.64171.65169.1936.00142182.76178.79171.86169.4436.25143182.85178.93172.08169.6936.50144182.95179.06172.28169.9336.75145183.04179.20172.49170.1637.00146183.13179.33172.69170.3937.25147183.22179.46172.89170.6237.50148183.31179.58173.08170.8537.75149183.40179.71173.27171.0638.00150183.48179.83173.46171.2838.25151183.56179.95173.64171.4938.50152183.64180.07173.82171.7038.75153183.72180.18174.00171.9039.00154183.80180.30174.17172.1039.25155183.88180.41174.35172.3039.50156183.95180.52174.51172.5039.75157184.03180.63174.68172.6940.00158184.10180.73174.84172.8740.25159184.17180.84175.00173.0640.50160184.24180.94175.16173.2440.75161184.31181.04175.32173.4241.00162184.37181.14175.47173.5941.25163184.44181.23175.62173.7641.50164184.51181.33175.76173.9341.75165184.57181.42175.91174.1042.00166184.63181.52176.05174.2642.25167184.69181.61176.19174.4242.50168184.75181.69176.33174.5842.75169184.81181.78176.47174.7443.00170184.87181.87176.60174.8943.25171184.93181.95176.73175.0443.50172184.98182.04176.86175.1943.75173185.04182.12176.99175.3444.00174185.09182.20177.12175.4844.25175185.15182.28177.24175.6344.50176185.20182.36177.36175.7744.75177185.25182.43177.48175.9045.00178185.30182.51177.60176.0445.25179185.35182.58177.72176.1745.50180185.40182.66177.83176.3045.75181185.45182.73177.95176.4346.00182185.50182.80178.06176.5646.25183185.54182.87178.17176.6946.50184185.59182.94178.28176.8146.75185185.63183.01178.38176.9347.00186185.68183.08178.49177.0547.25187185.72183.14178.59177.1747.50188185.77183.21178.69177.2947.75189185.81183.27178.79177.4048.00t(min) =6.106.968.919.926.257.009.0010.00

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &T"GRDSLAB.xls"written by: Alex Tomanovich, P.E.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Subgrade Soil Types and Approximate Subgrade Modulus (k) Values Type of Soil Support Provided k Values Range (pci) Fine-grained soils in whichsilt and clay-size particles Low 50 - 120predominate Sands and sand-gravelmixtures with moderate Medium 130 - 170amounts of silt and clay Sands and sand-gravelmixtures relatively free High 180 - 220of plastic fines Cement-treated subbases Very high 250 - 400Representative Axle Loads and Wheel Spacings for Various Lift Truck Capacities

Truck Rated Capacity (lbs.) Total Axle Load (lbs.) Wheel Spacing (in.) 2,000 5,600-7,200 24-32 3,000 7,800-9,400 26-34 4,000 9,800-11,600 30-36 5,000 11,600-13,800 30-36 6,000 13,600-15,500 30-36 7,000 15,300-18,100 34-37 8,000 16,700-20,400 34-38 10,000 20,200-23,800 37-45 12,000 23,800-27,500 38-40 15,000 30,000-35,300 34-43 20,000 39,700-43,700 36-53 Note: Axle loads are given for trucks handling the rated loads at 24 in. from load center to face of fork with mast vertical.

Reference: ACI 360R-10 - "Guide to Design of Slabs-on-Ground" (Table 5.1, page 19)Data for Construction Joint Dowels for Load Transfer Slab Depth Dowel Dia., db Total Dowel Length Dowel Spacing (c/c), s 5" - 6" 3/4" 16" 12" 7" - 8" 1" 18" 12" 9" - 11" 1-1/4" 18" 12"Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Slab Thickness Joint Spacing (ft.) < 3/4" Aggregate > 3/4" Aggregate Slump < 4" 5" 10 13 15 6" 12 15 18 7" 14 18 21 8" 16 20 24 9" 18 23 27 10" 20 25 30Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Recommendations for Input of Increase for 2nd Load (Wheel or Post), 'i':

(Note: input must be a value from 0 to 100.)

1. Please refer to the suggested rationale, located off of the page at the right and down, for help in determining the stress Increase due to a 2nd Load, i, as a percentage of the stress for single load (wheel or post). User should input the value of the spacing between 2 loads (wheel or post) in Cell AQ77. Then based on the results obtained from Cells AQ81 and AV81, the user can input an appropriate value of "i" in Cell C22.

3. For a single post load, input a value of i = 0%. Also, per suggested rationale mentioned above, for spacing between loads (wheels or posts) >=2*Lr

4. For situations involving more than 2 loads (wheel or post) and for a more in depth analysis and evaluation of slab bending and shear, please refer to the "BOEF.xls" (Beam On Elastic Foundation) spreadsheet workbook.Radius of Stiffness, "Lr", is a measure of the stiffness of the slab relative to the foundation (subgrade). It is a linear dimension and represents mathematically the 4th root of the ratio of the stiffness of the slab to the stiffness of the foundation.Subbase friction adjustment factor, 'C', is as follows:C = 0.65 for stabilized subbaseC = 0.80 for granular subbaseC = 1.00 for no subbaseValues of Portland Cement Concrete Coefficient of Shrinkage (e)Concrete Strength, Modulus of Rupture, Shrinkage Coefficient, f 'c (psi) MR (psi) e (in./in.) 3000 493 0.00046 3500 532 0.00040 4000 569 0.00035 4500 604 0.00030 5000 636 0.00026 5500 667 0.00023 6000 697 0.00020Note: Indirect tensile strength = Modulus of Rupture (MR) = 9*SQRT(f 'c)Note: Ao = Lr^2*(2*p/3-SQRT(3)/2), when S = Lr)Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.1.0*PcsLeLePtd1d2d3d2d3d4d4didi(1-(2-1)*s/Le)*Pc0*Pc0*Pc(1-(2-1)*s/Le)*Pc(1-(3-1)*s/Le)*Pc(1-(3-1)*s/Le)*Pc(1-(4-1)*s/Le)*Pc(1-(4-1)*s/Le)*Pct(Subgrade)t/2Contact Area, AcPlain DowelsPPWheelPostDirection of pourSet Value = 1 ("Unity")"Overlapped" Area, Ao"Overlapped" Area, AoNote: If S >= 2*Lr,then no overlapping areas and thus, negligible or no effect from 2nd load.P1Method #1Method #2P2 (2nd Load)P2(2nd Load)P1LrLr

PCA Fig. 3-Wheel LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Single Wheel Loading from Vehicles with Pneumatic TiresPer PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" - Figure 3, page 53000Pw =12500.00lbs.Pw = Pa/2 (assume 2 wheels per axle)Note: User MUST determine slab thickness fromJob Name:Subject:3500Ac =113.64in.^2Ac = Pw/IpFigure 3, and input the result in cell D51.Job Number:Originator:Checker:4000Ac(eff) =113.64in.^2Ac(eff) = determined from Figure 5, page 64500MR =636.40psiMR = 9*SQRT(f 'c)5000WS =318.20psiWS = MR/FS5500Ss =12.73psiSs = WS/(Pa/1000)6000t =(by user)in.t = determined from Figure 3, page 5Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)1234567Interpolate for "Ac(eff)" in PCA Fig. 5Load ContactSlab Thickness (in.)Effective Load Contact Area Based on Slab Thickness (From PCA Fig. 5)t(table)tt(table)Area, Ac (in.^2)4568101214Load ContactSlab Thickness (in.)4t Index:50881221.533.54865Area, Ac (in.^2)4568101214Ac Index:88.00010510.510.514.5243650.567.50881221.533.548651121.5021.5033.501013.513.517.527385370510.510.514.5243650.567.52224.0024.0036.001517172029.54156.572.51013.513.517.5273853703327.0027.0038.0020212122.532.5445875.51517172029.54156.572.54429.5029.5041.002525252735.547627820212122.532.5445875.55532.5032.5044.003030303038496581.52525252735.54762786635.5035.5047.0035353534425267.583.53030303038496581.57738.0038.0049.004040403945.555.570.58735353534425267.583.58842.0042.0052.0045454544.547.5587389.54040403945.555.570.5879945.5045.5055.5050505049.55262779245454544.547.5587389.5101047.5047.5058.0055555555566579.595.550505049.552627792111152.0052.0062.00606060606067.5829855555555566579.595.5121256.0056.0065.00656565656571.585.5101.5606060606067.58298131360.0060.0067.507068.568.568.568.574.588104656565656571.585.5101.5141465.0065.0071.50757373737377.5911077068.568.568.568.574.588104151568.5068.5074.5080787878788294110757373737377.591107161673.0073.0077.508582.582.582.582.58797.5112.580787878788294110171778.0078.0082.00908989898990.51011178582.582.582.582.58797.5112.5181882.5082.5087.009594.594.594.594.595104.5120908989898990.5101117191989.0089.0090.501009999999999.5107.5122.59594.594.594.594.595104.5120202094.5094.5095.001009999999999.5107.5122.5212199.0099.0099.50Input Data:Ac Index:Ac(eff) values:Concrete Strength, f 'c =5000psiInstructions for Use of Figure 3:21Ac(table)100.0099.00Subgrade Modulus, k =100.00pci1. Enter Design Chart with Slab Stress = 12.73Ac113.64113.64(Unfactored) Axle Load, Pa =25000.00lbs.2. Move to right to Eff. Contact Area = 113.6421Ac(table)100.0099.00Wheel Spacing, S =37.00in.3. Move up/down to Wheel Spacing = 37Tire Inflation Pressure, Ip =110.00psi4. Move to right to Subgrade Modulus = 100Factor of Safety, FS =2.005. Read required Slab Thk., t (Must input below)Results:Wheel Load, Pw =12500.00lbs.Pw = Pa/2 (1/2 of axle load for 2 wheels/axle)Tire Contact Area, Ac =113.64in.^2Ac = Pw/IpEffective Contact Area, Ac(eff) =113.64in.^2Ac(eff) = determined from Figure 5, page 6Concrete Flexual Strength, MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)Concrete Working Stress, WS =318.20psiWS = MR/FSSlab Stress/1000 lb. Axle Load =12.73psiSs = WS/(Pa/1000)Slab Thickness, t =8.000in.t = determined and input from Figure 3 aboveNote: User MUST determine slab thickness fromFigure 3, and input the result in cell D51.Convert Axle with Dual Wheels to Equivalent Axle with Single Wheels (if applicable):Note:For axles equipped with dual wheels, Figures 3 and 4are used together to determine floor slab thickness.First, Figure 4 is used to convert a dual-wheel axleload to an equivalent single-wheel axle load (the totalaxle load is multiplied by the factor, "F"). Then, inputthis value for equivalent single-wheel axle load aboveas the Axle Load, "Pa", and proceed using Figure 3to determine the required slab thickness, "t".Instructions for Use of Figure 4:1. Enter chart with dual wheel spac. = SdSd =in.2. Move to right to eff. contact area = 113.643. Move up/down to slab thickness = tt =8.000in.4. Move to right to equiv. load factor = FF =

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &TSubgrade Soil Types and Approximate Subgrade Modulus (k) Values Type of Soil Support Provided k Values Range (pci) Fine-grained soils in whichsilt and clay-size particles Low 50 - 120predominate Sands and sand-gravelmixtures with moderate Medium 130 - 170amounts of silt and clay Sands and sand-gravelmixtures relatively free High 180 - 220of plastic fines Cement-treated subbases Very high 250 - 400Representative Axle Loads and Wheel Spacings for Various Lift Truck Capacities

Truck Rated Capacity (lbs.) Total Axle Load (lbs.) Wheel Spacing (in.) 2,000 5,600-7,200 24-32 3,000 7,800-9,400 26-34 4,000 9,800-11,600 30-36 5,000 11,600-13,800 30-36 6,000 13,600-15,500 30-36 7,000 15,300-18,100 34-37 8,000 16,700-20,400 34-38 10,000 20,200-23,800 37-45 12,000 23,800-27,500 38-40 15,000 30,000-35,300 34-43 20,000 39,700-43,700 36-53 Note: Axle loads are given for trucks handling the rated loads at 24 in. from load center to face of fork with mast vertical.

