Shear stress formula
Shear stress is the force acting parallel to a surface divided by the area resisting it. It governs how pins, bolts, rivets, welds, and keys fail, since these are loaded across their section rather than along it.
Variables
| τ | Shear stress | psi or Pa |
| V | Shear force (parallel to area) | lb or N |
| A | Area resisting shear | in² or m² |
Rearranged
A = V / τ
Worked example
A 10 mm diameter pin in single shear (area about 78.5 mm²) carries a 5,000 N load.
Divide force by area: 5,000 / 78.5 = 63.7 MPa.
Shear stress acts across the section, so the resisting area is the cross-section of the pin or bolt, not its side. A pin in double shear has two planes carrying the load, halving the stress. Allowable shear stress is typically a little over half the tensile yield.
Sizing fasteners in shear?
See the Bolt Grade Chart and Bolt Torque Chart.
Single vs double shear
In single shear a fastener is cut across one plane, so the full load acts on one cross-section. In double shear, common in clevis joints, the fastener crosses two planes and the load splits between them, halving the shear stress for the same force. Recognizing which case applies can double or halve the calculated stress.
Shear strength vs tensile strength
Most ductile metals are weaker in shear than in tension, with shear yield around 0.577 of tensile yield by the von Mises criterion. That is why fasteners loaded across their section need checking specifically for shear, rather than assuming their tensile rating applies.
FAQ
What is the formula for shear stress?
Shear stress equals the shear force divided by the area resisting it, tau = V / A.
What is the difference between single and double shear?
Single shear has one cutting plane; double shear has two, which splits the load and halves the shear stress for the same force.
How strong is a material in shear?
Shear yield is roughly 0.577 of tensile yield for ductile metals, so design allowables for shear are lower than for tension.