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"GRDSLAB" Program

Doc"GRDSLAB" --- CONCRETE SLAB ON GRADE ANALYSISProgram Description:Descripcin del Programa:"GRDSLAB" is a spreadsheet program written in MS-Excel for the purpose of analysis of concrete slabs onGRDSLAB es un programa escrito en MS Excel para analisis de losas de concreto en pisos.grade. Specifically, a concrete slab on grade may be subjected to concentrated post or wheel loading. ThenEspecificamente, una losa de piso puede ser sujeta de postes concentrados y cargas mviles.for the given parameters, the slab flexural, bearing, and shear stresses are checked, the estimated crack width isPara los parmetros dados, se verifican los esfuerzos de flexin, cargas y cortes, se determinadetermined, the minimum required distribution reinforcing is determined, and the bearing stress on the dowelsel ancho agrietado, la mnima distribucion de refuerzo, y los esfuerzos de carga en las dovelas en lasat construction joints is checked. Also, design charts from the Portland Cement Association (PCA) are includedjuntas de construccin, se checan.. Tambin se incluye los cuadros de diseo de la PCA parato provide an additional method for determining/checking required slab thickness for flexure. The ability toproporcionar un mtoso adicional para dterminar y verificar el espesor de la losa para flexin. Laanalyze the capacity of a slab on grade subjected to continuous wall (line-type) load as well as stationary,habilidad para analizar la capacidad de la losa en piso sujeta a la carga de un muro contnuo as comouniformly distributed live loads is also provided.a una carga estacionaria uniformemente distribuida, tambien se incluye.This program is a workbook consisting of eight (8) 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 LoadsProgram Assumptions and Limitations:1. This program is based on the following references:a. "Load Testing of Instumented Pavement Sections - Improved Techniques for Appling the Finite ElementMethod to Strain Predition 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. "Dowel Bar Opimization: Phases I and II - Final Report" - by Max L. Porter (Iowa State University, 2001)e. "Design of Slabs on Grade" - ACI 360R-92 - by American Concrete Institute (from ACI Manual of ConcretePractice, 1999)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)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 flexual 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 generally varies between 15% to 30% as is to be input by the user.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 interation 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 1.4For Slab Subjected to Interior Concentrated Post or Wheel LoadingAssuming ACI-360 "Type B" Design - Reinforced for Shrinkage and Temperature Only3000Check Slab Flexural Stress:(assuming unreinforced slab with interior load condition)Job Name:Subject:3500a =6.024in.a = SQRT(Ac/p)Job Number:Originator:Checker:4000Ec =4286826psiEc = 33*wc^1.5*SQRT(f 'c)4500MR =636.40psiMR = 9*SQRT(f 'c)Input Data:5000Mr =6.79ft-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.Min. req'd. slab thk. for single interior load:Slab Thickness, t =8.000in.6000Lr =36.985in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25t(min) =7.25in.fb1(actual) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Ref. 1)Concrete Strength, f 'c =5000psi40000b =5.648in.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) =267.58psifb1(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=267.46psi= 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=258.09psi= 0.316*P/t^2*(LOG(t^3)-4*LOG(b)-LOG(k)+6.48) (Reference 3)3. "Design of Concrete Structures" - by Winter, Urquhart, O'Rourke, and Nilson" - (McGraw-Hill, 1962)thicknesses for corner and edge condtionsConcentrated Load, P =12500.00lbs.700002 Loads: fb2(actual) =307.72psifb2(actual) = fb1(actual)*(1+i/100)are shown below for comparison only.Contact Area, Ac =114.00in.^275000Fb(allow) =318.20psiFb(allow) = MR/FSFactor of Safety, FS =2.0080000Min. req'd. slab thk. for single corner load:Dowel Bar Dia., db =0.750in.Concrete Slab on Grade0.750(assuming unreinforced slab with corner load condition)t(min) =8.50in.fb1(actual) = 3*P/t^2*(1-(1.772*a/Lr)^(0.72)) (Ref. 1)Dowel Bar Spacing, s =12.000in.1.000fb1(actual) =346.45psifb1(actual) = 3*P/t^2*(1-(1.772*a/Lr)^(0.72)) (Reference 1)Min. req'd. slab thk. for single edge load (circular area):Const. Joint Width, z =0.2500in.Lubricate this endStop slab reinf. (As) at jointMin. of1.250=343.13psi= 3*P/t^2*(1-(SQRT(2)*a/Lr)^(0.6)) (References 2 and 3)t(min) =10.75in.fb1(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) (Ref. 1)Joint Spacing, L =20.000ft.of all Dowels1/8"-1/4" x t/4 formed jointt/3 or 2"Min. req'd. slab thk. for single edge load (semi-circular area):Temperature Range, DT =50.00deg.