Reference: ACI 360R-10 - "Guide to Design of Slabs-on-Ground" (Table 5.1, page 19)Representative Axle Loads and Wheel Spacings for Various Lift Truck Capacities

Truck Rated Capacity (lbs.) Total Axle Load (lbs.) Wheel Spacing (in.) 2,000 5,600-7,200 24-32 3,000 7,800-9,400 26-34 4,000 9,800-11,600 30-36 5,000 11,600-13,800 30-36 6,000 13,600-15,500 30-36 7,000 15,300-18,100 34-37 8,000 16,700-20,400 34-38 10,000 20,200-23,800 37-45 12,000 23,800-27,500 38-40 15,000 30,000-35,300 34-43 20,000 39,700-43,700 36-53 Note: Axle loads are given for trucks handling the rated loads at 24 in. from load center to face of fork with mast vertical.

Reference: ACI 360R-10 - "Guide to Design of Slabs-on-Ground" (Table 5.1, page 19)"GRDSLAB.xls"written by: Alex Tomanovich, P.E.Figure 3 Design Chart for Axles with Single WheelsFigure 4 Design Chart for Axles with Dual Wheels

PCA Fig. 7a-Post LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Concentrated Post Loading (for k = 50 pci)Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" - Figure 7a, page 93000Note: User MUST determine slab thickness fromJob Name:Subject:3500Figure 7a, and input the result in cell D50.Job Number:Originator:Checker:4000Ac(eff) =77.75in.^2Ac(eff) = determined from Figure 5, page 64500MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)5000WS =212.13psiWS = MR/FS5500Ss =16.32psiSs = WS/(P/1000)6000t =(by user)in.t = determined from Figure 7a, page 91234567Interpolate for "Ac(eff)" in PCA Fig. 5Effective Load Contact Area Based on Slab Thickness (From PCA Fig. 5)t(table)tt(table)Load ContactSlab Thickness (in.)5t Index:6Area, Ac (in.^2)4568101214Ac Index:1011.000120881221.533.548651133.5040.7548.00510.510.514.5243650.567.52236.0043.2550.501013.513.517.5273853703338.0045.5053.001517172029.54156.572.54441.0048.7556.5020212122.532.5445875.55544.0051.0058.002525252735.54762786647.0054.5062.003030303038496581.57749.0057.0065.0035353534425267.583.58852.0059.7567.504040403945.555.570.5879955.5063.0070.5045454544.547.5587389.5101058.0065.5073.0050505049.552627792111162.0069.5077.0055555555566579.595.5121265.0072.2579.50Figure 8 - Post Configurations and Loads606060606067.58298131367.5074.7582.00for which Figures 7a, 7b, and 7c Apply656565656571.585.5101.5141471.5078.5085.507068.568.568.568.574.588104151574.5081.2588.00757373737377.591107161677.5084.2591.00Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)80787878788294110171782.0088.0094.00Load ContactSlab Thickness (in.)8582.582.582.582.58797.5112.5181887.0092.2597.50Area (in.^2)4568101214908989898990.5101117191990.5095.75101.000881221.533.548659594.594.594.594.595104.5120202095.0099.75104.50510.510.514.5243650.567.51009999999999.5107.5122.5212199.50103.50107.501013.513.517.527385370Input Data:Ac Index:Ac(eff) values:1517172029.54156.572.5Concrete Strength, f 'c =5000psiInstructions for Use of Figure 7a:13Ac(table)60.0074.7520212122.532.5445875.5Subgrade Modulus, k =50pci1. Enter Design Chart with Slab Stress = 16.32Ac64.0077.752525252735.5476278(Unfactored) Post Load, P =13000.00lbs.2. Follow curve to right to Eff. Contact Area = 77.7514Ac(table)65.0078.503030303038496581.5Post Spacing, y =98.00in.3. Move to right to Post Spacing, y = 9835353534425267.583.5Post Spacing, x =66.00in.4. Move up/down to Post Spacing, x = 664040403945.555.570.587Load Contact Area, Ac =64.00in.^25. Move to right to get Slab Thk., t (Must input below)45454544.547.5587389.5Factor of Safety, FS =3.0050505049.55262779255555555566579.595.5Results:606060606067.58298Effective Contact Area, Ac(eff) =77.75in.^2Ac(eff) = determined from Figure 5, page 6656565656571.585.5101.5Concrete Flexual Strength, MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)7068.568.568.568.574.588104Concrete Working Stress, WS =212.13psiWS = MR/FS757373737377.591107Slab Stress/1000 lb. Post Load =16.32psiSs = WS/(P/1000)80787878788294110Slab Thickness, t =11.000in.t = determined and input from Figure 7a above8582.582.582.582.58797.5112.5908989898990.51011179594.594.594.594.595104.51201009999999999.5107.5122.5Note: User MUST determine slab thickness fromFigure 7a, and input the result in cell D50.

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &T"GRDSLAB.xls"written by: Alex Tomanovich, P.E.Figure 7a Design Chart for Post Loads, subgrade k = 50 pciP/2P/2PPPLoad oneach postxxy

