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Concrete Slab-on-grade Designer to AS3600's banner

Concrete Slab-on-grade Designer to AS3600

This calculator allows the user to design a rectangular concrete slab on soil, supporting walls and columns or vehicle load.
Detailed explanation of the behaviour of a slab-on-grade and required checks can be found in CalcTree's Design Guide: Concrete Footing to AS3600.
All calculations are performed in accordance with AS3600-2018.

Calculation

Assumptions

  1. The values
    
    assume to be the plan dimensions of a concrete column on the slab, or the end plate dimensions for a steel column on the slab
  2. There is no soil surcharge on the slab as it is poured over the soil

Inputs

Material Properties

Concrete:


f'c
:{"mathjs":"Unit","value":40,"unit":"MPa","fixPrefix":false}​



γc
:{"mathjs":"Unit","value":25,"unit":"kN / m^3","fixPrefix":false}​



Ec
:32800 MPa​



f'ct.f
:3.79 MPa​



f'ct
:2.28 MPa​

Reinforcement:


fsy
:{"mathjs":"Unit","value":500,"unit":"MPa","fixPrefix":false}​



Es
:200 GPa​

Soil:


μ
:0.40​



qa
:{"mathjs":"Unit","value":150,"unit":"kPa","fixPrefix":false}​



Slab-on-grade Geometry



L
:{"mathjs":"Unit","value":7,"unit":"m","fixPrefix":false}​



B
:{"mathjs":"Unit","value":5,"unit":"m","fixPrefix":false}​



T
:{"mathjs":"Unit","value":0.5,"unit":"m","fixPrefix":false}​



Slab self-weight
:438 kNkN​


Section x-x:


(x) Cover
:{"mathjs":"Unit","value":50,"unit":"mm","fixPrefix":false}​



(x) Reinforcement size
:{"mathjs":"Unit","value":16,"unit":"mm","fixPrefix":false}​



(x) Number of bars
:50​



(x) Reinforcement spacing
:140 mm​

Section y-y:


(y) Cover
:{"mathjs":"Unit","value":60,"unit":"mm","fixPrefix":false}​



(y) Reinforcement size
:{"mathjs":"Unit","value":16,"unit":"mm","fixPrefix":false}​



(y) Number of bars
:50​



(y) Reinforcement spacing
:99 mm​



Loads

1) Uniform Surcharge


Q
:{"mathjs":"Unit","value":5,"unit":"kPa","fixPrefix":false}​


2) Post or column loads
You may input up to four coincident design actions due to concentrated loads. Note, negative N* is compression.

Can’t display the image because of an internal error. Our team is looking at the issue.


2) Vehicle Load
If the vehicle can fit along the length of the slab, then the calculator positions the centreline of the axles to the centre of the slab.
If the vehicle is longer than the slab, then the calculator positions the largest axle load in the middle of the slab as it produces the most critical bending moment.
Vehicle load configuration



Axle spacing
:{"mathjs":"Unit","value":2.5,"unit":"m","fixPrefix":false}​



Wheel spacing
:{"mathjs":"Unit","value":2,"unit":"m","fixPrefix":false}​



Check
:Vehicle sits on slab​




Front axle load
:{"mathjs":"Unit","value":90,"unit":"kN","fixPrefix":false}​



Back axle load
:{"mathjs":"Unit","value":40,"unit":"kN","fixPrefix":false}​



Safety Factors



Factor of Safety
:1.5​



ϕ (bending)
:0.85​



ϕ (shear)
:0.7​

Note, ϕ shall be selected as per AS3600 Table 2.2.2.


Output

Resultant Forces



ΣPz
:-723 kN​


Resultant axial load

Resultant axial load is the sum of all column loads, the surcharge and the concrete self-weight:

∑Pz=∑(Ncol∗+Wcol)+Wslab+QsurchargeBL\sum P_z= \sum (N^*_{\text{col}}+ W_{\text{col}})+W_{\text{slab}}+Q_{\text{surcharge}}BL


ΣMx
:-233.0375​



ΣMy
:405.0625​


Resultant moments

Resultant moment about the x-axis:

∑Mx=Σ(Ncol∗×ey)\sum M_{x} = \Sigma (N^*_{\text{col}}\times e_y)
Resultant moment about the y-axis:

∑My=Σ(P × ex)\sum M_{y} = \Sigma (P\space\times\space e_x)


ex
:0.561 m​



ey
:-0.322 m​


Resultant eccentricities

Resultant eccentricity from the x-axis:

ey=ΣMyΣP e_y = \dfrac{\Sigma M_y}{\Sigma P}
Resultant eccentricity from the y-axis:

ex=ΣMxΣPe_x = \dfrac{\Sigma M_x}{\Sigma P} \\


Geotechnical Checks

Bearing Check


Allowable bearing capacity≥max(P1,P2,P3,P4)\text{Allowable bearing capacity} \geq \text{max}(P_1,P_2,P_3,P_4)