(assuming unreinforced slab with edge load condition)t(min) =11.75in.fb1(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)) (Ref. 1)Increase for 2nd Wheel, i =15%fb1(actual) =505.98psifb1(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) =603.42psifb1(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)=404.81psi= 0.572*P/t^2*(4*LOG(Lr/b)+0.359) (Reference 2)Results:Typical Construction Joint for Load Transfer=387.85psi= 0.572*P/t^2*(LOG(t^3)-4*LOG(b)-LOG(k)+5.77) (Reference 3)=506.12psi= 0.803*P/t^2*(4*LOG(Lr/a)+0.666*(a/Lr)-0.034) (for circle)Check Slab Flexural Stress:(assuming unreinforced slab with interior load condition)=399.70psi= 0.803*P/t^2*(4*LOG(Lr/a)+0.282*(a/Lr)-0.650) (for semi-circle)Effective Load Radius, a =6.024in.a = SQRT(Ac/p)Modulus of Elasticity, Ec =4286826psiEc = 33*wc^1.5*SQRT(f 'c)Check Slab Bearing Stress:(assuming working stress)Modulus of Rupture, MR =636.40psiMR = 9*SQRT(f 'c)fp(actual) =109.65psifp(actual) = P/AcCracking Moment, Mr =6.79ft-k/ft.Mr = MR*(12*t^2/6)/12000 (per 1' = 12" width)Fp(allow) =2672.86psiFp(allow) = 4.2*MRPoisson's Ratio, m =0.15m = 0.15 (assumed for concrete)Radius of Stiffness, Lr =36.985in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25Check Slab Punching Shear Stress:(assuming working stress)Equivalent Radius, b =5.648in.b = SQRT(1.6*a^2+t^2)-0.675*t , for a < 1.724*tbo =42.708in.bo = 4*SQRT(Ac) (assumed shear perimeter)1 Load: fb1(actual) =267.58psifb1(actual) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Ref. 1)fv(actual) =20.91psifv(actual) = P/(t*(bo+4*t))2 Loads: fb2(actual) =307.72psifb2(actual) =fb1(actual)*(1+i/100)Fv(allow) =171.83psiFv(allow) = 0.27*MRFb(allow) =318.20psiFb(allow) = MR/FSFb(allow) >= fb(actual), O.K.0Shrinkage and Temperature Reinf.:(assuming subgrade drag method)Check Slab Bearing Stress:(assuming working stress)(Ref. 4)F =1.50F = 1.5 (assumed friction factor between subgrade and slab)fp(actual) =109.65psifp(actual) = P/AcW =100.00psfW = wc*(t/12)Fp(allow) =2672.86psiFp(allow) = 4.2*MRFp(allow) >= fp(actual), O.K.fs =45000psifs = 0.75*fyAs =0.033in.^2/ft.As = F*L*W/(2*fs)Check Slab Punching Shear Stress:(assuming working stress)(Ref. 4)bo =42.708in.bo = 4*SQRT(Ac) (assumed shear perimeter)Slab Reinforcing:(assuming temperature method)fv(actual) =20.91psifv(actual) = P/(t*(bo+4*t))fr =318.20psifr = MR/FSFv(allow) =171.83psiFv(allow) = 0.27*MRFv(allow) >= fv(actual), O.K.fs =45000psifs = 0.75*fya =0.0000055a = 5.5x10^(-6) (assumed thermal expansion coefficient)Shrinkage and Temperature Reinf.:(assuming subgrade drag method)(Ref. 3)Es =29000000psiEs = 29x10^6 (modulus of elasticity for steel)Friction Factor, F =1.50F = 1.5 (assumed friction factor between subgrade and slab)As =0.413in.^2/ft.As = fr*(12)*t/(2*(fs-DT*a*Es))Slab Weight, W =100.00psfW = wc*(t/12)Reinf. Allow. Stress, fs =45000psifs = 0.75*fySlab Reinforcing:(assuming concrete-to-steel ratio method)As =0.033in.^2/ft.As = F*L*W/(2*fs)fr =318.20psifr = MR/FS(continued)fs =45000psifs = 0.75*fyAs =0.679in.^2/ft.As = fr*(12)*t/fsDetermine Estimated Crack Width:(assuming no use of stabilized or granular subbase)Slab Reinforcing:(assuming confirmed capacity method)Slab-base Frict. Adjust., C =1.00C = 1.0 (assumed value for no subbase)As =0.137in.^2/ft.As = 14.5*SQRT(f 'c)*t/fyThermal Expansion, a =0.0000055in./in./dega = 5.5x10^(-6) (assumed thermal expansion coefficient)As =0.747in.^2/ft.As = 4.4*MR*t/(fy/FS)Shrinkage Coefficient, e =0.00026in./in.e = 3.5x10^(-4) (assumed coefficient of shrinkage)As =0.589in.^2/ft.As = ((MR/FS*12*t^2/6)/(1.44*t/2))/12000Est. Crack Width, DL =0.1284in.DL = C*L*12*(a*DT+e)Check Bearing Stress on Dowels at Construction Joints with Load Transfer:(Ref. 2)Slab Reinforcing:(assuming crack restraint method)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)C =1.0C = 1.0 (assumed value for no subbase)a =0.0000055a = 5.5x10^(-6) (assumed thermal expansion coefficient)e =0.00026in./in.e = assumed coefficient of shrinkageDL =0.1284in.