"GRDSLAB" --- CONCRETE SLAB ON GRADE ANALYSISProgram Description: "GRDSLAB" is a spreadsheet program written in MS-Excel for the purpose of analysis of concrete slabs on grade. Specifically, a concrete slab on grade may be subjected to concentrated post or wheel loading. Then for the given parameters, the slab flexural, bearing, and shear stresses are checked, the estimated crack width is determined, the minimum required distribution reinforcing is determined, and the bearing stress on the dowels at construction joints is checked. Also, design charts from the Portland Cement Association (PCA) are included to provide an additional method for determining/checking required slab thickness for flexure. The ability to analyze 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. This program is a workbook consisting of eight (8) worksheets, described as follows: Worksheet Name Description Doc Slab on Grade PCA Fig. 3-Wheel Load PCA Fig. 7a-Post Load PCA Fig. 7b-Post Load PCA Fig. 7c-Post Load Wall Load Unif. Load This documentation sheet Concrete Slab on Grade Analysis for Concentrated Post or Wheel Loading PCA Figure 3 - Design Chart for Single Wheel Loads PCA Figure 7a - Design Chart for Post Loads (k = 50 pci) PCA Figure 7b - Design Chart for Post Loads (k = 100 pci) PCA Figure 7c - Design Chart for Post Loads (k = 200 pci) Concrete Slab on Grade Analysis for Wall Load Concrete Slab on Grade Analysis for Stationary Uniform Live Loads Program 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 Element Method to Strain Predition in PCC Pavement Structures" - by University of Minnesota, Department of Civil Engineering (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 Concrete Practice, 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 only for shrinkage and temperature. An interior load condition is assumed for flexural analysis. That is, the concentrated post or wheel load is assumed to be well away from a "free" slab edge or corner. The original theory and equations by H.M. Westergaard (1926) as modified by Reference (a) in item #1 above are used for the flexual stress analysis. Some of the more significant simplifying assumptions made in the Westergaard analysis 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. it may/may not change the effective contact area. and 7c are as follows: a. etc. e.15. equations used. = 0. Modulus of elasticity for concrete. 7b. 'i'.also known as "Winkler" foundation. Combination of flexural and direct tensile stresses will result in transverse and longitudinal cracks. In the four (4) worksheets pertaining to the PCA Figures 3. 7a. Toolbars. d.3. (Note: presence of a “comment box” is denoted by a “red triangle” in the upper right-hand corner of a cell. This program contains numerous “comment boxes” which contain a wide variety of information including explanations of input or output items. and 7c. 7a. Ec = 4. The increase in stress. regaining position after application of load. as when the slab thickness is input. Other basic assumptions used in the flexural analysis of the "Slab on Grade" worksheet are as follows: a. due to a 2nd wheel (or post) load expressed as a percentage of stress for a single wheel (or post) load generally varies between 15% to 30% as is to be input by the user. Other assumed values used in the development of the Figures 3. c.) .000. Merely move the mouse pointer to the desired cell to view the contents of that particular "comment box". data tables. Supporting subbase and/or subgrade act as elastic material. 