Westergaard Rigid Pavement Stress Calculator

Concrete pavement design & airfield engineering: Compute Westergaard analytical slab bending stresses ($sigma_{corner}, sigma_{edge}, sigma_{interior}$) and radius of relative stiffness ($ell$).

Concrete Slab & Subgrade Properties

Wheel Load P (lbs): Single wheel tire load (9,000 lbs = 18-kip axle)

Slab Thickness h (in): Concrete slab depth

Concrete Elastic Modulus E (psi): Concrete Young's modulus

Subgrade Reaction k (pci): Winkler modulus of subgrade reaction (lbs/in³)

Tire Contact Radius a (in): Circular footprint radius

Concrete Modulus of Rupture MR (psi): Flexural tensile strength

Westergaard Slab Stresses

Edge Tensile Stress (σ_edge)

Corner Tensile Stress (σ_corner)

Interior Stress (σ_interior)

Center of slab loading

Radius of Relative Stiffness (ℓ)

[ E·h³ / 12(1-ν²)k ]^0.25

Critical Loading Position

Edge Loading

Dominant fatigue crack source

Factor of Safety (vs Rupture)

MR / σ_max

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Frequently Asked Questions

Why is edge loading almost always more critical than interior loading?

At the interior, load is distributed radially in all 360° directions across a full slab basin. At a free edge, half of the structural support is missing, generating tensile bending stresses approximately 50% to 70% higher than at the interior.

How do tied concrete shoulders reduce edge stresses?

Tying a concrete shoulder with deformed steel tie bars allows 30% to 40% of the wheel load to transfer across the joint onto the shoulder, transforming severe free-edge loading into benign interior-like loading.

What is the PCA fatigue stress ratio limit?

The Portland Cement Association (PCA) design method dictates that if the stress ratio (σ / MR) is below 0.45, the pavement possesses an infinite fatigue life (unlimited allowable load applications).