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 =36.985in.Le = 1.0*Lr = applicable dist. each side of critical dowelLe =36.985in.Le = 1.0*Lr = applicable distance each side of critical dowelEffective Dowels, Ne =3.11barsNe = 1.0+2*S(1-d(n-1)*s/Le) (where: n = dowel #)Joint Load, Pt =6250.00lbs.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 JointCritical Dowel Load, Pc =2011.88lbs.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 #Mod. of Dowel Suppt., kc =1500000psikc = 1.5x10^6 (assumed for concrete)1234000000000000000000000Mod. of Elasticity, Eb =29000000psiEb = 29x10^6 (assumed for steel dowels)1.0000.6760.3510.0270.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.0000.000Inertia/Dowel Bar, Ib =0.0155in.^4Ib = p*db^4/64Relative Bar Stiffness, b =0.889b = (kc*db/(4*Eb*Ib))^(1/4)Ne =3.107barsNe = 1+2*S(1-d(i-1)*s/Le) (i = dowel #)fd(actual) =5299.09psifd(actual) = kc*(Pc*(2+b*z)/(4*b^3*Eb*Ib))Pt =6250.00lbs.Pt = 0.50*P (assumed load transferred across joint)Fd(allow) =5416.67psiFd(allow) = (4-db)/3*f 'cFd(allow) >= fd(actual), O.K.Pc =2011.88lbs.Pc = Pt/Nekc =1500000psikc = 1.5x10^6 (assumed for concrete)Eb =29000000psiEb = 29x10^6 (assumed for steel dowels)References:Ib =0.0155in.^4Ib = p*db^4/641. "Load Testing of Instumented Pavement Sections - Improved Techniques for Appling the Finite Elementb =0.889b = (kc*db/(4*Eb*Ib))^(1/4)Method to Strain Predition in PCC Pavement Structures" - by University of Minnesota, Department of Civilfd(actual) =5299.09psifd(actual) = kc*(Pc*(2+b*z)/(4*b^3*Eb*Ib))Engineering (submitted to MN/DOT, March 24, 2002)Fd(allow) =5416.67psiFd(allow) = ((4-db)/3)*f 'c2. "Dowel Bar Opimization: Phases I and II - Final Report" - by Max L. Porter (Iowa State University, 2001)3. "Design of Slabs on Grade" - ACI 360R-92 - by American Concrete Institute (from ACI Manual of ConcreteDetermine Minimum Slab Thickness for Flexure:Practice, 1999)Iteration #tEqn. for fbiEqn. for fbcEqn. for fbecEqn. for fbesc4. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) - by Robert G. Packard11.00-5660.659929.61-8969.45-12848.39(Portland Cement Association, 1976)21.25-4243.413046.70-6982.14-9759.0231.50-3266.71472.63-5561.99-7633.79Comments:41.75-2574.72-555.42-4523.77-6124.4152.00-2068.54-956.34-3744.26-5016.4962.25-1687.38-1083.25-3144.38-4179.2372.50-1393.10-1086.03-2672.61-3530.5982.75-1160.97-1032.86-2294.54-3017.3193.00-974.48-956.20-1986.60-2603.74103.25-822.27-871.93-1732.19-2265.26113.50-696.43-787.82-1519.38-1984.46123.75-595.91-707.55-1339.42-1748.74134.00-509.98-632.74-1185.75-1548.77144.25-435.91-563.89-1053.39-1377.56154.50-371.55-500.97-938.50-1229.74164.75-315.24-443.68-838.08-1101.17175.00-265.67-391.59-749.73-988.57185.25-221.77-344.24-671.57-889.37195.50-182.69-301.17-602.05-801.47205.75-147.75-261.94-539.91-723.20216.00-116.36-226.16-484.13-653.16226.25-88.04-193.48-433.85-590.23236.50-62.41-163.56-388.35-533.45246.75-39.13-136.13-347.03-482.03257.00-17.92-110.92-309.39-435.31267.251.47-87.72-274.98-392.71277.5019.24-66.32-243.45-353.77287.7535.57-46.55-214.48-318.05298.0050.62-28.25-187.78-285.22308.2564.50-11.29-163.13-254.96318.5077.354.47-140.31-227.00328.7589.2619.14-119.14-201.12339.00100.3232.80-99.46-177.11349.25110.6245.55-81.14-154.78359.50120.2157.46-64.05-133.99369.75129.1768.62-48.08-114.593710.00137.5479.07-33.12-96.453810.25145.3888.88-19.11-79.483910.50152.7498.10-5.95-63.564010.75159.64106.776.43-48.624111.00166.13114.9418.08-34.564211.25172.24122.6429.06-21.334311.50178.00129.9139.43-8.864411.75183.43136.7949.222.914512.00188.56143.2958.4914.044612.25193.41149.4567.2724.574712.50198.00155.2875.5934.544812.75202.35160.8283.4943.994913.00206.47166.0890.9952.965013.25210.38171.0898.1361.485113.50214.10175.84104.9269.585213.75217.63180.36111.3977.305314.00220.99184.68117.5684.645414.25224.19188.79123.4491.655514.50227.23192.71129.0698.335614.75230.14196.46134.43104.715715.00232.91200.04139.57110.805815.25235.56203.47144.48116.635915.50238.09206.75149.19122.216015.75240.50209.88153.70127.566116.00242.82212.89158.03132.686216.25245.03215.77162.18137.586316.50247.15218.54166.17142.296416.75249.18221.19170.00146.826517.00251.13223.74173.68151.166617.25253.00226.19177.22155.336717.50254.79228.54180.62159.356817.75256.52230.81183.90163.216918.00258.17232.99187.06166.937018.25259.76235.09190.11170.517118.50261.29237.11193.04173.977218.75262.77239.05195.88177.297319.00264.18240.93198.61180.517419.25265.55242.74201.25183.607519.50266.86244.49203.80186.607619.75268.13246.18206.26