7a. Slab is considered as unreinforced concrete beam. Note: the user may unprotect the worksheet (no password is required) and access the Drawing Toolbar (select: View. so that any contribution made to flexural strength by the inclusion of distribution reinforcement is neglected. The "Slab on Grade" worksheet allows the user to account for the effect of an additional post or wheel load. 6. the user must manually determine (read) the required slab thickness from the design chart and must manually input that thickness in the appropriate cell at the bottom of the page. All four (4) worksheets pertaining to the PCA Figures 3. and 7c from Reference (f) in item #1 above are based on interior load condition and other similar assumptions used in the "Slab on Grade" worksheet. Modulus of subgrade reaction ("k") is used to represent the subgrade. Slab viewed as a plate on a liquid foundation with full subgrade contact (subgrade modeled as a series of independent springs . 7. and Drawing) to manually draw in (superimpose) the lines on the chart which are used to determine the required slab thickness. An interation or two may be required. 7b. b. 5. Poisson's Ratio for concrete.) b. 7b. 4.000 psi. . 4) bo = 4*SQRT(Ac) (assumed shear perimeter) Slab Reinf fv(actual) = P/(t*(bo+4*t)) fr = Fv(allow) = 0. O. O.2*MR Fp(allow) >= fp(actual).K.708 fv(actual) = 20.75*fy Slab Reinf As = F*L*W/(2*fs) fr = 5 of 20 01/19/2015 18:10:42 . fy = Subgrade Modulus. k = Concentrated Load. t Contact Area.000 50.xls" Program Version 1.50 Slab Weight. O. (As) at joint Min.15 Radius of Stiffness.00 2. fs = As = (assuming working stress) (Ref. psi psi psf psi in.724*t bo = fb1(actual) = 3*P*(1+)/(2**t^2)*(LN(Lr/b)+0. db = Dowel Bar Spacing. Lubricate this end ft. = 0. 1) = fb2(actual) = fb1(actual)*(1+i/100) Fv(allow) = Fb(allow) = MR/FS Fb(allow) >= fb(actual).00 Reinf. L = Temperature Range.6*a^2+t^2)-0.25 Check Sla b = SQRT(1. of 1/8"-1/4" x t/4 formed joint ### t/3 or 2" t/2 fb1(actual) = fb1(actual) = 3/4" Plain Dowels @ 12" = Typical Construction Joint for Load Transfer = (assuming unreinforced slab with interior load condition) = a = SQRT(Ac/) Ec = 33*wc^1.^2/ft. of all Dowels deg.00 114. Direction of pour Stop slab reinf."GRDSLAB.00 0. z = Joint Spacing.58 2 Loads: fb2(actual) = 307.20 Post in.024 Modulus of Elasticity. a = 6.T = Increase for 2nd Wheel.000 5000 150 60000 100 12500.40 Cracking Moment. FS = Dowel Bar Dia.83 Shrinkage and Temperature Reinf.985 Equivalent Radius.. for a < 1. i = 8. Ec = 4286826 Modulus of Rupture. 4) fp(actual) = P/Ac W= Fp(allow) = 4. P = Contact Area. F = 1.91 Fv(allow) = 171.Reinforced for Shrinkage and Temperature Only Job Name: Subject: Job Number: Originator: Checker: ### ### ### ### ### ### ### Input Data: Slab Thickness. Allow. Ac in. fs = 45000 As = 0. Shrinkage (assuming working stress) (Ref.5 (assumed friction factor between subgrade and slab) As = W = wc*(t/12) fs = 0. t = Concrete Strength. Stress. Ac = Factor of Safety.033 Wheel P P psi pcf Top/Slab psi pci lbs.6159) fv(actual) (Ref.15 (assumed for concrete) Lr = (Ec*t^3/(12*(1-^2)*k))^0. Mr = 6.65 2672. in. f 'c = Conc.5*SQRT(f 'c) Check Sla MR = 9*SQRT(f 'c) fp(actual) = Mr = MR*(12*t^2/6)/12000 (per 1' = 12" width) Fp(allow) = = 0. 