Shear Stress Calculator

What is shear stress?

Shear stress is a force acting parallel to a surface divided by the area of that surface. It appears wherever forces try to slide one part past another, like scissors. Its simplest form is the average shear stress: τ = V / A.

Shear in bolts, pins and rivets

A bolt joining two plates is in single shear: the force crosses one section. In a three plate joint the middle plate pulls against the two outer ones, so the bolt is sheared at two sections. This is double shear, and the same bolt carries twice the force. For n fasteners and m shear planes τ = V / (n × m × A) with A = π × d² / 4.

Shear stress in a beam

Shear stress is not uniform over a beam section. It is zero at the top and bottom fibres and largest at the neutral axis. The general relation is τ = V × Q / (I × t). For common sections it reduces to a factor:

• Rectangle: τ_max = 1.5 × V / A
• Solid circle: τ_max = 4 × V / (3 × A)
• Thin walled tube: about 2 × V / A

Example

Two 12 mm bolts in single shear carry 30 kN. One section has an area of π × 12² / 4 = 113.1 mm², so the total shear area is 226.2 mm². The stress is 30 000 / 226.2 = 132.6 MPa. In double shear it would halve to 66.3 MPa.

Limits

The fastener calculation assumes the force is shared equally and looks only at shearing of the fastener. Bearing and tear out of the plate are separate checks. For a bolt sheared through its thread use the threaded section, not the shank diameter. The beam factors apply in the elastic range.