189.487720.00269.36247.81208.65192.287820.25270.54249.38210.95194.987920.50271.67250.91213.18197.598020.75272.77252.38215.34200.118121.00273.84253.80217.43202.568221.25274.86255.18219.45204.928321.50275.85256.51221.42207.228421.75276.81257.81223.32209.448522.00277.74259.06225.16211.598622.25278.64260.27226.95213.688722.50279.50261.45228.69215.708822.75280.35262.59230.37217.678923.00281.16263.69232.01219.579023.25281.95264.76233.60221.429123.50282.71265.80235.14223.229223.75283.46266.81236.64224.979324.00284.17267.80238.10226.679424.25284.87268.75239.52228.329524.50285.55269.68240.90229.929624.75286.21270.58242.25231.489725.00286.84271.45243.55233.009825.25287.46272.30244.82234.479925.50288.06273.13246.06235.9110025.75288.65273.94247.27237.3110126.00289.22274.72248.45238.6810226.25289.77275.49249.59240.0010326.50290.30276.23250.71241.3010426.75290.83276.95251.80242.5610527.00291.33277.66252.86243.7910627.25291.83278.35253.89244.9910727.50292.31279.02254.90246.1510827.75292.78279.67255.89247.3010928.00293.23280.31256.85248.4111028.25293.68280.93257.79249.4911128.50294.11281.53258.71250.5511228.75294.53282.12259.60251.5911329.00294.94282.70260.48252.6011429.25295.34283.26261.33253.5811529.50295.73283.81262.16254.5511629.75296.11284.35262.98255.4911730.00296.48284.87263.78256.4111830.25296.85285.38264.56257.3111930.50297.20285.88265.32258.1912030.75297.54286.37266.07259.0512131.00297.88286.85266.80259.8912231.25298.21287.32267.51260.7112331.50298.53287.77268.21261.5212431.75298.84288.22268.89262.3112532.00299.15288.66269.56263.0812632.25299.45289.08270.22263.8312732.50299.74289.50270.86264.5712832.75300.03289.91271.49265.2912933.00300.31290.31272.10266.0013033.25300.58290.70272.71266.6913133.50300.85291.09273.30267.3713233.75301.11291.46273.88268.0413334.00301.36291.83274.45268.6913434.25301.61292.19275.00269.3313534.50301.86292.54275.55269.9613634.75302.09292.89276.08270.5713735.00302.33293.22276.61271.1713835.25302.56293.56277.12271.7613935.50302.78293.88277.63272.3414035.75303.00294.20278.12272.9114136.00303.22294.51278.61273.4714236.25303.43294.82279.08274.0114336.50303.63295.12279.55274.5514436.75303.83295.41280.01275.0814537.00304.03295.70280.46275.5914637.25304.23295.99280.90276.1014737.50304.42296.26281.34276.6014837.75304.60296.54281.77277.0914938.00304.79296.80282.19277.5715038.25304.96297.07282.60278.0415138.50305.14297.33283.00278.5015238.75305.31297.58283.40278.9615339.00305.48297.83283.79279.4015439.25305.65298.07284.17279.8415539.50305.81298.31284.55280.2715639.75305.97298.55284.92280.7015740.00306.12298.78285.29281.1115840.25306.28299.00285.64281.5215940.50306.43299.23286.00281.9216040.75306.58299.45286.34282.3216141.00306.72299.66286.68282.7116241.25306.86299.87287.02283.0916341.50307.00300.08287.35283.4716441.75307.14300.29287.67283.8416542.00307.27300.49287.99284.2016642.25307.41300.69288.30284.5616742.50307.54300.88288.61284.9116842.75307.67301.07288.92285.2616943.00307.79301.26289.22285.6017043.25307.91301.44289.51285.9417143.50308.04301.63289.80286.2717243.75308.15301.81290.08286.5917344.00308.27301.98290.37286.9117444.25308.39302.15290.64287.2317544.50308.50302.33290.91287.5417644.75308.61302.49291.18287.8417745.00308.72302.66291.45288.1417845.25308.83302.82291.71288.4417945.50308.93302.98291.96288.7318045.75309.04303.14292.21289.0218146.00309.14303.29292.46289.3018246.25309.24303.45292.71289.5818346.50309.34303.60292.95289.8518446.75309.44303.74293.19290.1218547.00309.53303.89293.42290.3918647.25309.63304.03293.65290.6518747.50309.72304.17293.88290.9118847.75309.81304.31294.10291.1718948.00309.90304.45294.33291.42t(min) =7.258.5010.7511.75

&R"GRDSLAB.xls" ProgramVersion 1.4&C&P of &N&R&D &Tt(Subgrade)t/2Contact Area, Ac3/4"f Plain Dowels @ 12"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)*PcPPWheelPostDirection of pour"GRDSLAB.xls"written by: Alex Tomanovich, P.E.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 30Values of Portlant Cement Concrete Coefficient of Shrinkage (e)Concrete Strength, Modulus of Rupture, Srinkage 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)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"Subbase friction adjustment factor, 'C', is as follows:C = 0.65 for stabilized subbaseC = 0.80 for granular subbaseC = 1.00 for no subbaseRepresentative 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.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 - 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.