3) F = 1. s = Const.2500 20.K. psi psi psi psi psi in. fs = = (assuming subgrade drag method) (Ref.72 Fb(allow) = 318. ### ### ### ### ### Concrete Slab on Grade in. in.27*MR Fv(allow) >= fv(actual).K. wc = Reinforcing Yield.: Friction Factor.86 Check Slab Punching Shear Stress: bo = 42.4 CONCRETE SLAB ON GRADE ANALYSIS For Slab Subjected to Interior Concentrated Post or Wheel Loading Assuming ACI-360 "Type B" Design . b = 5. psi psi ft-k/ft. in. Unit Weight. W = 100.00 15 Check Slab Bearing Stress: fp(actual) = Fp(allow) = 109. Lr = 36.79 Poisson's Ratio.648 1 Load: fb1(actual) = 267.000 0. % in.675*t .^2 (Subgrade) in. MR = 636.750 12. Results: Check Slab Flexural Stress: Effective Load Radius. Joint Width. 4 (continued) 6 of 20 01/19/2015 18:10:42 .xls" Program Version 1."GRDSLAB. by University of Minnesota. = 0. 1999) Iteration # 4. 2) Pt Le Le s di d4 d3 d2 d1 0*Pc (1-(4-1)*s/Le)*Pc (1-(3-1)*s/Le)*Pc (1-(2-1)*s/Le)*Pc d2 d3 d4 di 0*Pc (1-(4-1)*s/Le)*Pc (1-(3-1)*s/Le)*Pc (1-(2-1)*s/Le)*Pc 1. Ib = 0.K. Mod. Packard ## (Portland Cement Association.0+2*(1-d(n-1)*s/Le) (where: n = dowel #) Pt = Table 0."GRDSLAB. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195. each side of critical dowel Le = Ne = 1.0*Pc = A= Ecm = L= As = Determine C= = = L = Assumed Load Transfer Distribution for Dowels at Construction Joint Le = 36. Adjust. = 3. O.11 bars Joint Load.1284 in.09 psi Fd(allow) = 5416.0 (assumed value for no subbase) As = Thermal Expansion.50*Pfor(assumed Determining loadthe transferred Total Number across of Dowel joint) Bars Effective in Tra Pc = Pt/Ne Dowel # kc = 1..00026 in.0*Lr = applicable dist. Pc = kc = Eb = Ib = References: = 1.by Robert G. of Dowel Suppt. Effective Dowels.4 As = Determine Estimated Crack Width: (assuming no use of stabilized or granular subbase) Slab Reinf Slab-base Frict.. = 0. Ne = 3. L = L = C*L*12*(*T+) 0.ACI 360R-92 . March 24. Eb = 29000000 psi Inertia/Dowel Bar.0155 in.by American Concrete Institute (from ACI Manual of Concrete Practice. Department fd(actual) of Civil = Engineering (submitted to MN/DOT./deg = 5. 2001) 3.00 C = 1.Final Report" .67 psi Le = 1.00 lbs.0000055 in. Porter (Iowa State University. of Elasticity. 2002) Fd(allow) = 2.Improved Techniques for Appling the Finite Element Method to Strain Predition in PCC Pavement Structures" . "Dowel Bar Opimization: Phases I and II .5x10^6 (assumed for concrete) ### Eb = 29x10^6 (assumed for steel dowels) ### Ib = *db^4/64 = (kc*db/(4*Eb*Ib))^(1/4) Ne = fd(actual) = kc*(Pc*(2+*z)/(4*^3*Eb*Ib)) Pt = Fd(allow) = (4-db)/3*f 'c Fd(allow) >= fd(actual). "Load Testing of Instumented Pavement Sections .xls" Program Version 1.^4 Relative Bar Stiffness.by Max L.5x10^(-4) (assumed coefficient of shrinkage) As = Est.889 fd(actual) = 5299. Pc = 2011.88 lbs. Pt = 6250. "Design of Slabs on Grade" .5x10^(-6) (assumed thermal expansion coefficient) As = Shrinkage Coefficient.01D) . kc = 1500000 psi Mod. Critical Dowel Load. C = 1. Crack Width./in.985 in. 1976) ## ## Comments: ## ## ## ## ## ## # # 7 of 20 01/19/2015 18:10:42 ./in. Check Bearing Stress on Dowels at Construction Joints with Load Transfer: (Ref. = 0. 