PCA Fig. 7b-Post LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Concentrated Post Loading (for k = 100 pci)Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" - Figure 7b, page 103000Note: User MUST determine slab thickness fromJob Name:Subject:3500Figure 7b, and input the result in cell D50.Job Number:Originator:Checker:4000Ac(eff) =70.70in.^2Ac(eff) = determined from Figure 5, page 64500MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)5000WS =212.13psiWS = MR/FS5500Ss =16.32psiSs = WS/(P/1000)6000t =(by user)in.t = determined from Figure 7b, page 101234567Interpolate for "Ac(eff)" in PCA Fig. 5Effective Load Contact Area Based on Slab Thickness (From PCA Fig. 5)t(table)tt(table)Load ContactSlab Thickness (in.)5t Index:6Area, Ac (in.^2)4568101214Ac Index:1010.000120881221.533.548651133.5033.5048.00510.510.514.5243650.567.52236.0036.0050.501013.513.517.5273853703338.0038.0053.001517172029.54156.572.54441.0041.0056.5020212122.532.5445875.55544.0044.0058.002525252735.54762786647.0047.0062.003030303038496581.57749.0049.0065.0035353534425267.583.58852.0052.0067.504040403945.555.570.5879955.5055.5070.5045454544.547.5587389.5101058.0058.0073.0050505049.552627792111162.0062.0077.0055555555566579.595.5121265.0065.0079.50Figure 8 - Post Configurations and Loads606060606067.58298131367.5067.5082.00for which Figures 7a, 7b, and 7c Apply656565656571.585.5101.5141471.5071.5085.507068.568.568.568.574.588104151574.5074.5088.00757373737377.591107161677.5077.5091.00Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)80787878788294110171782.0082.0094.00Load ContactSlab Thickness (in.)8582.582.582.582.58797.5112.5181887.0087.0097.50Area (in.^2)4568101214908989898990.5101117191990.5090.50101.000881221.533.548659594.594.594.594.595104.5120202095.0095.00104.50510.510.514.5243650.567.51009999999999.5107.5122.5212199.5099.50107.501013.513.517.527385370Input Data:Ac Index:Ac(eff) values:1517172029.54156.572.5Concrete Strength, f 'c =5000psiInstructions for Use of Figure 7b:13Ac(table)60.0067.5020212122.532.5445875.5Subgrade Modulus, k =100pci1. Enter Design Chart with Slab Stress = 16.32Ac64.0070.702525252735.5476278(Unfactored) Post Load, P =13000.00lbs.2. Follow curve to right to Eff. Contact Area = 70.714Ac(table)65.0071.503030303038496581.5Post Spacing, y =98.00in.3. Move to right to Post Spacing, y = 9835353534425267.583.5Post Spacing, x =66.00in.4. Move up/down to Post Spacing, x = 664040403945.555.570.587Load Contact Area, Ac =64.00in.^25. Move to right to get Slab Thk., t (Must input below)45454544.547.5587389.5Factor of Safety, FS =3.0050505049.55262779255555555566579.595.5Results:606060606067.58298Effective Contact Area, Ac(eff) =70.70in.^2Ac(eff) = determined from Figure 5, page 6656565656571.585.5101.5Concrete Flexual Strength, MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)7068.568.568.568.574.588104Concrete Working Stress, WS =212.13psiWS = MR/FS757373737377.591107Slab Stress/1000 lb. Post Load =16.32psiSs = WS/(P/1000)80787878788294110Slab Thickness, t =10.000in.t = determined and input from Figure 7b above8582.582.582.582.58797.5112.5908989898990.51011179594.594.594.594.595104.51201009999999999.5107.5122.5Note: User MUST determine slab thickness fromFigure 7b, and input the result in cell D50.

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &T"GRDSLAB.xls"written by: Alex Tomanovich, P.E.P/2P/2PPPLoad oneach postxxyFigure 7b Design Chart for Post Loads, subgrade k = 100 pci

PCA Fig. 7c-Post LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Concentrated Post Loading (for k = 200 pci)Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" - Figure 7c, page 113000Note: User MUST determine slab thickness fromJob Name:Subject:3500Figure 7c, and input the result in cell D50.Job Number:Originator:Checker:4000Ac(eff) =67.35in.^2Ac(eff) = determined from Figure 5, page 64500MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)5000WS =212.13psiWS = MR/FS5500Ss =16.32psiSs = WS/(P/1000)6000t =(by user)in.t = determined from Figure 7c, page 111234567Interpolate for "Ac(eff)" in PCA Fig. 5Effective Load Contact Area Based on Slab Thickness (From PCA Fig. 5)t(table)tt(table)Load ContactSlab Thickness (in.)4t Index:5Area, Ac (in.^2)4568101214Ac Index:89.000100881221.533.548651121.5027.5033.50510.510.514.5243650.567.52224.0030.0036.001013.513.517.5273853703327.0032.5038.001517172029.54156.572.54429.5035.2541.0020212122.532.5445875.55532.5038.2544.002525252735.54762786635.5041.2547.003030303038496581.57738.0043.5049.0035353534425267.583.58842.0047.0052.004040403945.555.570.5879945.5050.5055.5045454544.547.5587389.5101047.5052.7558.0050505049.552627792111152.0057.0062.0055555555566579.595.5121256.0060.5065.00Figure 8 - Post Configurations and Loads606060606067.58298131360.0063.7567.50for which Figures 7a, 7b, and 7c Apply656565656571.585.5101.5141465.0068.2571.507068.568.568.568.574.588104151568.5071.5074.50757373737377.591107161673.0075.2577.50Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)80787878788294110171778.0080.0082.00Load ContactSlab Thickness (in.)8582.582.582.582.58797.5112.5181882.5084.7587.00Area (in.^2)4568101214908989898990.5101117191989.0089.7590.500881221.533.548659594.594.594.594.595104.5120202094.5094.7595.00510.510.514.5243650.567.51009999999999.5107.5122.5212199.0099.2599.501013.513.517.527385370Input Data:Ac Index:Ac(eff) values:1517172029.54156.572.5Concrete Strength, f 'c =5000psiInstructions for Use of Figure 7c:13Ac(table)60.0063.7520212122.532.5445875.5Subgrade Modulus, k =200pci1. Enter Design Chart with Slab Stress = 16.32Ac64.0067.352525252735.5476278(Unfactored) Post Load, P =13000.00lbs.2. Follow curve to right to Eff. Contact Area = 67.3514Ac(table)65.0068.253030303038496581.5Post Spacing, y =98.00in.3. Move to right to Post Spacing, y = 9835353534425267.583.5Post Spacing, x =66.00in.4. Move up/down to Post Spacing, x = 664040403945.555.570.587Load Contact Area, Ac =64.00in.^25. Move to right to get Slab Thk., t (Must input below)45454544.547.5587389.5Factor of Safety, FS =3.0050505049.55262779255555555566579.595.5Results:606060606067.58298Effective Contact Area, Ac(eff) =67.35in.^2Ac(eff) = determined from Figure 5, page 6656565656571.585.5101.5Concrete Flexual Strength, MR =636.40psiMR = 9*SQRT(f 'c) (Modulus of Rupture)7068.568.568.568.574.588104Concrete Working Stress, WS =212.13psiWS = MR/FS757373737377.591107Slab Stress/1000 lb. Post Load =16.32psiSs = WS/(P/1000)80787878788294110Slab Thickness, t =9.000in.t = determined and input from Figure 7c above8582.582.582.582.58797.5112.5908989898990.51011179594.594.594.594.595104.51201009999999999.5107.5122.5Note: User MUST determine slab thickness fromFigure 7c, and input the result in cell D50.

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &T"GRDSLAB.xls"written by: Alex Tomanovich, P.E.Figure 7c Design Chart for Post Loads, subgrade k = 200 pciP/2P/2PPPLoad oneach postxxy

Wall LoadCONCRETE SLAB ON GRADE ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Continuous Line Loading from Wall3000Design Parameters:Job Name:Subject:3500MR =569.21psiMR = 9*SQRT(f 'c)Job Number:Originator:Checker:4000Fb =101.19psiFb = 1.6*SQRT(f 'c)4500FS =5.625FS = MR/Fb5000S =128.00in.^3S = b*t^2/6Input Data:5500Ec =3604997psiEc = 57000*SQRT(f 'c)6000b =12.00in.b = 12" (assumed)Slab Thickness, t =8.000in.Top/SlabI =512.00in.^4I = b*t^3/12Concrete Strength, f 'c =4000psil =0.0201l = (k*b/(4*Ec*I))^(0.25)Subgrade Modulus, k =100pciBlx =0.3224Blx = coefficient from "Beams on Elastic Foundations" by M. HetenyiMin. req'd. slab thk. for center or keyed/doweled joints:Wall Load, P =800.00lb./ft.Near Center of Slab or Keyed/Doweled Joints:t(min) =6.50in.Set Pc(allow) = 12.8*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)Pc =1040.30lb./ft.Pc = 4*Fb*S*l1040.30= 12.8*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)Concrete Slab Loaded Near Center or at JointNear Free Edge of Slab:Pe =806.68lb./ft.Pe = Fb*S*l/Blx806.68= 9.9256*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)Top/SlabDetermine Minimum Slab Thickness for Given Wall Loading: (iterative solutions for t(min))Iteration #Eqn. for PcEqn. for PetiMin. req'd. slab thk. for free edge load:1-722.68-740.041.00t(min) =8.00in.Set Pe(allow) = 9.9256*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)2-697.80-720.751.25Results:3-671.65-700.471.50Concrete Slab Loaded Near Free Edge4-644.37-679.321.75Design Parameters:5-616.10-657.402.00Modulus of Rupture, MR =569.21psiMR = 9*SQRT(f 'c)6-586.93-634.782.25Allow. Bending Stress, Fb =101.19psiFb = 1.6*SQRT(f 'c) (as recommended in reference below)7-556.94-611.522.50Factor of Safety, FS =5.625FS = MR/Fb8-526.18-587.672.75Section Modulus, S =128.00in.^3/ft.S = b*t^2/69-494.72-563.283.00Modulus of Elasticity, Ec =3604997psiEc = 57000*SQRT(f 'c)10-462.60-538.373.25Width, b =12.00in.b = 12" (assumed)11-429.85-512.973.50Moment of Inertia, I =512.00in.^4I = b*t^3/1212-396.51-487.123.75Stiffness Factor, l =0.0201l = (k*b/(4*Ec*I))^(0.25)13-362.61-460.834.00Coefficient, Blx =0.3224Blx = coefficient from "Beams on Elastic Foundations"14-328.18-434.134.25by M. Hetenyi15-293.23-407.034.5016-257.80-379.564.75Wall Load Near Center of Slab or Keyed/Doweled Joints:17-221.90-351.725.00Allowable Wall Load, Pc =1040.30lb./ft.Pc = 4*Fb*S*l18-185.54-323.535.25= 12.8*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)19-148.75-295.005.50Pc(allow) >= P, O.K.20-111.54-266.145.75Wall Load Near Free Edge of Slab:21-73.92-236.976.00Allowable Wall Load, Pe =806.68lb./ft.Pe = Fb*S*l/Blx22-35.91-207.506.25= 9.9256*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)232.48-177.736.50Reference:Pe(allow) >= P, O.K.2441.25-147.676.75"Concrete Floor Slabs on Grade Subjected to Heavy Loads"2580.37-117.337.00Army Technical Manual TM 5-809-12, Air Force Manual AFM 88-3, Chapter 15 (1987)26119.85-86.727.2527159.67-55.847.50Comments:28199.82-24.717.7529240.306.688.0030281.0938.318.2531322.1970.198.5032363.60102.308.7533405.31134.649.0034447.30167.209.2535489.58199.999.5036532.14232.999.7537574.97266.2010.0038618.07299.6210.2539661.44333.2510.5040705.06367.0810.7541748.94401.1011.0042793.07435.3211.2543837.44469.7311.5044882.06504.3311.7545926.91539.1112.0046972.00574.0712.25471017.32609.2112.50481062.87644.5312.75491108.64680.0213.00501154.63715.6813.25511200.84751.5213.50521247.26787.5113.75531293.89823.6714.00541340.73860.0014.25551387.78896.4814.50561435.03933.1214.75571482.49969.9215.00581530.141006.8715.25591577.981043.9715.50601626.021081.2215.75611674.251118.6216.00621722.671156.1716.25631771.281193.8616.50641820.071231.6916.75651869.041269.6717.00661918.191307.7817.25671967.531346.0317.50682017.031384.4217.75692066.721422.9518.00702116.571461.6118.25712166.601500.4018.50722216.791539.3318.75732267.161578.3819.00742317.691617.5619.25752368.381656.8719.50762419.241696.3119.75772470.251735.8720.00782521.431775.5520.25792572.771815.3620.50802624.261855.2920.75812675.911895.3421.00822727.711935.5121.25832779.661975.7921.50842831.772016.2021.75852884.022056.7222.00862936.432097.3522.25872988.982138.1022.50883041.682178.9722.75893094.522219.9423.00903147.512261.0323.25913200.632302.2323.50923253.912343.5423.75933307.322384.9524.00943360.872426.4824.25953414.552468.1124.50963468.382509.8524.75973522.342551.6925.00983576.442593.6425.25993630.672635.6925.501003685.032677.8525.751013739.532720.1126.001023794.162762.4726.251033848.912804.9326.501043903.802847.4926.751053958.812890.1527.001064013.962932.9127.251074069.232975.7627.501084124.623018.7227.751094180.143061.7728.001104235.783104.9228.251114291.553148.1628.501124347.443191.5028.751134403.453234.9329.001144459.583278.4629.251154515.843322.0829.501164572.213365.7929.751174628.703409.6030.001184685.313453.4930.251194742.033497.4830.501204798.873541.5630.751214855.833585.7231.001224912.903629.9831.251234970.093674.3231.501245027.393718.7531.751255084.803763.2732.001265142.323807.8832.251275199.963852.5732.501285257.713897.3532.751295315.563942.2233.001305373.533987.1733.251315431.614032.2033.501325489.794077.3233.751335548.084122.5234.001345606.484167.8134.251355664.994213.1834.501365723.604258.6334.751375782.324304.1635.001385841.154349.7735.251395900.074395.4735.501405959.104441.2435.751416018.244487.1036.001426077.484533.0336.251436136.824579.0436.501446196.264625.1436.751456255.804671.3137.001466315.444717.5637.251476375.194763.8837.501486435.034810.2937.751496494.974856.7738.001506555.014903.3338.251516615.154949.9638.501526675.394996.6738.751536735.725043.4639.001546796.155090.3239.251556856.685137.2539.501566917.305184.2639.751576978.025231.3440.001587038.835278.5040.251597099.745325.7340.501607160.745373.0340.751617221.845420.4141.001627283.035467.8641.251637344.315515.3841.501647405.685562.9741.751657467.155610.6342.001667528.705658.3642.251677590.355706.1742.501687652.095754.0442.751697713.925801.9943.001707775.845850.0043.251717837.855898.0843.501727899.955946.2443.751737962.135994.4644.001748024.416042.7544.251758086.776091.1144.501768149.226139.5344.751778211.766188.0345.001788274.396236.5945.251798337.106285.2245.501808399.906333.9145.751818462.786382.6846.001828525.756431.5146.251838588.806480.4046.501848651.946529.3646.751858715.176578.3947.001868778.476627.4847.251878841.876676.6347.501888905.346725.8547.751898968.906775.1448.00t(min) =6.487.956.508.00

