Calculate the average shear stress (τ) acting on a surface based on applied force and cross-sectional area.
Last updated: March 2026 | By ForgeCalc Engineering
Shear stress (τ) is the component of stress coplanar with a material cross-section. It arises from the force vector component parallel to the cross-section. Unlike normal stress (which acts perpendicular to the surface), shear stress acts along the surface.
In engineering, shear stress is critical for designing bolts, rivets, and beams. If the shear stress exceeds the material's shear strength, the material will fail by sliding or "shearing" apart.
Where:
• τ (tau) is the average shear stress (Pa or MPa)
• F is the applied shear force (N)
• A is the cross-sectional area parallel to the force (m² or mm²)
In single shear, one cross-section of a bolt resists the load. In double shear, two cross-sections resist the load, effectively doubling the area and halving the stress for the same force.
Within the elastic limit, shear stress is proportional to shear strain (γ) via the shear modulus (G): τ = G × γ.
Pure shear is a state of stress where only shear stresses act on the element, and normal stresses are zero. This is common in shafts under torsion.
For many ductile materials like steel, the shear yield strength is approximately 57.7% (1/√3) of the tensile yield strength, according to the Von Mises yield criterion.
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