Shear stress
-Bending stress
-Bearing, lug
-Bearing, legs
-Safety factors
| Pin shear (0.577 Sy / tau) | - |
| Pin bending (Sy / sigma) | - |
| Bearing (lug Sy / worst bearing stress) | - |
| Governing check | - |
Method and formulas
Pin of diameter d loaded by F through a central lug (thickness t1) and two clevis legs (thickness t2 each).
| Quantity | Formula |
|---|---|
| Shear stress | τ = F / (n π d²/4), n = 2 (double) or 1 (single) |
| Bearing, central lug | σb1 = F / (d t1) |
| Bearing, each leg | σb2 = F / (2 d t2) |
| Pin bending (point load, simple supports) | M = F L / 4, σ = 32 M / (π d³) |
| Allowable shear | 0.577 Sy (von Mises shear yield) |
Worked example: 20 mm pin, 20 kN
F = 20 kN, d = 20 mm, t1 = 20 mm, t2 = 12 mm, L = 30 mm, pin Sy = 350 MPa, lug Sy = 250 MPa, double shear. τ = 2 x 20000 / (π x 400) = 31.83 MPa. Lug bearing = 20000 / (20 x 20) = 50.0 MPa; leg bearing = 20000 / (2 x 20 x 12) = 41.67 MPa. M = 20000 x 30 / 4 = 150000 N mm, σ = 32 x 150000 / (π x 8000) = 191.0 MPa. Safety factors: shear 6.34, bending 1.83, bearing 5.00.
Questions
How do I calculate shear stress in a clevis pin?
In double shear (a pin through a central lug between two clevis legs) the load is carried by two cross sections: tau = F / (2 x pi d^2 / 4) = 2F / (pi d^2). In single shear one section carries the load: tau = 4F / (pi d^2).
What allowable shear stress should I use?
For ductile steel a common basis is the shear yield strength, about 0.577 x tensile yield (von Mises). Then apply a safety factor suitable to your application, code or customer. This page reports the factor against 0.577 Sy so you can compare it with your own target.
What is bearing stress on a pin joint?
Bearing stress is the load divided by the projected area of the pin in the hole: F / (d x t). The central lug of thickness t1 carries all the load; each clevis leg of thickness t2 carries half. The softer of pin and lug material governs.
Why check pin bending?
A pin loaded at the lug and supported at the clevis legs bends across the gap. With a point load at mid span and simple supports M = F L / 4 and sigma = 32 M / (pi d^3). Because the real load is spread across the lug thickness, this is conservative; with long gaps or thin pins bending often governs over shear.
Single or double shear: how do I choose?
Count the shear planes the load passes through. A pin through a tang and a two-leg clevis has two planes (double shear). A pin joining two plates, one on each side, has one plane (single shear). This page lets you choose.
What does this calculator not cover?
Fatigue, fretting, tear-out and net-section stress of the lug, hole clearance, pin retention, and dynamic loading. It is an engineering aid for sizing: verify critical joints against your applicable standard.
Engineering aid for guidance. Does not cover fatigue, fretting, lug tear-out or dynamic loads: verify critical joints against your applicable standard.