// multi-utility computation suite · offline · instant · precise
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sci.Hertzian-contact-stress-sphere Calculator
Calculates Hertzian contact radius a = (3FR/4E*)^(1/3) and peak pressure p₀ = 3F/(2πa²) for a sphere-on-flat contact. Hertz contact stress scales as F^(2/3) — doubling the load increases contact area and peak pressure by 59% and 26% respectively.
Inputs
F N
Applied force or weight (N or kN). Divide into dead load (permanent) and live load (variable — people, wind, etc.).
R1 Mm
Distance from centre to edge of a circle. Radius = diameter / 2.
R2 Mm
Distance from centre to edge of a circle. Radius = diameter / 2.
E1 Gpa
Material stiffness (GPa). Stress divided by strain in the elastic range. Steel: 200 GPa. Aluminium: 70 GPa. Rubber: 0.01–0.1 GPa.
E2 Gpa
Material stiffness (GPa). Stress divided by strain in the elastic range. Steel: 200 GPa. Aluminium: 70 GPa. Rubber: 0.01–0.1 GPa.
Nu1
Reference formula or conversion factor shown for context.
Nu2
Reference formula or conversion factor shown for context.
Results
contact radius a (mm)
The computed radius -- half the diameter.
peak Hertzian pressure p0 (MPa)
Sample size or count used in the calculation.
central approach δ (mm)
Sample size or count used in the calculation.
a = (3FR*/(4E*))^(1/3)
Reference formula or conversion factor shown for context.
effective modulus E* (GPa)
Reference formula or conversion factor shown for context.
subsurface max shear stress
Internal force per unit area (Pa or MPa). Must stay below yield strength in service. Beyond yield: permanent deformation. Beyond tensile strength: fracture.