Bolt Proof Load⚠ unverified
Mechanical / Fasteners · Proof load of a bolt
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| At | At | m^2 | 8.4e-05 | Tensile stress area |
| Sp | Sp | Pa | 600000000.0 | Proof strength |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| Fp | Fp | N | Proof load |
The science & history
Understanding the Parameters
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Tensile stress area $A_t$ — the effective load-carrying area across the threads (from Bolt Tensile Stress Area), not the nominal shank area. Using $A_t$ is essential — the threads, not the shank, are where a loaded bolt fails.
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Proof strength $S_p$ — a specified stress a little below the yield strength (roughly $S_p \approx 0.85$–$0.90\,S_y$), chosen so a bolt loaded to $F_p$ is guaranteed to return to length with no permanent set. It is fixed by the property class: e.g. metric grade 8.8 has $S_p \approx 600$ MPa, grade 10.9 $\approx 830$ MPa, grade 12.9 $\approx 970$ MPa.
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Proof load $F_p$ — the certified elastic capacity. Preload targets are set as a fraction of it (e.g. $F_i = 0.75\,F_p$) to keep the bolt elastic with margin for the external service load.
Derivation (Approaching a Proof)
Proof load is definitional rather than derived, but it rests on the uniaxial stress–area relation. Tensile stress is force over area; requiring the stress across the effective thread section not to exceed the proof strength gives the limiting force:
$$\sigma = \frac{F}{A_t} \le S_p \;\Longrightarrow\; F \le A_t S_p \equiv F_p.$$
The subtlety is entirely in the two inputs. $A_t$ is the empirically calibrated effective area (mean of pitch and root diameters — see Bolt Tensile Stress Area) rather than a naive geometric area, and $S_p$ is a specified stress deliberately set below yield so the "no permanent set" guarantee holds with margin. Multiplying the two converts the material's certified elastic stress limit into a certified force limit for that specific bolt size.
Dimensional check. $[F_p] = \text{m}^2 \cdot \text{Pa} = \text{m}^2 \cdot (\text{N/m}^2) = \text{N}$. ✓
History and Development
Proof loading became a fastener-quality standard in the mid-20th century, codified in SAE J429, ASTM F568/F606, and ISO 898-1, which define property classes and their proof strengths. The proof-load concept — a certified, tested elastic limit — is what makes bolted joints reliable across millions of interchangeable parts, and it underlies the preload recommendations in Shigley, VDI 2230, and NASA fastener manuals.
Related Concepts: Bolt Tensile Stress Area, Bolt Preload from Torque, Bolt Yield Torque, Bolt Torque Preload, Bolt Shank Stiffness
Notes: Use the tensile stress area $A_t$ (not shank area). $S_p$ is grade-specific. Design preload is a fraction of $F_p$ (≈0.75 reusable, ≈0.90 permanent). Proof strength ≈ 0.85–0.90 × yield.