Pin Contact Stress Lookup Tool

Geometry

Pin diameter (in)

Engagement length L (in)

Total radial load F (kip)

Applied moment M (kip·in) — eccentric load

Factor of Safety (FS)

Materials

Pin material

Lug material

Display

Show yield / bearing allowable

Show fit class shading

Clearance Range

Min (mils)

Max (mils)

Lookup Table

How to read the chart. The blue solid line is the peak contact stress. When a moment is applied, the purple curve shows peak with bending amplification. When FS > 1, a black curve shows the design stress (limit × FS) — if this stays below the yield/bearing-allowable lines, you have positive margin. In the flat region at small clearance, the pin is hugged by the hole over a full ~180° arc — conformal territory, where clearance has no effect on peak stress. Background shading shows fit class regions: green = precision, yellow = close running, orange = free running, pink = loose / structural. The lookup table below gives Margin of Safety values: MS = Allowable / (Limit × FS) − 1. MS ≥ 0 passes; MS < 0 fails (red).

Theory and limitations

Contact model: peak = max(Hertz, sinusoidal floor) — conservative envelope.

Hertz peak: p_max = √(Q · E* / (π R_eff)), R_eff = R²/ΔR
Sinusoidal floor: p_max = 4F / (π · D · L) — lower bound (zero-clearance elastic)
Effective modulus: 1/E* = (1−ν&sub1;²)/E&sub1; + (1−ν&sub2;²)/E&sub2;

Bending amplification (eccentric load): when load F is applied at offset e = M/F from the pin centerline, the contact pressure becomes non-uniform along the engagement length. Linearized peak: p_{peak,with bend} = p_peak · (1 + 6e/L). Valid for e/L ≤ 1/6; beyond that the pin gaps off one side of the bore and the linear formula understates peak (use FEA).

References: Persson (1964) Chalmers PhD; Ciavarella & Decuzzi (2001) Int. J. Solids Struct. 38; Johnson, Contact Mechanics (1985), Ch. 4. Bending amplification: standard combined stress P/A + Mc/I formulation, e.g. Bruhn Ch. D1.

Limitations: plane strain (good for L ≥ 2D), frictionless, elastic, static. True Persson value in transition zone may be 5–15% above this envelope. For fatigue, apply your own Kt & SN curves. Material yields are typical book values — confirm with certs.