Elastic Contact Stress Formulae

Consider two bodies in contact identified with the suffixes 1 and 2.

Young's Modulus, E1

Poisson's ratio n1

Young's Modulus, E2

Poisson's ratio, n2


 R1 and R2 are the principal radii of curvature of the two bodies (convex positive).

Effective curvature

Contact Modulus

Hertzian Contact Equations


Line contact

(Width 2a; Load P'/unit length)

Circular contact

Diameter 2a; Load P

Semi-contact width or contact radius

Maximum contact pressure (Hertz stress)

Approach of centres

Mean contact pressure

Maximum shear stress

Maximum tensile stress


An initial estimate of the value of tmax for many materials is H/6 where H is the material hardness

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