Concrete Slab on Grade Analysis Calculator (for Post or Wheel Loading)

For Slab Subjected to Interior Concentrated Post or Wheel Loading
Assuming Slab is Reinforced for Shrinkage and Temperature Only

Input Data

Slab Thickness, t =		in.
Concrete Strength, f 'c =	3000350040004500500055006000	psi
Conc. Unit Weight, wc =		pcf
Reinforcing Yield, fy =	40000500006000065000700007500080000	psi
Subgrade Modulus, k =		pci
Concentrated Load, P =		lbs.
Contact Area, Ac =		in.^2
Factor of Safety, FS =		pci
Dowel Bar Dia., db =	0.7511.25	in.
Dowel Bar Spacing, s =		in.
Const. Joint Width, z =		in.
Joint Spacing, L =		ft.
Temperature Range, DT =		deg.
Increase for 2nd Wheel, i =		%

 

Result :

Check Slab Flexural Stress:
Effective Load Radius, a =		in.	a = SQRT(Ac/p)
Modulus of Elasticity, Ec =		psi	Ec = 33*wc^1.5*SQRT(f 'c)
Modulus of Rupture, MR =		psi	MR = 9*SQRT(f 'c)
Cracking Moment, Mr =		ft-k/ft.	Mr = MR*(12*t^2/6)/12000 (per 1' = 12" width)
Poisson's Ratio, m =			m = 0.15 (assumed for concrete)
Radius of Stiffness, Lr =		in.	Lr = (Ec*t^3/(12*(1-m^2)*k))^0.25
Equivalent Radius, b =		in.
1 Load: fb1(actual) =		psi	fb1(actual) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Ref. 1)
2 Loads: fb2(actual) =		psi	fb2(actual) =
Fb(allow) =		psi	Fb(allow) = MR/FS
Check Slab Bearing Stress:
fp(actual) =		psi	fp(actual) = P/Ac
Fp(allow) =		psi	Fp(allow) = 4.2*MR
Check Slab Punching Shear Stress:
bo =		in.	bo = 4*SQRT(Ac) (assumed shear perimeter)
fv(actual) =		psi	fv(actual) = P/(t*(bo+4*t))
Fv(allow) =		psi	Fv(allow) = 0.27*MR
Shrinkage and Temperature Reinf.:(assuming subgrade drag method)
Friction Factor, F =			F = 1.5 (assumed friction factor between subgrade and slab)
Slab Weight, W =		psf	W = wc*(t/12)
Reinf. Allow. Stress, fs =		psf	fs = 0.75*fy
As =		in.^2/ft.	As = F*L*W/(2*fs)
Determine Estimated Crack Width:(assuming no use of stabilized or granular subbase)
Slab-base Frict. Adjust., C =			C = 1.0 (assumed value for no subbase)
Thermal Expansion, a =		in./in./deg	a = 5.5x10^(-6) (assumed thermal expansion coefficient)
Shrinkage Coefficient, e =		in./in.	e = 3.5x10^(-4) (assumed coefficient of shrinkage)
Est. Crack Width, DL =		in.	DL = C*L*12*(a*DT+e)

Check Bearing Stress on Dowels at Construction Joints with Load Transfer:

Le =		in.	Le = 1.0*Lr = applicable dist. each side of critical dowel
Effective Dowels, Ne =		bars	Ne = 1.0+2*S(1-d(n-1)*s/Le) (where: n = dowel #)
Joint Load, Pt =		lbs.	Pt = 0.50*P (assumed load transferred across joint)
Critical Dowel Load, Pc =		lbs.	Pc = Pt/Ne
Mod. of Dowel Suppt., kc =		psi	kc = 1.5x10^6 (assumed for concrete)
Mod. of Elasticity, Eb =		psi	Eb = 29x10^6 (assumed for steel dowels)
Inertia/Dowel Bar, Ib =		in.^4	Ib = p*db^4/64
Relative Bar Stiffness, b =			b = (kc*db/(4*Eb*Ib))^(1/4)
fd(actual) =		psi	fd(actual) = kc*(Pc*(2+b*z)/(4*b^3*Eb*Ib))
Fd(allow) =		psi	Fd(allow) = (4-db)/3*f 'c
Min. req'd. slab thk. for single interior load:
t(min) =		in.	Set Fb(allow) = 3*P*(1+m)/(2*p*t^2)*(LN(Lr/b)+0.6159) (Ref. 1)
Min. req'd. slab thk. for single corner load:
t(min) =		in.	Set Fb(allow) = 3*P/t^2*(1-(1.772*a/Lr)^(0.72)) (Ref. 1)
Min. req'd. slab thk. for single edge load (circular area):
t(min) =		in.	SSet 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)
Min. req'd. slab thk. for single edge load (semi-circular area):
t(min) =		in.	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)

References:
1. "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)
2. "Dowel Bar Opimization: Phases I and II - Final Report" - by Max L. Porter (Iowa State University, 2001)
3. "Design of Slabs-on-Ground" - ACI 360R-06 - by American Concrete Institute (2006)
4. "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) - by Robert G. Packard
     (Portland Cement Association, 1976)
5. "Streses and Stains in Rigid Pavements" (Lecture Notes 3) - by Charles Nunoo, Ph.D., P.E.
     (Florida International University, Miami FL - Fall 2002)

Note : there will be a few situations where certain combinations of the Concentrated
     Load, P, Subgrade Modulus, k, and Contact Area, Ac, result in a #N/A error message
     and thus no solution for the minimum slab thickness, t(min), for one or more of the
     equations listed above. For those cases, the user would then manually iterate the
     input slab thickness to determine the minimum value if desired.