Shear Stress Calculator

Shear stress: τ = F/A

Shear stress τ = F/A measures the tangential force F (parallel to the surface) divided by the area A on which it acts. The unit is N/m² (Pa) or, more commonly in engineering, MPa. It differs from normal stress, where the force acts perpendicular to the surface. The shear strength of structural steel is roughly τ_max ≈ 0.6·σ_yield ≈ 150 MPa. Shear governs the design of bolts, rivets, and welds (NBR 8800 — steel; NBR 6118 — concrete). A pair of scissors cuts by shear. In a flowing fluid, shear follows Newton's law of viscosity: τ = μ·(dv/dy), with μ the dynamic viscosity. Example: a 1,000 N tangential force on a 0.01 m² area gives τ = 100,000 Pa = 0.1 MPa — far below steel's limit but already meaningful for plastics.

Applications

Bolt, rivet and weld sizing, beams under transverse loads (shear diagram), geotechnics (slope and embankment stability), tribology (lubrication and friction films), safety pin or shear pin design (calibrated to break first), and fluid-flow pressure-drop calculations.

FAQ

What's the difference between τ and σ? τ is tangential (parallel to surface); σ is normal (perpendicular). Both have the same units (Pa), but they describe different failure modes.

Why is τ_max ≈ 0.6·σ_yield? It comes from the von Mises criterion: in pure shear, an isotropic material yields when τ reaches about 0.577·σ_yield. Engineering codes round it to 0.6 for safety.

Does shear stress matter in fluids? Yes — it's the basis of viscosity. Internal shear creates the pressure drop in pipe flow and is what your stirring spoon overcomes.