PCA Fig. 3-Wheel LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 1.4For 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.)3t Index:40881221.533.54865Area, Ac (in.^2)4568101214Ac Index:67.9008510.510.514.5243650.567.50881221.533.548651112.0021.0321.501013.513.517.527385370510.510.514.5243650.567.52214.5023.5324.001517172029.54156.572.51013.513.517.5273853703317.5026.5327.0020212122.532.5445875.51517172029.54156.572.54420.0029.0329.502525252735.547627820212122.532.5445875.55522.5032.0032.503030303038496581.52525252735.54762786627.0035.0835.5035353534425267.583.53030303038496581.57730.0037.6038.004040403945.555.570.58735353534425267.583.58834.0041.6042.0045454544.547.5587389.54040403945.555.570.5879939.0045.1845.5050505049.55262779245454544.547.5587389.5101044.5047.3547.5055555555566579.595.550505049.552627792111149.5051.8852.00606060606067.5829855555555566579.595.5121255.0055.9556.00656565656571.585.5101.5606060606067.58298131360.0060.0060.007068.568.568.568.574.588104656565656571.585.5101.5141465.0065.0065.00757373737377.5911077068.568.568.568.574.588104151568.5068.5068.5080787878788294110757373737377.591107161673.0073.0073.008582.582.582.582.58797.5112.580787878788294110171778.0078.0078.00908989898990.51011178582.582.582.582.58797.5112.5181882.5082.5082.509594.594.594.594.595104.5120908989898990.5101117191989.0089.0089.001009999999999.5107.5122.59594.594.594.594.595104.5120202094.5094.5094.501009999999999.5107.5122.5212199.0099.0099.00Input 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 chart with slab stress = 12.73Ac113.64113.64Axle 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 thickness, tResults: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 Tickness, t =7.900in.t = determined from Figure 3 aboveNote: User MUST determine slab thickness fromFigure 3, and input the result in cell D51.

&R"GRDSLAB.xls" ProgramVersion 1.4&C&P of &N&R&D &TFigure 3 Design Chart for Axles with Single Wheels"GRDSLAB.xls"written by: Alex Tomanovich, P.E.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.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.

PCA Fig. 7a-Post LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 1.4For 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) =76.34in.^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:1010.800120881221.533.548651133.5039.3048.00510.510.514.5243650.567.52236.0041.8050.501013.513.517.5273853703338.0044.0053.001517172029.54156.572.54441.0047.2056.5020212122.532.5445875.55544.0049.6058.002525252735.54762786647.0053.0062.003030303038496581.57749.0055.4065.0035353534425267.583.58852.0058.2067.504040403945.555.570.5879955.5061.5070.5045454544.547.5587389.5101058.0064.0073.0050505049.552627792111162.0068.0077.0055555555566579.595.5121265.0070.8079.50Figure 8 - Post Configurations and Loads606060606067.58298131367.5073.3082.00for which Figures 7a, 7b, and 7c Apply656565656571.585.5101.5141471.5077.1085.507068.568.568.568.574.588104151574.5079.9088.00757373737377.591107161677.5082.9091.00Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)80787878788294110171782.0086.8094.00Load ContactSlab Thickness (in.)8582.582.582.582.58797.5112.5181887.0091.2097.50Area (in.^2)4568101214908989898990.5101117191990.5094.70101.000881221.533.548659594.594.594.594.595104.5120202095.0098.80104.50510.510.514.5243650.567.51009999999999.5107.5122.5212199.50102.70107.501013.513.517.527385370Input Data:Ac Index:Ac(eff) values:1517172029.54156.572.5Concrete Strength, f 'c =5000psiInstructions for Use of Figure 7a:13Ac(table)60.0073.3020212122.532.5445875.5Subgrade Modulus, k =50.00pci1. Enter chart with slab stress = 16.32Ac64.0076.342525252735.5476278Post Load, P =13000.00lbs.2. Move to right to eff. contact area = 76.3414Ac(table)65.0077.103030303038496581.5Post 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 slab thickness, t45454544.547.5587389.5Factor of Safety, FS =3.0050505049.55262779255555555566579.595.5Results:606060606067.58298Effective Contact Area, Ac(eff) =76.34in.^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 Tickness, t =10.800in.t = determined 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 1.4&C&P of &N&R&D &TFigure 7a Design Chart for Post Loads, subgrade k = 50 pciP/2P/2PPPLoad oneach postxxyy"GRDSLAB.xls"written by: Alex Tomanovich, P.E.

