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Concrete Slab-on-grade Calculator to ACI 360R-10's banner

Concrete Slab-on-grade Calculator to ACI 360R-10

Verified by the CalcTree engineering team on June 27, 2024

This calculator analyses the soil conditions below a concrete slab to determine the required thickness of the slab. The calculator checks the flexural, bearing and shear stresses in the slab and determines the minimum required slab thickness, the minimum required distribution reinforcement and the estimated crack width. The calculator also checks the bearing stress on the dowels at construction joints.
All calculations are performed in accordance with ACI 360R-10, which is the American Concrete Institute's "Guide to Design of Slabs-on-Ground".
A concrete slab-on-ground subjected to concentrated post and wheel loading


Technical notes and assumptions

  1. Slab is idealized as a homogenous, isotropic material with uniform thickness and no discontinuities. Though in reality, a slab-on-ground is generally exposed to more rougher conditions during construction than others.
  2. The subgrade is represented by the modulus of subgrade, k and is modelled as a series of independent springs.
  3. All loads are assumed to be applied normal to the slab surface. Any braking or traction forces, which act at an angle to the surface, are not accounted for.
  4. Any contribution to flexural strength made by the reinforcement is neglected. The slab is only reinforced for crack width limit control due to shrinkage and temperature.
  5. Dowels are assumed to be plain bars.

Calculation

Inputs

Loads



P
:7000lbs​



FoS
:5​



i (%)
:5​




Slab and Ground Properties



t
:8.00inch​



f'c
:3500.00psi​



wc, pcf
:150.00​



fy
:60000.00psi​



Ac
:144.00sqin​



ΔT
:50.00degF​



k, pci
:500.00​


Dowel and Joint Properties



db
:0.75inch​



s
:12inches​



z
:0.25inches​



L
:20ft​


Outputs

Slab Properties



W
:100lb/sqft​



Ec
:3.6e+6psi​



μ
:0.15​



MR
:532.45psi​



Mr
:5.68ft*kip/ft​



Lr
:23.65in​



F
:1.5​



C
:1​



α
:5.5e-6​



ε
:4.0e-4​



a
:6.77in​



b
:6.32in​



bo
:48.00in​


Equations


W=wc×t12Ec=33×wc1.5×fc′MR=9×fc′Mr=MR×(12×t2612000)μ=0.15 (assumed for concrete)Lr=Ec×t312(1−μ2)×k0.25F=1.5 (assumed friction factor between subgradeand slab)C=1.0 assumed value for no subbasea=Acπb=1.6×a2+t2−0.675t for a<1.724tbo=4×Ac W = w_c \times \frac{t}{12}\\ E_c = 33\times {w_c}^{1.5}\times \sqrt{f'_c}\\{} M_R = 9\times \sqrt{f'_c} \\ M_r = M_R\times (\frac{12\times \frac{t^2}{6}}{12000}) \\ \mu = 0.15 \space \text{(assumed for concrete)}\\ L_r ={ \frac{E_c\times{t^3}}{12(1-\mu^2)\times{k}}}^{0.25}\\F = 1.5\space\text{(assumed friction factor between subgrade}\\\text{and slab)} \\C = 1.0 \space\text{assumed value for no subbase} \\a = \sqrt{\frac{A_c}{\pi}} \\ b = \sqrt{1.6\times a^2+t^2} - 0.675t \space \text{for} \space a < 1.724t \\ b_o = 4\times\sqrt{A_c}


Dowel Properties



Ne
:2​



Pt
:3500.00lbs​



Pc
:1762.86lbs​



kc
:1.5e+6psi​



Eb
:2.9e+7psi​



Ib
:0.0155in4​



β
:0.889​


Equations


Ne=1+2Σ(1−s×d×(n−1)Le)Pt=0.5×PPc=PtNekc=1.5×106 (assumed for concrete)Eb=29×106Ib=π×db464β=kcdb4EbIb0.25N_e = 1 + 2\Sigma(1-\frac{s\times d\times(n-1)}{L_e}) \\ P_t =0.5\times P \\ P_c = \frac{P_t}{N_e} \\ k_c =1.5 \times 10^6 \text{ (assumed for concrete)} \\ E_b = 29 \times 10^6 \\ I_b = \frac{\pi \times {d_b}^4}{64} \\ \beta = \frac{k_cd_b}{4E_bI_b} ^{0.25}


