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.
❗ This calculation has been written in accordance with the American Concrete Institute's "Guide to Design of Slabs-on-Ground", also known as ACI 360R-10.
A concrete slab-on-ground subjected to concentrated post and wheel loading
Technical notes and assumptions
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.
The subgrade is represented by the modulus of subgrade, k and is modelled as a series of independent springs.
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.
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.
Dowels are assumed to be plain bars.
⬇️Inputs
Loads
Concentrated Load, P
:6000lbs
Factor of Safety, FoS
:5
Increase for 2nd Load, i (%)
:0
Slab and Ground Properties
Slab Thickness, t
:8.00inch
Concrete Strength, f'c
:4000.00psi
Concrete Unit Weight, wc (pcf)
:150.00
Steel yield limit, fy
:60000.00psi
Contact Area, Ac
:144.00sqin
Temperature range of the slab, ΔT
:50.00degF
Subgrade Modulus, k (pci)
:500.00
Dowel and Joint Properties
Dowel diameter, db
:0.75inch
Dowel spacing, s
:12inches
Joint width, z
:0.25inches
Joint spacing, L
:20ft
⬇️Outputs
Slab Properties
Slab weight, W (psf)
:100
Modulus of Elasticity, Ec
:3.8e+6psi
Poisson's ratio, μ
:0.15
Modulus of Rupture, MR
:569.21psi
Cracking moment, Mr (ft-k/ft)
:6.07
Radius of relative stiffness, Lr
:24.05in
Friction factor, F
:1.5
Slab base friction adjustment, C
:1
Thermal expansion, α
:5.5e-6
Shrinkage coefficient, ε
:3.5e-4
Effective load radius, a
:6.77in
Equivalent radius, b
:6.32in
Shear perimeter, bo
:48.00in
Equations
Dowel Properties
Number of effective dowels, Ne
:2
Joint load, Pt
:3000.00lbs
Critical dowel load, Pc
:1495.05lbs
Modulus of dowel support, kc
:1.5e+6psi
Modulus of Elasticity for steel dowels, Eb
:2.9e+7psi
Inertia/Dowel Bar, Ib (in^4)
:0.0155
Relative Bar Stiffness, β
:0.889
Equations
⬇️Design Checks
Minimum Required Slab Thickness
For single interior load:
t(min) IL
:7.50in
For single corner load:
t(min) CL
:8.00in
For single edge load (circular area):
t(min) EL circular
:10.75in
For single edge load (semi-circular area):
t(min) EL (semi-circular)
:12.25in
Required Shrinkage and Temperature Reinforcement
Estimated Crack Width
Slab Flexural Stress
Slab Bearing Stress
Slab Punching Shear Stress
Bearing Stress on Dowels
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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:
There are multiple failure modes of a slab-on-ground:
Flexural failure of the slab, when the slab develops tension stresses in its soffit that exceed its flexural capacity
Bearing failure of the slab, when the slab bearing stresses exceed its bearing strength
Punching failure of the slab, when the slab shear stresses exceed its shear strength
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: