Concrete Slab on Grade — A Structural Engineer's Design Handbook

1. What is a concrete slab on grade?

• A concrete slab placed directly on the ground (subgrade / subbase).
• Not a structural element of the building — it is non-structural per ACI 360.
• Its purpose is to provide a flat surface carrying operational loads such as forklifts, racks and partition walls.
• Design focuses on serviceability: crack control, curling and flatness.

2. The Winkler subgrade model

• The subgrade is modelled as a system of independent springs (dense liquid foundation).
• Each point reacts linearly with settlement: q = k × δ.
• The model is simple yet accurate enough for practical design.

Modulus of subgrade reaction, k

k is the pressure required to cause one unit of deformation, in pci (lb/in³) or MN/m³. It is measured by a field plate load test (Ø750 mm plate) or estimated from a CBR correlation. Remember that k is not a constant — it depends on soil type, moisture content and plate size.

3. Radius of relative stiffness — the key parameter

Lr = ⁴√[ E·t³ / ( 12·k·(1 − μ²) ) ]

Lr represents the zone of influence of a load on the slab. A large Lr means the slab is stiff relative to the subgrade, the load spreads further and stresses are lower. A small Lr means the slab is flexible relative to the subgrade, the load concentrates and stresses are higher.

4. Westergaard theory — three loading positions

Interior loading

• The load sits far from any edge or corner.
• Maximum tensile stress is at the bottom of the slab, directly under the load.
• This is the most common case in industrial buildings — forklifts and rack posts.

fb = [ 3P(1+μ) / (2π·t²) ] × [ ln(2Lr/b) + 0.5 − γ ]

P = concentrated load      γ ≈ 0.5772 (Euler's constant)
b = equivalent radius of the resisting section
  when a < 1.724t :  b = √(1.6a² + t²) − 0.675t
  when a ≥ 1.724t :  b = a

Edge and corner loading

• Edge loading: on the slab edge but away from corners. Tensile stress is higher than interior loading because support is lost on one side — check it separately.
• Corner loading: the maximum tensile stress is at the top of the slab — the opposite of the other two cases.

Corner:    fc = [ 3P / t² ] × [ 1 − (a√2 / Lr)^0.6 ]

5. Slab thickness design — the PCA / ACI 360 method

This is an allowable stress approach: compute the applied stress and compare it with the allowable stress, which is the modulus of rupture divided by a factor of safety.

MR = 9 × √f'c      (f'c in psi)
MR = 0.75 × √f'c   (f'c in MPa)

Allowable stress   WS = MR / FoS

Case 1 — concentrated or wheel load

• Sources: rack posts, forklift wheels, equipment legs.
• Checks: Westergaard flexure, punching shear, bearing, and dowel bearing if near a joint.
• Inputs: P, contact area Ac, f'c, t, k and FoS — where Ac = P / p, with p the tyre or post pressure.

Case 2 — continuous wall load

The load comes from masonry or partition walls built on the slab. It is analysed as a beam on elastic foundation per TM 5-809-12, checked at two positions: near the centre (or a joint) and near a free edge.

Case 3 — uniform load

The load comes from stacked goods or stored materials. The critical condition is the aisle width between loaded areas: the maximum stress occurs when the aisle is narrow, where the slab bends in the opposite direction.

Punching shear and finding the minimum thickness

fv = P / (b₀ × t)

b₀ = perimeter of the critical section, taken at d/2 from the load edge
Allowable stress  Fv = 4√f'c (psi)  or  0.33√f'c (MPa)

• Assume a trial thickness t.
• Compute Lr, fb and fv for each load case.
• Check fb ≤ MR/FoS and fv ≤ the allowable Fv.
• If a check fails, increase t and repeat; t_min is the smallest thickness at which every check passes.

6. Joint design

Joint spacing

• Rule of thumb: L = (24 to 36) × slab thickness. A 150 mm slab gives L = 3.6–5.4 m; a 200 mm slab gives L = 4.8–7.2 m.
• Prefer square panels; if rectangular, keep the length-to-width ratio below 1.5.
• Align joints with the column grid where possible.

Dowel bars

• Purpose: transfer vertical load across the joint and prevent faulting between panels.
• Use a smooth round bar; one half must be debonded so the joint can open and close.
• The diameter is typically ≈ t/8 (about 20–25 mm for a 150–200 mm slab).
• Length 400–500 mm with 200–250 mm projecting each side; spacing 300 mm.

Dowel bearing stress:   fb,dowel = P_dowel / (d × t_eff)
Allowable (Friberg/PCA): Fb,allow = (4/3 − d/3t) × f'c

7. Reinforcement and crack control

Reinforcement becomes necessary when joint spacing is large, when crack width must be controlled, or when the temperature differential is significant.

Shrinkage and temperature reinforcement

As = ( f × L × W × t × γ ) / ( 2 × fs )

• Crack-control reinforcement is placed in the upper third of the slab depth.
• Do not run deformed bars through a contraction joint — it stops the joint working and moves the crack elsewhere.
• Crack width is estimated as w = ε × L_joint / 2, where ε combines drying shrinkage and thermal contraction.

8. Subgrade preparation and curling

• Subgrade: must be compacted and uniform; remove weak and organic soils.
• Subbase: 100–150 mm of sand or crushed stone to spread load, drain water and provide a working platform.
• Vapour barrier: a PE film ≥ 0.15 mm beneath the slab to stop moisture rising from the ground.
• Slip membrane: reduces slab-to-subgrade friction and therefore shrinkage stress.

Curling and how to reduce it

Slab edges curl upward because of moisture and temperature gradients between top and bottom: the top dries and shrinks faster while the underside stays damp. The slab then loses contact with the subgrade at edges and corners, load concentrates there and cracking follows.

• Reduce the water–cement ratio to reduce shrinkage.
• Use the largest practical aggregate size to reduce water demand.
• Cure properly for at least seven days to reduce the moisture gradient.
• Keep joint spacing sensible so panels stay small.
• Provide top reinforcement to control curling cracks.

9. Quick reference tables

Concrete properties

Factor of safety and working stress

Typical slab thickness

10. Design checklist from A to Z

Survey and input data

• Geotechnical report available: soil type, k-value, groundwater level?
• Operational loads defined: forklifts (P, Ac), rack posts, walls?
• Flatness requirements (FF/FL) specified?
• Environmental conditions considered: temperature differential, moisture?

Design phase

• f'c selected and MR, Ec calculated?
• k-value determined by test or lookup table?
• Radius of relative stiffness Lr calculated?
• Flexure checked for all three load cases?
• Punching shear and bearing checked?
• Minimum thickness t_min determined?
• Joints designed: location, spacing, type?
• Dowel bars designed where needed?
• Shrinkage/temperature reinforcement calculated and crack width checked?

Construction phase

• Subgrade compacted and uniform?
• Subbase placed to the correct thickness?
• Vapour barrier installed?
• Reinforcement or mesh placed correctly in the upper third?
• Dowels placed correctly and debonded on one side?
• Concrete placed at the correct slump and grade?
• Contraction joints cut at the right time (4–12 hours after placement)?
• Cured for at least seven days?

11. Related standards

Supporting design tools

Closing — ten things to remember

Part of the series "Structural design for industrial facilities" — Roberto Structural. The content is technical guidance; the engineer remains responsible for checking and adapting it to the conditions of each project and the requirements of the governing code.