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &TSubgrade Soil Types and Approximate Subgrade Modulus (k) Values Type of Soil Support Provided k Values Range (pci) Fine-grained soils in whichsilt and clay-size particles Low 50 - 120predominate Sands and sand-gravelmixtures with moderate Medium 130 - 170amounts of silt and clay Sands and sand-gravelmixtures relatively free High 180 - 220of plastic fines Cement-treated subbases Very high 250 - 400Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness."GRDSLAB.xls"written by: Alex Tomanovich, P.E.t(Subgrade)PWallPWallt(Subgrade)PWallDowel(at Joint)

Unif. LoadCONCRETE SLAB ON GRADE ANALYSISCALCULATIONS:Version 2.0For Slab Subjected to Stationary Uniformly Distributed Live Loads3000Design Parameters:Job Name:Subject:3500MR =569.21psiMR = 9*SQRT(f 'c)Job Number:Originator:Checker:4000Fb =284.60psiFb = MR/FS4500Ec =3604997psiEc = 57000*SQRT(f 'c)5000m =0.15m = 0.15 (assumed for concrete)Input Data:5500Lr =28.544in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25*Aisle Width6000Wcr =5.254ft.Wcr = (2.209*Lr)/12Slab Thickness, t =6.000in.wLLwLLwLL(allow) =946.84psfwLL(allow) = 257.876*Fb*SQRT(k*t/Ec) (Reference 1)Concrete Strength, f 'c =4000psiTop/SlabwLL(allow) =857.48psfwLL(allow) = 0.123*Fb*SQRT(k*t) (Reference 2)Subgrade Modulus, k =100pciFactor of Safety, FS =2.000References:Min. req'd. slab thk. for stationary uniform loads per Reference #1:Uniform Live Load, wLL =850.00psf1. "Concrete Floor Slabs on Grade Subjected to Heavy Loads"t(min) =5.00in.t(min) = Ec*(wLL/(257.876*Fb))^2/k (Ref. 1)Army Technical Manual TM 5-809-12, Air Force Manual AFM 88-3, Chapter 15 (1987)2. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) - by Robert G. PackardMin. req'd. slab thk. for stationary uniform loads per Reference #2:Concrete Slab on Grade with Uniform Loads(Portland Cement Association, 1976)t(min) =6.00in.t(min) = (wLL/(0.123*Fb))^2/k (Ref. 2)3. "Design of Slabs-on-Ground" - ACI 360R-06 - by American Concrete Institute*Note:In an unjointed aisleway between uniformly distributed load areas,negative bending moment in slab may be up to twice as great aspositive moment in slab beneath loaded area. Allowable uniformMin. req'd. slab thk. for stationary uniform loads: (back solving for t(min))load determined below is based on critical aisle width and as at(min) =4.84in.t(min) = Ec*(wLL/(257.876*Fb))^2/k (Ref. 1)result, there are no restrictions on load layout configuration ort(min) =5.00in.t(min) rounded up to nearest 1/4" inchuniformity of loading.Results:Min. req'd. slab thk. for stationary uniform loads: (back solving for t(min))Note: For additional in depth analysis please refer to "BOEF.xls"t(min) =5.90in.t(min) = (wLL/(0.123*Fb))^2/k (Ref. 2)(Beam On Elastic Foundation) spreadsheet workbook.Design Parameters:t(min) =6.00in.t(min) rounded up to nearest 1/4" inchModulus of Rupture, MR =569.21psiMR = 9*SQRT(f 'c)Allow. Bending Stress, Fb =284.60psiFb = MR/FSModulus of Elasticity, Ec =3604997Ec = 57000*SQRT(f 'c)Determine Minimum Slab Thickness for Given Uniform Loading:: (iterative solutions for t(min))Poisson's Ratio, m =0.15m = 0.15 (assumed for concrete)Iteration #Eqn. 1 w(allow)Eqn. 2 w(allow)tiRadius of Stiffness, Lr =28.54in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.251-463.45-499.941.00Critical Aisle Width, Wcr =5.25ft.Wcr = (2.209*Lr)/12 (Ref. 3, Appendix 2 page 64)2-417.83-458.621.25(presented for information only)3-376.58-421.261.50Stationary Uniformly Distributed Live Loads:4-338.65-386.911.75Per Ref. #1: wLL(allow) =946.84psfwLL(allow) = 257.876*Fb*SQRT(k*t/Ec)5-303.34-354.932.00wLL(allow) >= wLL, O.K.6-270.18-324.902.257-238.82-296.502.50Per Ref. #2: wLL(allow) =857.48psfwLL(allow) = 0.123*Fb*SQRT(k*t)8-208.99-269.482.75wLL(allow) >= wLL, O.K.9-180.48-243.673.0010-153.14-218.913.25Reference:11-126.84-195.093.501. "Concrete Floor Slabs on Grade Subjected to Heavy Loads"12-101.46-172.103.75Army Technical Manual TM 5-809-12, Air Force Manual AFM 88-3, Chapter 15 (1987)13-76.91-149.874.002. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D)14-53.12-128.324.25by Robert G. Packard (Portland Cement Association, 1976)15-30.01-107.404.503. "Design of Slabs-on-Ground" - ACI 360R-06 - by American Concrete Institute16-7.54-87.054.751714.34-67.235.00Comments:1835.69-47.905.251956.53-29.035.502076.90-10.585.752196.847.486.0022116.3625.166.2523135.5042.496.5024154.2859.496.7525172.7076.187.0026190.8192.587.2527208.60108.697.5028226.10124.547.7529243.32140.138.0030260.27155.488.2531276.97170.608.5032293.42185.508.7533309.64200.199.0034325.63214.689.2535341.41228.979.5036356.99243.079.7537372.37257.0010.0038387.55270.7510.2539402.55284.3410.5040417.38297.7610.7541432.03311.0311.0042446.51324.1511.2543460.84337.1311.5044475.01349.9611.7545489.03362.6612.0046502.91375.2212.2547516.65387.6612.5048530.24399.9812.7549543.71412.1713.0050557.05424.2513.2551570.26436.2213.5052583.35448.0713.7553596.32459.8214.0054609.18471.4614.2555621.92483.0014.5056634.56494.4514.7557647.09505.7915.0058659.51517.0415.2559671.83528.2015.5060684.06539.2715.7561696.18550.2616.0062708.22561.1516.2563720.16571.9716.5064732.01582.7016.7565743.77593.3517.0066755.45603.9317.2567767.04614.4217.5068778.55624.8517.7569789.98635.2018.0070801.32645.4718.2571812.60655.6818.5072823.79665.8218.7573834.91675.8919.0074845.96685.9019.2575856.94695.8419.5076867.85705.7219.7577878.69715.5320.0078889.46725.2920.2579900.16734.9820.5080910.80744.6220.7581921.38754.2021.0082931.89763.7221.2583942.34773.1821.5084952.73782.5921.7585963.06791.9522.0086973.33801.2522.2587983.55810.5022.5088993.71819.7022.75891003.81828.8523.00901013.86837.9523.25911023.85847.0023.50921033.79856.0023.75931043.68864.9624.00941053.52873.8724.25951063.30882.7324.50961073.04891.5524.75971082.73900.3225.00981092.37909.0525.25991101.96917.7425.501001111.51926.3825.751011121.00934.9826.001021130.46943.5426.251031139.87952.0726.501041149.23960.5526.751051158.55968.9927.001061167.83977.3927.251071177.06985.7527.501081186.26994.0827.751091195.411002.3728.001101204.521010.6228.251111213.591018.8328.501121222.621027.0128.751131231.611035.1529.001141240.571043.2629.251151249.481051.3329.501161258.361059.3729.751171267.201067.3830.001181276.001075.3530.251191284.771083.2930.501201293.501091.2030.751211302.201099.0731.001221310.861106.9231.251231319.481114.7331.501241328.081122.5131.751251336.631130.2632.001261345.161137.9832.251271353.651145.6732.501281362.111153.3332.751291370.541160.9733.001301378.931168.5733.251311387.301176.1433.501321395.631183.6933.751331403.931191.2134.001341412.201198.7034.251351420.441206.1634.501361428.651213.6034.751371436.841221.0135.001381444.991228.3935.251391453.111235.7535.501401461.211243.0835.751411469.281250.3836.001421477.311257.6736.251431485.331264.9236.501441493.311272.1536.751451501.271279.3637.001461509.201286.5437.251471517.101293.7037.501481524.981300.8337.751491532.831307.9438.001501540.651315.0338.251511548.451322.0938.501521556.231329.1338.751531563.981336.1539.001541571.701343.1539.251551579.401350.1239.501561587.081357.0739.751571594.731364.0040.001581602.361370.9140.251591609.961377.7940.501601617.541384.6640.751611625.101391.5041.001621632.641398.3341.251631640.151405.1341.501641647.641411.9141.751651655.101418.6742.001661662.551425.4242.251671669.971432.1442.501681677.371438.8442.751691684.751445.5243.001701692.111452.1943.251711699.441458.8343.501721706.761465.4643.751731714.061472.0644.001741721.331478.6544.251751728.581485.2244.501761735.821491.7744.751771743.031498.3045.001781750.221504.8245.251791757.391511.3145.501801764.551517.7945.751811771.681524.2546.001821778.801530.6946.251831785.891537.1246.501841792.971543.5346.751851800.021549.9247.001861807.061556.2947.251871814.081562.6547.501881821.081568.9947.751891828.071575.3248.00t(min) =4.845.905.006.00

