Calculate average pin shear stress, allowable shear load, or minimum theoretical pin diameter for single or double shear using metric and imperial engineering units. These shear-only estimates do not establish the capacity of the whole joint.

Average shear for a solid circular pin with equal load sharing. Use a design allowable that already includes the required safety factor; bearing, bending, fatigue and joint failure need separate checks.

Pin Shear Formula

The following formula is used to calculate average pin shear stress in single shear.

SS = 4 × AF / (π × D²)
BS = AF / (t × D)
  • Where SS is the pin shear stress (N/mm², lbf/in² (psi))
  • BS is the bearing area stress (N/mm², lbf/in² (psi))
  • AF is the applied force (N, kN, lbf)
  • D is the diameter of the pin (mm, cm, in)
  • t is the thickness of the plate (mm, cm, in)

Pin Shear Definition

What is pin shear?

Pin shear stress is the average shear stress a pin will see (for a single shear plane) given an applied force and diameter. Pin shear is used to design safe bearing and other mechanical assemblies.

Use an allowable shear stress established for the material, loading and governing design standard, including the required safety factor. Do not substitute tensile ultimate strength directly. Double shear uses two equally loaded shear planes, so SS = 4 × AF / (2 × π × D²).

However, since pins can often hold a large amount of shear stress relative to other components, they are not always the limiting factor.

Example Problem

How to calculate average pin shear?

First, determine the applied force acting on the pin assembly. In this example, the applied force is measured to be 5000 N.

Next, determine the diameter of the pin. In this example, the pin has a diameter of 35 mm.

Finally, calculate the pin shear using the formula above:

SS = 4*AF / (Ï€*D^2)

SS = 4*5000 / (3.14159*35^2)

SS ≈ 5.197 N/mm²

For a separate average bearing-stress calculation on a plate carrying the full force, determine its thickness (in this case, 40 mm) and use BS = AF / (t × D). This calculator evaluates pin shear; bearing stress is a separate joint check:

BS = AF / (t*D)

BS = 5000 / (35*40)

BS = 3.571 N/mm^2