PCA Fig. 7b-Post LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 1.4For 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) =70.03in.^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.)4t Index:5Area, Ac (in.^2)4568101214Ac Index:89.800100881221.533.548651121.5032.3033.50510.510.514.5243650.567.52224.0034.8036.001013.513.517.5273853703327.0036.9038.001517172029.54156.572.54429.5039.8541.0020212122.532.5445875.55532.5042.8544.002525252735.54762786635.5045.8547.003030303038496581.57738.0047.9049.0035353534425267.583.58842.0051.0052.004040403945.555.570.5879945.5054.5055.5045454544.547.5587389.5101047.5056.9558.0050505049.552627792111152.0061.0062.0055555555566579.595.5121256.0064.1065.00Figure 8 - Post Configurations and Loads606060606067.58298131360.0066.7567.50for which Figures 7a, 7b, and 7c Apply656565656571.585.5101.5141465.0070.8571.507068.568.568.568.574.588104151568.5073.9074.50757373737377.591107161673.0077.0577.50Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)80787878788294110171778.0081.6082.00Load ContactSlab Thickness (in.)8582.582.582.582.58797.5112.5181882.5086.5587.00Area (in.^2)4568101214908989898990.5101117191989.0090.3590.500881221.533.548659594.594.594.594.595104.5120202094.5094.9595.00510.510.514.5243650.567.51009999999999.5107.5122.5212199.0099.4599.501013.513.517.527385370Input Data:Ac Index:Ac(eff) values:1517172029.54156.572.5Concrete Strength, f 'c =5000psiInstructions for Use of Figure 7b:13Ac(table)60.0066.7520212122.532.5445875.5Subgrade Modulus, k =100.00pci1. Enter chart with slab stress = 16.32Ac64.0070.032525252735.5476278Post Load, P =13000.00lbs.2. Move to right to eff. contact area = 70.0314Ac(table)65.0070.853030303038496581.5Post 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 slab thickness, t45454544.547.5587389.5Factor of Safety, FS =3.0050505049.55262779255555555566579.595.5Results:606060606067.58298Effective Contact Area, Ac(eff) =70.03in.^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 Tickness, t =9.800in.t = determined 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 1.4&C&P of &N&R&D &TP/2P/2PPPLoad oneach postxxyyFigure 7b Design Chart for Post Loads, subgrade k = 100 pci"GRDSLAB.xls"written by: Alex Tomanovich, P.E.

PCA Fig. 7c-Post LoadCONCRETE SLAB ON GRADE THICKNESS ANALYSISCALCULATIONS:Version 1.4For 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) =68.02in.^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:89.200100881221.533.548651121.5028.7033.50510.510.514.5243650.567.52224.0031.2036.001013.513.517.5273853703327.0033.6038.001517172029.54156.572.54429.5036.4041.0020212122.532.5445875.55532.5039.4044.002525252735.54762786635.5042.4047.003030303038496581.57738.0044.6049.0035353534425267.583.58842.0048.0052.004040403945.555.570.5879945.5051.5055.5045454544.547.5587389.5101047.5053.8058.0050505049.552627792111152.0058.0062.0055555555566579.595.5121256.0061.4065.00Figure 8 - Post Configurations and Loads606060606067.58298131360.0064.5067.50for which Figures 7a, 7b, and 7c Apply656565656571.585.5101.5141465.0068.9071.507068.568.568.568.574.588104151568.5072.1074.50757373737377.591107161673.0075.7077.50Effective Load Contact Area Based on Slab Thickness (values from PCA Fig. 5)80787878788294110171778.0080.4082.00Load ContactSlab Thickness (in.)8582.582.582.582.58797.5112.5181882.5085.2087.00Area (in.^2)4568101214908989898990.5101117191989.0089.9090.500881221.533.548659594.594.594.594.595104.5120202094.5094.8095.00510.510.514.5243650.567.51009999999999.5107.5122.5212199.0099.3099.501013.513.517.527385370Input Data:Ac Index:Ac(eff) values:1517172029.54156.572.5Concrete Strength, f 'c =5000psiInstructions for Use of Figure 7c:13Ac(table)60.0064.5020212122.532.5445875.5Subgrade Modulus, k =200.00pci1. Enter chart with slab stress = 16.32Ac64.0068.022525252735.5476278Post Load, P =13000.00lbs.2. Move to right to eff. contact area = 68.0214Ac(table)65.0068.903030303038496581.5Post 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 slab thickness, t45454544.547.5587389.5Factor of Safety, FS =3.0050505049.55262779255555555566579.595.5Results:606060606067.58298Effective Contact Area, Ac(eff) =68.02in.^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 Tickness, t =9.200in.t = determined 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 1.4&C&P of &N&R&D &TFigure 7c Design Chart for Post Loads, subgrade k = 200 pciP/2P/2PPPLoad oneach postxxyy"GRDSLAB.xls"written by: Alex Tomanovich, P.E.

Wall LoadCONCRETE SLAB ON GRADE ANALYSISCALCULATIONS:Version 1.4For 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 = coef. for beam on elastic foundationMin. 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.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:Iteration #tEqn. for PcEqn. for Pe11.00-722.68-740.04Min. req'd. slab thk. for free edge load:21.25-697.80-720.75t(min) =8.00in.31.50-671.65-700.47Results:41.75-644.37-679.32Concrete Slab Loaded Near Free Edge52.00-616.10-657.40Design Parameters:62.25-586.93-634.78Modulus of Rupture, MR =569.21psiMR = 9*SQRT(f 'c)72.50-556.94-611.52Allow. Bending Stress, Fb =101.19psiFb = 1.6*SQRT(f 'c) (as recommended in reference below)82.75-526.18-587.67Factor of Safety, FS =5.625FS = MR/Fb93.00-494.72-563.28Section Modulus, S =128.00in.^3/ft.S = b*t^2/6103.25-462.60-538.37Modulus of Elasticity, Ec =3604997psiEc = 57000*SQRT(f 'c)113.50-429.85-512.97Width, b =12.00in.b = 12" (assumed)123.75-396.51-487.12Moment of Inertia, I =512.00in.^4I = b*t^3/12134.00-362.61-460.83Stiffness Factor, l =0.0201l = (k*b/(4*Ec*I))^(0.25)144.25-328.18-434.13Coefficient, Blx =0.3224Blx = coef. for beam on elastic foundation154.50-293.23-407.03164.75-257.80-379.56Wall Load Near Center of Slab or Keyed/Doweled Joints:175.00-221.90-351.72Allowable Wall Load, Pc =1040.30lb./ft.Pc = 4*Fb*S*l185.25-185.54-323.53= 12.8*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)195.50-148.75-295.00Pc(allow) >= P, O.K.205.75-111.54-266.14Wall Load Near Free Edge of Slab:216.00-73.92-236.97Allowable Wall Load, Pe =806.68lb./ft.Pe = Fb*S*l/Blx226.25-35.91-207.50= 9.9256*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0.25)236.502.48-177.73Reference:Pe(allow) >= P, O.K.246.7541.25-147.67"Concrete Floor Slabs on Grade Subjected to Heavy Loads"257.0080.37-117.33Army Technical Manual TM 5-809-12, Air Force Manual AFM 88-3, Chapter 15 (1987)267.25119.85-86.72277.50159.67-55.84Comments:287.75199.82-24.71298.00240.306.68308.25281.0938.31318.50322.1970.19328.75363.60102.30339.00405.31134.64349.25447.30167.20359.50489.58199.99369.75532.14232.993710.00574.97266.203810.25618.07299.623910.50661.44333.254010.75705.06367.084111.00748.94401.104211.25793.07435.324311.50837.44469.734411.75882.06504.334512.00926.91539.114612.25972.00574.074712.501017.32609.214812.751062.87644.534913.001108.64680.025013.251154.63715.685113.501200.84751.525213.751247.26787.515314.001293.89823.675414.251340.73860.005514.501387.78896.485614.751435.03933.125715.001482.49969.925815.251530.141006.875915.501577.981043.976015.751626.021081.226116.001674.251118.626216.251722.671156.176316.501771.281193.866416.751820.071231.696517.001869.041269.676617.251918.191307.786717.501967.531346.036817.752017.031384.426918.002066.721422.957018.252116.571461.617118.502166.601500.407218.752216.791539.337319.002267.161578.387419.252317.691617.567519.502368.381656.877619.752419.241696.317720.002470.251735.877820.252521.431775.557920.502572.771815.368020.752624.261855.298121.002675.911895.348221.252727.711935.518321.502779.661975.798421.752831.772016.208522.002884.022056.728622.252936.432097.358722.502988.982138.108822.753041.682178.978923.003094.522219.949023.253147.512261.039123.503200.632302.239223.753253.912343.549324.003307.322384.959424.253360.872426.489524.503414.552468.119624.753468.382509.859725.003522.342551.699825.253576.442593.649925.503630.672635.6910025.753685.032677.8510126.003739.532720.1110226.253794.162762.4710326.503848.912804.9310426.753903.802847.4910527.003958.812890.1510627.254013.962932.9110727.504069.232975.7610827.754124.623018.7210928.004180.143061.7711028.254235.783104.9211128.504291.553148.1611228.754347.443191.5011329.004403.453234.9311429.254459.583278.4611529.504515.843322.0811629.754572.213365.7911730.004628.703409.6011830.254685.313453.4911930.504742.033497.4812030.754798.873541.5612131.004855.833585.7212231.254912.903629.9812331.504970.093674.3212431.755027.393718.7512532.005084.803763.2712632.255142.323807.8812732.505199.963852.5712832.755257.713897.3512933.005315.563942.2213033.255373.533987.1713133.505431.614032.2013233.755489.794077.3213334.005548.084122.5213434.255606.484167.8113534.505664.994213.1813634.755723.604258.6313735.005782.324304.1613835.255841.154349.7713935.505900.074395.4714035.755959.104441.2414136.006018.244487.1014236.256077.484533.0314336.506136.824579.0414436.756196.264625.1414537.006255.804671.3114637.256315.444717.5614737.506375.194763.8814837.756435.034810.2914938.006494.974856.7715038.256555.014903.3315138.506615.154949.9615238.756675.394996.6715339.006735.725043.4615439.256796.155090.3215539.506856.685137.2515639.756917.305184.2615740.006978.025231.3415840.257038.835278.5015940.507099.745325.7316040.757160.745373.0316141.007221.845420.4116241.257283.035467.8616341.507344.315515.3816441.757405.685562.9716542.007467.155610.6316642.257528.705658.3616742.507590.355706.1716842.757652.095754.0416943.007713.925801.9917043.257775.845850.0017143.507837.855898.0817243.757899.955946.2417344.007962.135994.4617444.258024.416042.7517544.508086.776091.1117644.758149.226139.5317745.008211.766188.0317845.258274.396236.5917945.508337.106285.2218045.758399.906333.9118146.008462.786382.6818246.258525.756431.5118346.508588.806480.4018446.758651.946529.3618547.008715.176578.3918647.258778.476627.4818747.508841.876676.6318847.758905.346725.8518948.008968.906775.14t(min) =6.508.00

