Guides & Support

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


💬 We'd love your feedback on this template! It takes 1 min!

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.