&R"GRDSLAB.xls" ProgramVersion 2.0&C&P of &N&R&D &TSubgrade Soil Types and Approximate Subgrade Modulus (k) Values Type of Soil Support Provided k Values Range (pci) Fine-grained soils in whichsilt and clay-size particles Low 50 - 120predominate Sands and sand-gravelmixtures with moderate Medium 130 - 170amounts of silt and clay Sands and sand-gravelmixtures relatively free High 180 - 220of plastic fines Cement-treated subbases Very high 250 - 400Radius of Stiffness, "Lr", is a measure of the stiffness of the slab relative to the foundation (subgrade). It is a linear dimension and represents mathematically the 4th root of the ratio of the stiffness of the slab to the stiffness of the foundation.For a given slab thickness and subgrade strength there is a critical aisle width for which the slab stress in the aisleway is maximum. The critical aisle width exists when the maximum bending moment in the aisle due to a load on one side of the aisle coincides with the point of maximum moment due to the load on the other side of the aisle. This doubles the negative bending moment (tension in top of slab) at the aisle centerline. For aisle widths other than the critial aisle width, the bending moments due to the loads on each side of the aisle are not maximum.The allowable uniformly distributed live loading, "wLL", is based on the most critical aisle width condition. Using this criteria, there are no restrictions on the load layout configuration or the uniformity of the loading. Loads up to this calculated maximum may be placed nonuniformly in any configuration and changed during the service life of the floor.The allowable uniformly distributed live loading, "wLL", is based on the most critical aisle width condition. Using this criteria, there are no restrictions on the load layout configuration or the uniformity of the loading. Loads up to this calculated maximum may be placed nonuniformly in any configuration and changed during the service life of the floor.Note: direct solution for t(min) has been rounded up to nearest 1/4" thickness.Note: direct solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness.Note: iterative solution for t(min) has been rounded up to nearest 1/4" thickness."GRDSLAB.xls"written by: Alex Tomanovich, P.E.t(Subgrade)

Forklift Truck DataReference: ACI 360R-10 - "Guide to Design of Slabs-on-Ground" (page 19)Website Links to Data from Various Forklift Truck Vendors:http://www.worldwideforklifts.com/pdffiles.htmlhttp://www.forklifttrucks.biz/product-details.asphttp://www.cat-lift.com/_cat/index.cfm/north-america/english/products/lift-trucks/http://www.clarkmheu.com/cms/products/diesel-lpg-forklifts-pneumatic-tire/c20253035-gen2-series/?L=5http://www.yale.com/north-america/en-us/product-selector/http://www.mitforklift.com/index.php?MENU_ID=11&LANGUAGE=ENGLISH&PD=http://www.mit-lift.com/tasks/sites/_mit/assets/File/MECM0012.pdfhttp://www.hyster.com/north-america/en-us/products/overview/http://www.hyster-bigtrucks.com/Products/Range/Heavy-Duty-Forklift-Trucks/http://www.kmhsystems.com/pdfs/Nissan-Cushion-Tire-Trucks-Spec-Sheets.pdfhttp://www.volvorentsconstructionequipment.com/sites/default/files/equipment/specifications/DG7ton%20Spec.pdfhttp://www.linde-world.de/mh-products/start.view?dealer=1http://www.taylormachineworks.com/industrial.htmReference: "Slab Thickness Design for Industrial Concrete Floors on Grade"by Robert G. Packard (Portland Cement Association, 1976)Document No. IS195.01DReference: Ohio Gratings, Inc. Product Catalog (7-05, page 73)Reference: "Concrete Floor Slabs on Grade Subjected to Heavy Loads"by U.S. Department of the Army (1987)Manual TM 5-809-12 / AFM 88-3 (Chapter 15, page 3-1)Reference: Concrete Ground Floors & Pavements for Commercial and Industrial Use -Part Two: Specific Design (TM 38)by CCANZ (Cement & Concrete Association of New Zealand)

http://www.worldwideforklifts.com/pdffiles.htmlhttp://www.forklifttrucks.biz/product-details.asphttp://www.mitforklift.com/index.php?MENU_ID=11&LANGUAGE=ENGLISH&PD=http://www.hyster.com/north-america/en-us/products/overview/http://www.cat-lift.com/_cat/index.cfm/north-america/english/products/lift-trucks/http://www.kmhsystems.com/pdfs/Nissan-Cushion-Tire-Trucks-Spec-Sheets.pdfhttp://www.clarkmheu.com/cms/products/diesel-lpg-forklifts-pneumatic-tire/c20253035-gen2-series/?L=5http://www.volvorentsconstructionequipment.com/sites/default/files/equipment/specifications/DG7ton%20Spec.pdfhttp://www.hyster-bigtrucks.com/Products/Range/Heavy-Duty-Forklift-Trucks/http://www.mit-lift.com/tasks/sites/_mit/assets/File/MECM0012.pdfhttp://www.linde-world.de/mh-products/start.view?dealer=1http://www.yale.com/north-america/en-us/product-selector/http://www.taylormachineworks.com/industrial.htm

AASHTO Truck DataAASHTO Highway Loads:AASHTO Highway Loads Carried by Wheel SetH-10H-15 or HS-15H-20 or HS-20H-25 or HS-25(lbs.)(lbs.)(lbs.)(lbs.)Nomenclature:W20,00030,00040,00050,000W = Total vehicle weightF2,0003,0004,0005,000F = Front axle wheel loadR8,00012,00016,00020,000R = Rear axle wheel loadRaxle16,00024,00032,00040,000Raxle = Total rear axle loadAASHTO Wheel Loads and Wheel Spacings:AASHTO Wheel Load Surface Contact Area (Foot Print):