Thread Stress Tensile⚠ unverified
Mechanical / Power Screws · Compute the tensile (axial) stress in the screw core
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 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | σ | Pa | Tensile stress in the core, in pascals (Pa). Returns 0.0 if the core diameter is not positive |
The science & history
Understanding the Parameters
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Axial load $F$ — the full axial load passes through the screw body; stress is directly proportional to it. (For a long screw in compression this must be paired with a buckling check — a slender screw can buckle before it yields; see Euler Buckling Load column.)
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Core diameter $d_c$ — the root (minor) diameter, the smallest section of the screw and therefore the highest-stressed. Using $d_c$ (not the mean or major diameter) is essential — sizing on the nominal diameter would non-conservatively under-predict the stress. The stress falls as $1/d_c^2$, so core diameter is the dominant strength lever.
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The area $\pi d_c^2/4$ — the full circular area of the core. This is a first approximation; the effective tensile area is sometimes taken slightly larger (between root and pitch diameter, as with the bolt tensile stress area — see Bolt Tensile Stress Area).
Derivation (Approaching a Proof)
This is the definition of direct axial stress — force divided by the area over which it acts:
$$\sigma = \frac{F}{A}.$$
The load-bearing section of a screw is its solid core, a circle of the root diameter $d_c$, with area
$$A = \frac{\pi d_c^2}{4}.$$
Substituting gives
$$\sigma = \frac{F}{\pi d_c^2/4} = \frac{4F}{\pi d_c^2}.$$
The only modelling choice is which diameter defines the area: the root diameter is used because it is the minimum section and yields the maximum (most conservative) stress. The result is compared against the material's allowable (yield strength divided by a factor of safety), and combined with the thread shear and bending stresses via a von Mises equivalent stress (Von Mises Stress) for a complete check.
Dimensional check. $[\sigma] = \dfrac{\text{N}}{\text{m}^2} = \text{Pa}$. ✓
History and Development
The root-area axial-stress check is elementary strength of materials applied to screws, standard in Shigley's power-screw design procedure. It is the screw analogue of the bolt proof-stress check (Bolt Proof Load), and for slender screws in compression it is always paired with Euler buckling — the two competing failure modes that bound a power screw's load capacity.
Related Concepts: Thread Shear Stress, Thread Bending Stress, Bolt Tensile Stress Area, Euler Buckling Load column, Von Mises Stress, Factor of Safety
Notes: Uses the root/core diameter (minimum section). Pair with a buckling check for screws in compression. Combine with thread shear/bending via von Mises for the full stress state.