Uniaxial​
22.58​
38.56​
18.72​
2.74​
7​
5​
100​

Cases of biaxial bearing pressure

Different cases of biaxial bearing pressure



qmax
:38.56 kPa​



Bearing check
:PASS​

Bearing corner pressures


Overturning


ΣMo =Total overturning momentΣMr =Total resisting moment\small{ΣM_o}\ = \text{Total\ overturning\ moment}\\\small{ΣM_r\ =\text{Total\ resisting\ moment}}
Section x-x


(x) ΣMr
:1336 kNm​



(x) ΣMo
:-200 kNm​

Section y-y


(y) ΣMr
:1862 kNm​



(y) ΣMo
:350 kNm​



Overturning check
:PASS​


Uplift Check



ΣPz (1)
:548 kN​



ΣPu
:0 kN​



Uplift check
:PASS​


Sliding Check


Ff = Frictional resistance=μ×vertical reaction=μ×(Wconcrete+Qsurcharge×BL−∑N∗)F∗ = Pushing force = applied shear in the direction being considered\small{F_f\ =\ \text{Frictional\ resistance}}=\mu \times \text{vertical reaction}\\\hspace{3.8cm}=\mu \times (W_{concrete}+Q_{surcharge}\times BL-\sum N^*) \\\small{F^*\ =\ \text{Pushing\ force}\ =\ \text{applied\ shear\ in\ the\ direction\ being\ considered}}
Section x-x


(x) Ff
:289 kN​



(x) F*
:50 kN​

Section y-y


(y) Ff
:289 kN​



(y) F*
:70 kN​



Sliding check
:PASS​


Structural Checks (ULS)

Beam Shear


Vu = kvbwdvfc′V_u\ =\ k_vb_wd_v\sqrt{f'_c}
Section x-x


(x) V*
:79 kN​



(x) kv
:0.15 ​



(x) dv
:450 mm​



(x) ϕVu/m
:299 kN​



(x) V*/ϕVu
:0.2655263358358268​

Section y-y


(y) V*
:118 kN​



(y) kv
:0.15 ​



(y) dv
:450 mm​



(y) ϕVu/m
:299 kN​



(y) V*/ϕVu
:0.3958380944335831​



Flexure


Mu = Astfsy(do−γkudo2)\large{M_u\ =\ A_{st}f_{sy}(d_o-\frac{{\gamma}k_{u}d_o}{2})}


α2
:0.79​



γ
:0.77​

Section x-x


(x) M*
:236 kNm​



(x) ku
:0.067​



(x) do
:442 mm​



(x) ϕMu
:263 kNm​



(x) M* / ϕMu
:0.8984564718446567​

Section y-y


(y) M*
:120 kNm​



(y) ku
:0.096​



(y) do
:432 mm​



(y) ϕMu
:356 kNm​



(y) M* / ϕMu
:0.3388712036262608​


Explanation

A slab-on-grade (also called slab-on-ground) is a type of foundation mainly used for lightly loaded structures such as residential and small commercial buildings. Concrete is poured directly onto the prepared ground, without any basement or crawl space beneath it. This concrete slab serves as both the foundation and the floor of the building.
Detailed explanation of the behaviour of a slab-on-grade and required checks can be found in CalcTree's Design Guide: Concrete Footing to AS3600.

Note

Typically, slab designs can be done by hand as the required calculations are relatively simple. However, it should be noted that the most accurate method of structural analysis of design forces is finite element modelling (FEA). FEA allows the engineer to capture information that would otherwise be near-impossible to incorporate into hand calculations, such as soil spring stiffness, two-way load distribution and other boundary conditions.
Slab-on-grade for residential housing (Source: RAMJACK)


Design Considerations

Choosing the appropriate foundation type for the structure above is essential; each have their advantages and disadvantages, and every site has its own constraints. Slab-on-grade is generally used when the following conditions are met:
  1. Warm climate - heat-loss occurs quickly in buildings built on slab-on-grade, as there is no space provision for heating ducts under the floor (the slab). To prevent heat-loss, often insulation is put in between the slab and ground surface.
  2. Utilities can be routed above ground - any underground gas and drainage pipes must surface may need to routed into the building externally, without penetrations in the slab.
  3. Ground profile is generally flat - uneven ground profile requires excavation, at which point it may be easier to utilise other types of foundations

Freshly poured slab-on-grade (Source: DesignwithFrank)

Let's also look at the advantages and disadvantages of using a slab-on-grade.
Advantages:
  1. fast and cheap construction
  2. minimal preparation for concrete pouring, little to no excavation required.
  3. reduced likelihood of moisture issues e.g. water infiltration, swelling, etc. which are common in embedded foundations
Disadvantages:
  1. underground utilities cannot be checked or maintained and any damage can only be detected after it has occurred e.g. leakage
  2. exposed to structural damage during flooding events, since building is constructed on low elevation

Related Resources

  1. Design Guide: Concrete Footing to AS3600-2018
  2. Foundation Bearing Failure Modes and Capacities
  3. Rectangular Footing Design to AS3600
  4. Concrete Beam Design Calculator to AS3600-2018
  1. Concrete Slab-on-grade Calculator to ACI 360R-10

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