&R"GRDSLAB.xls" ProgramVersion 1.4&C&P of &N&R&D &Tt(Subgrade)PWallPWallt(Subgrade)PWallDowel(at Joint)"GRDSLAB.xls"written by: Alex Tomanovich, P.E.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 - 400

Unif. LoadCONCRETE SLAB ON GRADE ANALYSISCALCULATIONS:Version 1.4For 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 =35.418in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25*Aisle Width6000Wcr =6.520ft.Wcr = (2.209*Lr)/12Slab Thickness, t =8.000in.wLLwLLwLL(allow) =1093.32psfwLL(allow) = 257.876*Fb*SQRT(k*t/Ec) (Reference 1)Concrete Strength, f 'c =4000psiTop/SlabwLL(allow) =990.13psfwLL(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:Uniform Live Load, wLL =1000.00psf1. "Concrete Floor Slabs on Grade Subjected to Heavy Loads"t(min) =6.75in.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. PackardConcrete Slab on Grade with Uniform Loads(Portland Cement Association, 1976)*Note: in an unjointed aisleway between uniformly distributed load areas,Determine Minimum Slab Thickness for Given Uniform Loading:negative bending moment in slab may be up to twice as great asIteration #tEqn. for w(allow)positive moment in slab beneath loaded area. Allowable uniform11.00-613.45load determined below is based on critical aisle width and as a21.25-567.83result, there are no restrictions on load layout configuration or31.50-526.58uniformity of loading.41.75-488.65Results:52.00-453.3462.25-420.18Design Parameters:72.50-388.82Modulus of Rupture, MR =569.21psiMR = 9*SQRT(f 'c)82.75-358.99Allow. Bending Stress, Fb =284.60psiFb = MR/FS93.00-330.48Modulus of Elasticity, Ec =3604997Ec = 57000*SQRT(f 'c)103.25-303.14Poisson's Ratio, m =0.15m = 0.15 (assumed for concrete)113.50-276.84Radius of Stiffness, Lr =35.42in.Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25123.75-251.46Critical Aisle Width, Wcr =6.52ft.Wcr = (2.209*Lr)/12134.00-226.91144.25-203.12Stationary Uniformly Distributed Live Loads:154.50-180.01wLL(allow) =1093.32psfwLL(allow) = 257.876*Fb*SQRT(k*t/Ec)164.75-157.54wLL(allow) >= wLL, O.K.175.00-135.66185.25-114.31Reference:195.50-93.471. "Concrete Floor Slabs on Grade Subjected to Heavy Loads"205.75-73.10Army Technical Manual TM 5-809-12, Air Force Manual AFM 88-3, Chapter 15 (1987)216.00-53.162. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D)226.25-33.64by Robert G. Packard (Portland Cement Association, 1976)236.50-14.50246.754.28Comments:257.0022.70267.2540.81277.5058.60287.7576.10298.0093.32308.25110.27318.50126.97328.75143.42339.00159.64349.25175.63359.50191.41369.75206.993710.00222.373810.25237.553910.50252.554010.75267.384111.00282.034211.25296.514311.50310.844411.75325.014512.00339.034612.25352.914712.50366.654812.75380.244913.00393.715013.25407.055113.50420.265213.75433.355314.00446.325414.25459.185514.50471.925614.75484.565715.00497.095815.25509.515915.50521.836015.75534.066116.00546.186216.25558.226316.50570.166416.75582.016517.00593.776617.25605.456717.50617.046817.75628.556918.00639.987018.25651.327118.50662.607218.75673.797319.00684.917419.25695.967519.50706.947619.75717.857720.00728.697820.25739.467920.50750.168020.75760.808121.00771.388221.25781.898321.50792.348421.75802.738522.00813.068622.25823.338722.50833.558822.75843.718923.00853.819023.25863.869123.50873.859223.75883.799324.00893.689424.25903.529524.50913.309624.75923.049725.00932.739825.25942.379925.50951.9610025.75961.5110126.00971.0010226.25980.4610326.50989.8710426.75999.2310527.001008.5510627.251017.8310727.501027.0610827.751036.2610928.001045.4111028.251054.5211128.501063.5911228.751072.6211329.001081.6111429.251090.5711529.501099.4811629.751108.3611730.001117.2011830.251126.0011930.501134.7712030.751143.5012131.001152.2012231.251160.8612331.501169.4812431.751178.0812532.001186.6312632.251195.1612732.501203.6512832.751212.1112933.001220.5413033.251228.9313133.501237.3013233.751245.6313334.001253.9313434.251262.2013534.501270.4413634.751278.6513735.001286.8413835.251294.9913935.501303.1114035.751311.2114136.001319.2814236.251327.3114336.501335.3314436.751343.3114537.001351.2714637.251359.2014737.501367.1014837.751374.9814938.001382.8315038.251390.6515138.501398.4515238.751406.2315339.001413.9815439.251421.7015539.501429.4015639.751437.0815740.001444.7315840.251452.3615940.501459.9616040.751467.5416141.001475.1016241.251482.6416341.501490.1516441.751497.6416542.001505.1016642.251512.5516742.501519.9716842.751527.3716943.001534.7517043.251542.1117143.501549.4417243.751556.7617344.001564.0617444.251571.3317544.501578.5817644.751585.8217745.001593.0317845.251600.2217945.501607.3918045.751614.5518146.001621.6818246.251628.8018346.501635.8918446.751642.9718547.001650.0218647.251657.0618747.501664.0818847.751671.0818948.001678.07t(min) =6.75

&R"GRDSLAB.xls" ProgramVersion 1.4&C&P of &N&R&D &Tt(Subgrade)"GRDSLAB.xls"written by: Alex Tomanovich, P.E.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 - 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.