4 # 8 of 20 01/19/2015 18:10:42 .xls" Program Version 1."GRDSLAB. 2. f 'c = 3000 Instructions for Use of Figure 3: ### psi Subgrade Modulus.00 Tire Contact Area. page 6 MR = 9*SQRT(f 'c) (Modulus of Rupture) WS = MR/FS Ss = WS/(Pa/1000) t = determined from Figure 3 above 01/19/2015 18:10:42 . Pw = 12500.00 3. in. FS = 2. t Results: Wheel Load.64 ### Wheel Spacing."GRDSLAB. WS = 246.64 Concrete Flexual Strength.00 5. Ac = 113.^2 in. Read required slab thickness. Axle Load = 9. k = 200.900 lbs.48 Slab Stress/1000 lb.86 Slab Tickness.^2) ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### Figure 3 Design Chart for Axles with Single Wheels ### Input Data: Ac Index: Concrete Strength.xls" Program Version 1. Tire Inflation Pressure. Enter chart with slab stress = 9.Figure 3. page 5 Job Name: Subject: Job Number: Originator: Checker: ### ### ### ### ### ### ### Effective Load Contact Area Based on Slab Thickn Load Contact Area.4 CONCRETE SLAB ON GRADE THICKNESS ANALYSIS For Slab Subjected to Single Wheel Loading from Vehicles with Pneumatic Tires Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" . Ip = 110.95 Concrete Working Stress.00 psi 4. S = 37. Move to right to subgrade modulus = 200 Factor of Safety.86 Ac Axle Load. MR = 492.00 lbs. Ac(eff) = 113.64 Effective Contact Area.^2 psi psi psi in. contact area = 113. Move to right to eff.00 pci 1. Move up/down to wheel spacing = 37 in. Pa = 25000. 9 of 20 Pw = Pa/2 (1/2 of axle load for 2 wheels/axle) Ac = Pw/Ip Ac(eff) = determined from Figure 5. t = 7. Ac (in. "GRDSLAB.4 10 of 20 01/19/2015 18:10:43 .xls" Program Version 1. Figure 7a.32 10. MR = Concrete Working Stress. contact area = 76.^2 psi psi psi in.xls" Program Version 1. y = 98. Post Spacing. Move to right to post spacing.800 in. page 6 MR = 9*SQRT(f 'c) (Modulus of Rupture) WS = MR/FS Ss = WS/(P/1000) t = determined from Figure 7a above 01/19/2015 18:10:43 . x = 66 in. Move up/down to post spacing. t in. Ac = 64.^2 Factor of Safety. t = 76. P = 13000. Enter chart with slab stress = 16.32 Ac pci Post Load. Load Contact Area.4 CONCRETE SLAB ON GRADE THICKNESS ANALYSIS For Slab Subjected to Concentrated Post Loading (for k = 50 pci) Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" . Ac(eff) = Concrete Flexual Strength. page 9 Job Name: Subject: Job Number: Originator: Checker: ### ### ### ### ### ### ### Effective Load Contact Area Based on Slab Thickn Load Contact Area. f 'c = 5000 Instructions for Use of Figure 7a: ### psi Subgrade Modulus. Move to right to slab thickness.^2) ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### Figure 7a Design Chart for Post Loads.00 4. Post Load = Slab Tickness.13 16.00 1.00 3. Move to right to eff. FS = 3.00 5.34 ### Post Spacing. subgrade k = 50 pci ### ### Input Data: Ac Index: Concrete Strength. 11 of 20 Ac(eff) = determined from Figure 5."GRDSLAB.40 212. WS = Slab Stress/1000 lb. k = 50.00 Results: Effective Contact Area. y = 98 in.00 lbs.34 636. x = 66. Ac (in. 2. 