Thread Shear Stress⚠ unverified
Mechanical / Power Screws · Compute the shear stress in the engaged threads
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Axial load on the screw |
| dc | dc | m | 1.0 | Core (root) diameter of the screw |
| h | h | m | 1.0 | Axial height of thread engagement |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | τ | Pa | Shear stress in the threads, in pascals (Pa). Returns 0.0 if the product ``dc * h`` is not positive |
The science & history
Understanding the Parameters
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Axial load $F$ — the load the threads must transfer from screw to nut by shear; stress scales directly with it.
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Core diameter $d_c$ — sets the circumference $\pi d_c$ of the shear cylinder. For an external thread (screw) the strip cylinder is near the root diameter; for the internal thread (nut) it is near the major diameter. The weaker of the two governs.
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Engagement height $h$ — the axial length of engaged thread (the nut height). Shear stress falls as $1/h$: more engagement spreads the load over more thread area, which is exactly why a minimum nut height (~0.5–1× the diameter) is specified so the screw yields in tension before the threads strip (see Nut Height Minimum).
Derivation (Approaching a Proof)
Thread stripping is a shear failure across the cylindrical surface where the threads engage. The shear stress is the load divided by the shear area — approximated as the cylinder of circumference $\pi d_c$ and length $h$:
$$\tau = \frac{F}{A_{\text{shear}}} = \frac{F}{\pi d_c h}.$$
The model assumes the load is uniformly carried over the full engaged cylinder. In reality the first engaged thread carries a disproportionate share (thread load is not uniform — the nut and screw strain mismatch concentrates load at the first thread), so a more detailed analysis and a thread-form factor (the fraction of the pitch that is actually thread material, typically ~0.5–0.6) refine the shear area. This simplified $\pi d_c h$ form is a first-order sizing estimate; compare it against the material's shear allowable ($\approx 0.5$–$0.577\,S_y$).
Dimensional check. $[\tau] = \dfrac{\text{N}}{\text{m}\cdot\text{m}} = \dfrac{\text{N}}{\text{m}^2} = \text{Pa}$. ✓
History and Development
Thread shear/stripping analysis is standard in Shigley and codified for fasteners in ASME/FED-STD-H28. The goal — engage enough thread that the screw fails in tension (ductile, visible) rather than stripping (sudden) — governs nut heights and tapped-hole depths, and is especially important in soft nut materials (bronze power-screw nuts, aluminium) where extra engagement is needed.
Related Concepts: Thread Stress Tensile, Thread Bending Stress, Thread Stripping Strength, Nut Height Minimum, Shear Stress
Notes: Simplified $\pi d_c h$ shear cylinder (uniform-load assumption; apply a thread-form factor and account for first-thread load concentration for design). Use the weaker of screw/nut material. Sets the minimum engagement/nut height.