Design Checks

Minimum Required Slab Thickness

For single interior load:


t(min) IL
:8.50in​

For single corner load:


t(min) CL
:9.25in​

For single edge load (circular area):


t(min) EL circular
:12.25in​

For single edge load (semi-circular area):


t(min) EL (semi-circular)
:13.75in​



Required Shrinkage and Temperature Reinforcement



fs
:45000.00psi​



As (in2/ft)
:0.033​


fs=0.75×fyAs=F×L×W2×fs f_s = 0.75 \times f_y \\ A_s = F\times L \times \frac{W}{2\times f_s}
Shrinkage and temperature reinforcement


Estimated Crack Width



ΔL
:0.16in​


ΔL=C×L×12×(αΔT+ε) \Delta L=C\times L\times 12\times(\alpha\Delta T+\varepsilon)
Crack widths


Slab Flexural Stress



For 1 Load: fb1 (actual)
:116.26psi​



For 2 Loads: fb2 (actual)
:122.07psi​



Fb(allow)
:106.49psi​


fb1 (actual)=3P(1+μ)2πt2×ln⁡(Lrb+0.6159)fb2 (actual)=fb1 (actual)×(1+i100)Fb (allow)=MRFoSf_{b1 \space(actual)} = \frac{3P(1+\mu)}{2\pi t^2}\times \ln(\frac{L_r}{b} + 0.6159) \\ f_{b2\space(actual)} = f_{b1\space(actual)}\times (1+\frac{i}{100}) \\ F_{b\space(allow)}= \frac{M_R}{\text{FoS}}


CHECK #1
: Fb(allow) < fb(actual)​

Flexural cracks


Slab Bearing Stress



fp(actual) =
:48.61psi​



Fp(allow) =
:447.26psi​


fp, (actual)=PAcFp (allow)=4.2MRFoSf_{p,\space(actual)} = \frac{P}{A_c} \\ F_{p\space(allow)} = \frac{4.2M_R}{\text{FoS}}


CHECK #2
: Fp(allow) >= fp(actual), O.K.​

Bearing failure



Slab Punching Shear Stress



fv(actual) =
:10.94psi​



Fv(allow) =
:29psi​


fv (actual)=Pt×(bo+4t)Fv (allow)=0.27MRFoSf_{v\space(actual)} = \frac{P}{t\times(b_o + 4t)} \\ F_{v\space(allow)}=\frac{0.27M_R}{\text{FoS}}


CHECK #3
: Fv(allow) >= fv(actual), O.K.​

Punching failure



Bearing Stress on Dowels



fd(actual) =
:4643.18psi​



Fd(allow) =
:3791.67psi​


fd (actual)=kc×Pc×(2+βz)4β3EbIbFd (allow)=4−db3×fc′f_{d\space(actual)} = k_c \times \dfrac{P_c \times (2 + \beta z)}{4\beta^3 E_b I_b} \\ F_{d\space(allow)} = \frac{4-d_b}{3} \times f'_c


CHECK #4
: Fd(allow) < fd(actual)​

Assumed load transfer distribution for dowels at construction joint ("Dowel Bar Optimization: Phases I and II - Final Report" - by Max L. Porter)




Explanation

A slab-on-ground, also referred to as slab-on-grade, is a slab supported by the ground whose main purpose is to support the applied loads by bearing on the ground.
The American and British Standards method for design is to compare "allowable stresses" against "actual stresses", where actual stresses are based upon characteristic loads with an overall Factor of Safety (FoS). The designer choses the FoS to minimise the likelihood of serviceability failure such as cracking and decrease to surface durability. In contrast, the Eurocode is based upon limit state design with partial factors of safety on materials and loads.
The design checks to ACI 360R-22 are based upon ensuring:

actual stress≤allowable stressFoS\text{actual stress}\le\dfrac{\text{allowable stress}}{\text{FoS}}

There are multiple failure modes of a slab-on-ground:
  1. Flexural failure of the slab, when the slab develops tension stresses in its soffit that exceed its flexural capacity
  2. Bearing failure of the slab, when the slab bearing stresses exceed its bearing strength
  3. Punching failure of the slab, when the slab shear stresses exceed its shear strength
  4. Bearing stress of dowels that causes the slab to fail, where the effectiveness of the dowel bars depend on the relative stiffness between the slab compared to its subgrade

Recommended values for some input parameters are provided:

Factor of Safety, FoS

Concentrated load, P

Modulus of subgrade, k

Dowel and joint parameters

This calculator is courtesy of Alex Tomanovich P.E.