Question 1

What is the modulus of subgrade reaction k and how is it estimated?

Accepted Answer

k (MN/m³ or pci) represents the stiffness of the subgrade per unit area. It ranges from 15–30 MN/m³ for soft clay, 30–60 for stiff clay, 60–150 for sand, and 150–300 for dense gravel. Obtained from plate load tests or estimated from CBR or SPT values.

Question 2

How does the PCA/Westergaard method determine slab thickness?

Accepted Answer

The slab is modeled as an elastic plate on a Winkler foundation. Maximum stress is calculated under the critical load position, then compared to the allow concrete flexural stress (fr/SF, where SF ≈ 2.0). Thickness is iterated until stress is acceptable.

Question 3

What is the radius of relative stiffness l in slab-on-grade design?

Accepted Answer

l = (Eh³/12(1–μ²)k)^0.25, where E is concrete elastic modulus, h is slab thickness, μ = 0.15 (Poisson's ratio), and k is subgrade modulus. l determines how the slab distributes load over the subgrade.

Question 4

What concrete strength is typically used for slabs on grade?

Accepted Answer

f'c = 25–35 MPa (3,500–5,000 psi) is typical. Higher strength increases modulus of rupture fr = 0.62√f'c, allowing thinner slabs or heavier loads. Fiber reinforcement is often used to control shrinkage cracking.

Question 5

How are contraction joints designed for slabs on grade?

Accepted Answer

Contraction (control) joints are spaced at 24–36 × slab thickness (max 6 m) to control random shrinkage cracking. Joints are saw-cut to 1/4 of slab depth within 12–24 hours after placing concrete.

Step	Formula	Substitution	Result
MOR	f_r = 0.62√f'c	0.62×√28	3.281 MPa
Allowable	σ_allow = f_r / SF	3.281/2	1.64 MPa

Step	Formula	Substitution	Result
Rel. Stiffness	ℓ = (Ec·h³/12(1-ν²)k)^0.25	890.3	890.3 mm
Applied Stress	σ_applied (Westergaard)	0.769	0.769 MPa
DCR	σ_applied / σ_allow	0.769/1.64	0.469	✓

Step	Formula	Substitution	Result
MOR	f_r = 0.62√f'c	0.62×√28	3.281 MPa
Allowable	σ_allow = f_r / SF	3.281/2	1.64 MPa

Step	Formula	Substitution	Result
Rel. Stiffness	ℓ = (Ec·h³/12(1-ν²)k)^0.25	890.3	890.3 mm
Applied Stress	σ_applied (Westergaard)	0.769	0.769 MPa
DCR	σ_applied / σ_allow	0.769/1.64	0.469	✓

Slab on Grade

Slab on Grade

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Material

Design

Slab on Grade Design

Given:

Concrete Properties

Stress Analysis

Slab on Grade

Slab on Grade

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Material

Design

Slab on Grade Design

Given:

Concrete Properties

Stress Analysis