Introduction

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

  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.

⬇️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:
  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.