Shear Stress⚠ unverified
Physics / Materials · Average shear stress from force and area
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| force | V | N | 1000.0 | Shear force |
| area | A | m^2 | 0.01 | Cross-sectional area |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| tau | τ | Pa | Shear stress |
The science & history
Understanding the Parameters
- $V$ — shear force (registry may label the input
forcewith symbol $V$). -
$A$ — for a pin or bolt in single shear, the cross-section; for beams use $VQ/(It)$ for local $\tau$, not $V/A$.
-
$\tau$ — same units as normal stress (Pa).
Derivation (Approaching a Proof)
Definition of average traction: $\tau_{\mathrm{avg}} = V/A$ when $V$ is the total shear force on area $A$. Equilibrium of a free body cut by that plane requires the integrated shear traction equal $V$.
History
Shear stress is fundamental to beam theory (Jourawski) and fastener design.
Related Concepts: Von Mises Stress, Section Modulus, Factor of Safety
Notes: Registry calculator shear-stress (unverified). Average shear only.