Bolt Yield Torque⚠ unverified
Mechanical / Fasteners · Compute the tightening torque that yields the bolt
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| At | At | m**2 | 1.0 | Tensile stress area |
| Sy | Sy | Pa | 1.0 | Yield strength of the bolt material |
| d | d | m | 1.0 | Nominal bolt diameter |
| mu | μ | — | 1.0 | Coefficient of friction at the threads |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | T | N.m | Yield torque, in newton-metres (N.m) |
The science & history
Understanding the Parameters
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Tensile stress area $A_t$ and yield strength $S_y$ — their product $F_y = A_t S_y$ is the axial force at yield, the maximum preload the bolt can hold elastically. Everything else in the formula converts that force into a torque.
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Nominal diameter $d$ — the moment-arm scale for the friction/lead term.
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Thread friction $\mu$ — the variable friction contribution; lower friction means less torque needed to reach the same (yield) tension.
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The constant $0.15$ — a lumped stand-in for the collar friction plus thread-lead contribution (the parts not captured by the explicit thread-friction $\mu$). Effectively the formula uses a nut factor $K \approx (\mu + 0.15)/2$, with $0.15$ representing the fixed collar+lead share.
Derivation (Approaching a Proof)
Two steps: find the yield force, then convert to torque.
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Yield force. Yielding occurs when the tensile stress across the effective thread area reaches the yield strength: $$F_y = A_t S_y.$$
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Torque for that force. Using the simplified nut-factor torque relation (friction + lead, as in Bolt Torque Preload), with the explicit thread-friction term $\mu$ and a lumped collar-plus-lead constant $0.15$: $$T = F_y\,\frac{d}{2}(\mu + 0.15) = \frac{A_t S_y\, d}{2}(\mu + 0.15).$$
The $0.15$ collapses the collar-friction and thread-lead moments (which the full power-screw analysis carries as separate $\mu_c d_c/2$ and $\tan\lambda$ terms) into one representative constant for typical steel fasteners. It is an approximation: real collar friction and lead depend on geometry and lubrication, so the achieved yield torque scatters just like any torque method.
Dimensional check. $[T] = (\text{m}^2 \cdot \text{Pa}) \cdot \text{m} \cdot (\text{dimensionless}) = \text{N} \cdot \text{m} = \text{N}\cdot\text{m}$. ✓
History and Development
Torque-to-yield tightening emerged as engines and structures demanded higher, more consistent preload than the ±25 % scatter of ordinary torque control allows. Tightening into the yield region flattens the torque–tension curve, so preload becomes insensitive to friction — the basis of the angle-control (turn-of-nut past snug) method in Shigley, VDI 2230, and automotive practice. The trade-off is that a yielded bolt has consumed its ductility and is single-use.
Related Concepts: Bolt Torque Preload, Bolt Preload from Torque, Bolt Proof Load, Bolt Tensile Stress Area, Thread Stripping Strength
Notes: Uses realistic thread friction $\mu$ (≈0.12–0.2), not the 1.0 default. The $0.15$ lumps collar+lead effects. Torque-to-yield bolts are typically single-use. Yield force $F_y = A_t S_y$.