4 12 of 20 01/19/2015 18:10:43 ."GRDSLAB.xls" Program Version 1. Move up/down to post spacing. P = 13000.00 Results: Effective Contact Area. y = 98 in. Ac (in. Load Contact Area. Enter chart with slab stress = 16. MR = Concrete Working Stress.03 636. Ac = 64. FS = 3. t in. x = 66.00 lbs.4 CONCRETE SLAB ON GRADE THICKNESS ANALYSIS For Slab Subjected to Concentrated Post Loading (for k = 100 pci) Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" .xls" Program Version 1. subgrade k = 100 pci ### ### Input Data: Ac Index: Concrete Strength.03 ### Post Spacing. Post Spacing. Ac(eff) = Concrete Flexual Strength. Move to right to slab thickness.32 Ac Post Load.32 9. page 10 Job Name: Subject: Job Number: Originator: Checker: ### ### ### ### ### ### ### Effective Load Contact Area Based on Slab Thickn Load Contact Area.00 4.00 5. contact area = 70. WS = Slab Stress/1000 lb. Move to right to post spacing.40 212. y = 98.^2 psi psi psi in."GRDSLAB. k = 100. f 'c = 5000 Instructions for Use of Figure 7b: ### psi Subgrade Modulus.Figure 7b. 2.800 in. Post Load = Slab Tickness. x = 66 in.^2) ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### Figure 7b Design Chart for Post Loads. Move to right to eff. t = 70.00 pci 1. page 6 MR = 9*SQRT(f 'c) (Modulus of Rupture) WS = MR/FS Ss = WS/(P/1000) t = determined from Figure 7b above 01/19/2015 18:10:44 .00 3.13 16. 13 of 20 Ac(eff) = determined from Figure 5.^2 Factor of Safety. "GRDSLAB.xls" Program Version 1.4 14 of 20 01/19/2015 18:10:44 . 00 5. page 6 MR = 9*SQRT(f 'c) (Modulus of Rupture) WS = MR/FS Ss = WS/(P/1000) t = determined from Figure 7c above 01/19/2015 18:10:44 . 2.64 Ac Post Load. 15 of 20 Ac(eff) = determined from Figure 5.00 3. P = 13000. Post Spacing.Figure 7c. Ac(eff) = Concrete Flexual Strength. k = 200. Ac (in. x = 66.95 164. Load Contact Area. Move up/down to post spacing.00 Results: Effective Contact Area.02 492.32 12. WS = Slab Stress/1000 lb."GRDSLAB. y = 98.^2 Factor of Safety.4 CONCRETE SLAB ON GRADE THICKNESS ANALYSIS For Slab Subjected to Concentrated Post Loading (for k = 200 pci) Per PCA "Slab Thickness Design for Industrial Concrete Floors on Grade" .^2) ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### Figure 7c Design Chart for Post Loads. Move to right to post spacing.00 lbs. Post Load = Slab Tickness.02 ### Post Spacing. contact area = 68.200 in. FS = 3. Move to right to slab thickness.^2 psi psi psi in. t = 68. t in.xls" Program Version 1.00 pci 1.64 9.00 4. x = 66 in. Enter chart with slab stress = 12. f 'c = 3000 Instructions for Use of Figure 7c: ### psi Subgrade Modulus. Move to right to eff. Ac = 64. page 11 Job Name: Subject: Job Number: Originator: Checker: ### ### ### ### ### ### ### Effective Load Contact Area Based on Slab Thickn Load Contact Area. MR = Concrete Working Stress. subgrade k = 200 pci ### ### Input Data: Ac Index: Concrete Strength. y = 98 in. xls" Program Version 1.4 16 of 20 01/19/2015 18:10:45 ."GRDSLAB. Pc = 1040. # Wall Load Near Free Edge of Slab: # Pe = Fb*S*/Bx Allowable Wall Load.0201 0.K.25) # Pc(allow) >= P.25) # Bx = coef. I = Stiffness Factor.21 101.000 4000 100 800.30 lb. S = Modulus of Elasticity.19 5.