Pinned Joint Calculator
Screen a cylindrical transverse pin that connects a shaft and hub under transmitted torque.
Engineering screening tool—verify inputs and results independently. Use at your own risk.
How to use
- No mode selection is required; this calculator represents one cylindrical transverse pin through a shaft and hub.
- Enter shaft diameter dₛ, pin diameter dₚ, and hub thickness t in millimetres. The pin must be smaller than the shaft; 0.20–0.30dₛ is the customary screening range shown by the geometry advisory.
- Enter the positive transmitted torque magnitude T in N·m. The calculation converts it to N·mm internally.
- Select Calculate, or edit a field for an immediate update. Select Reset to restore dₛ = 10 mm, dₚ = 2 mm, T = 10 N·m, and t = 5 mm.
- Read pin shear stress as the canonical result. The supporting results show shear force, hub/pin bearing pressure, the drilled-shaft torsional stress estimate, and correction factor C₁.
- Displayed outputs follow the implemented two-decimal rounding. Correct any red input warning before interpreting the values.
- Compare pin shear, bearing pressure, and shaft stress against verified allowables with an appropriate safety factor; check fatigue and cyclic reversal separately.
- Do not use this model for multiple pins, tapered or grooved pins, clearance-impact loading, eccentric joints, plastic bearing, detailed hole stress concentration, pin bending, fretting life, or safety-critical final design.
Worked example
1. Use dₛ = 10 mm, dₚ = 2 mm, T = 10 N·m, and t = 5 mm. 2. The pin carries Fₛ = 1000.00 N and C₁ = 0.82. 3. Pin shear stress is 318.31 MPa, bearing pressure is 66.67 MPa, and the shaft torsional-stress estimate is 62.11 MPa. 4. For the illustrative 95MnPb28 note below, shear is below 0.9Rₘ = 459 MPa and pressure is below Rₘ/3 = 170 MPa, but this does not replace verified material data, fatigue, retention, and safety-factor checks.
Equations used
Pin shear force: Fₛ = T/dₛ
Pin shear stress: τₛ = Fₛ/[(3.1416/4)dₚ²]
Bearing pressure: p = T/[(dₛ + t)dₚt]
Shaft correction: C₁ = 1 − 0.9dₚ/dₛ
Shaft torsional stress: τₜ = 16T/(πdₛ³C₁)
Here T is torque converted from N·m to N·mm; dₛ is shaft diameter, dₚ is pin diameter, t is hub thickness, Fₛ is pin shear force, τₛ is average pin shear stress, p is nominal bearing pressure, C₁ is dimensionless, and τₜ is the drilled-shaft torsional-stress estimate. All inputs are positive magnitudes; torque direction and stress sign are not represented. The value 3.1416 is retained in the pin-area equation while π uses full floating-point precision in the torsion equation.
Theory and method
The torque-to-force relation distributes the applied torque through the transverse pin using the shaft diameter as the lever measure. Average pin shear is calculated over one circular pin section. The nominal bearing-pressure expression uses shaft diameter, hub thickness, and pin diameter. The torsion relation adjusts the solid-round-shaft expression with C₁ to screen the weakened cross-drilled section.
Assumptions and limits: one straight cylindrical pin, concentric shaft and hub, quasi-static torque, average shear and bearing stress, elastic response, and positive dimensions. The model omits pin bending, double-versus-single-shear detail, hole clearance, local edge pressure, notch concentration, fatigue, shock, wear, fretting, corrosion, temperature, manufacturing tolerance, and retention. A pin diameter series often used for screening is 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16… mm.
Material note: an unhardened 95MnPb28 / 1.0718 free-cutting-steel example with Rₘ = 510 MPa uses illustrative limits τallow = 0.9Rₘ and pallow = Rₘ/3. Do not transfer those limits to another pin, hub, load spectrum, or code without verification.
Reference: A. van Beek, Advanced Engineering Design: Lifetime Performance and Reliability, cylindrical-pin joint calculation collection. Use applicable shaft/hub design standards, verified material data, and manufacturer guidance for final design.
Continue in TriboSolver to refine stress concentration, contact pressure, fatigue, and load-spectrum effects.
Related calculator
Clamp Bushing Torque Capacity Calculator screens a frictional shaft–hub connection when torque is carried without a transverse pin.