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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

The calculator recommends a minimum FoS of 1.5 for wheel loadings and a larger FoS of say 2.0 up to 5.0 for post loading. ACI recommends the FoS values as per the table below.
Snippet from ACI 360R-10 page 22.



Concentrated load, P

Wheel loadings are converted into a static concentrated load, P for the purpose of analysing a slab-on-ground. To replicate the load of a truck, ACI 360R-10 provides representative axle loads and wheel spacings for various lift truck capacities, see below.
Snippet from ACI 360R-10 page 19.


The calculator also asks for the stress increase due to a second load, 'i', as a percentage of the stress for a single load (wheel or post). Recommendations for values of "i" is provided below. The source spreadsheet also has a calculation in cell AQ78 to determine an appropriate 'i' value.
Recommendations for Input of Increase for 2nd Wheel (or Post), 'i'



Modulus of subgrade, k

The modulus of subgrade, k is also known as the modulus of soil reaction of Winkler foundation. It is a spring constant that assumes a linear response between load and deformation from the subgrade, although in reality the relationship is non-linear. The load-deformation relationship depends on factors including the density, moisture content and prior loading of the soil and the width of the loaded area.
Nonetheless, tests performed on site called "plate load field tests" are used to estimate k for the purposes of slab-on-ground design.
Recommended modulus of subgrade values are provided below.
Subgrade Soil Types and Approximate Subgrade Modulus (k) Values


Dowel and joint parameters

Dowels are used to transfer shear force over construction joints in slabs. This calculator assumes use of plain bars. The following are recommended values for the dowel diameter, db and the joint spacing, L.
Snippet from "Dowel Bar Optimization: Phases I and II - Final Report" by Max L. Porter

Snippet from "Slab Thickness Design for Industrial Concrete Floors on Grade" (IS195.01D) by Robert G. Packard

This calculator is courtesy of Alex Tomanovich P.E.

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