^4 = (k*b/(4*Ec*I))^(0. f 'c = Subgrade Modulus.K.3224 psi 17 of 20 01/19/2015 18:10:45 .68 # lb. O. FS = Section Modulus. Pe = 806. t = Concrete Strength. = Coefficient.00 3604997 12.4 CONCRETE SLAB ON GRADE ANALYSIS For Slab Subjected to Continuous Line Loading from Wall Job Name: Job Number: Subject: Originator: Slab Thickness.00 Wall P in. P = Checker: Wall Input Data: 8. k = Wall Load.25) # Reference: Pe(allow) >= P. Bx = ## MR = 9*SQRT(f 'c) ## Fb = 1. Ec = Width. # = 12. I = b*t^3/12 # in.00 0./ft.8*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0. Chapter 15 (1987) # # Comments: # # # # 569.^3/ft. Bending Stress. O. for beam on elastic foundation # # Wall Load Near Center of Slab or Keyed/Doweled Joints: # Pc = 4*Fb*S* Allowable Wall Load. Pc = ### (Subgrade) Concrete Slab Loaded Near Center or at Joint Pe = ### Wall P Top/Slab Iteration # ## t ## ## ## (Subgrade) Results: Concrete Slab Loaded Near Free Edge Design Parameters: Modulus of Rupture.6*SQRT(f 'c) (as recommended in reference below) ## psi FS = MR/Fb ## S = b*t^2/6 # in./ft. Fb = Factor of Safety. P Dowel (at Joint) psi ### ### ### ### ### ### ### Top/Slab pci = Bx = t lb. = 9.9256*SQRT(f 'c)*t^2*(k/(19000*SQRT(f 'c)*t^3))^(0. Ec = 57000*SQRT(f 'c) # psi b = 12" (assumed) # in. # "Concrete Floor Slabs on Grade Subjected to Heavy Loads" # Army Technical Manual TM 5-809-12.00 512.xls" Program Version 1."GRDSLAB. b = Moment of Inertia./ft. Air Force Manual AFM 88-3. MR = Allow.625 128. xls" Program Version 1."GRDSLAB.4 # 18 of 20 01/19/2015 18:10:45 . Lr = Critical Aisle Width.4 CONCRETE SLAB ON GRADE ANALYSIS For Slab Subjected to Stationary Uniformly Distributed Live Loads Job Name: INDUSTRIAL COMPLEX CHILCA Job Number: ### ### ### ### wLL(allow) = Input Data: *Aisle Width Slab Thickness. Wcr = 492.xls" Program Version 1. FS = Uniform Live Load. = Radius of Stiffness. Bending Stress. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.95 246. Allowable uniform load determined below is based on critical aisle width and as a result. 1976) Comments: 19 of 20 # ## ## ## ## ## ## ## ## ## # # # # # # # # # # # # # # # # # # # # # # # 01/19/2015 18:10:45 . "Concrete Floor Slabs on Grade Subjected to Heavy Loads" Army Technical Manual TM 5-809-12. Ec = Poisson's Ratio.25 Wcr = (2.01D) by Robert G. O. Results: Design Parameters: Modulus of Rupture. Stationary Uniformly Distributed Live Loads: wLL(allow) = 2786. Reference: 1.36 3.39 psf MR = 9*SQRT(f 'c) Fb = MR/FS Ec = 57000*SQRT(f 'c) = 0.15 19.00 in."GRDSLAB.876*Fb*SQRT(k*t/Ec) wLL(allow) >= wLL. Fb = Modulus of Elasticity. ft. ### ### Subject: LOSA DE CONCRETO Originator: JMC Checker: JBE wLL wLL psi Top/Slab pci t psf (Subgrade) Concrete Slab on Grade with Uniform Loads *Note: in an unjointed aisleway between uniformly distributed load areas. there are no restrictions on load layout configuration or uniformity of loading.15 (assumed for concrete) Lr = (Ec*t^3/(12*(1-^2)*k))^0. Chapter 15 (1987) 2. Air Force Manual AFM 88-3. MR = Allow. f 'c = Subgrade Modulus. Iteration negative bending moment in slab may be up to twice as great as positive moment in slab beneath loaded area.K.500 3000 800 2. wLL = 7. k = Factor of Safety.000 2700.48 3122019 0. t = Concrete Strength.209*Lr)/12 wLL(allow) = 257. Packard (Portland Cement Association.56 psi psi in. 4 # 20 of 20 01/19/2015 18:10:45 ."GRDSLAB.xls" Program Version 1.