Bolt Tensile Strength Area⚠ unverified

Understanding the Parameters

• Nominal diameter $d$ — the major thread diameter naming the bolt. The stress area is smaller than the nominal circle area because threads remove material.

• The constant $0.9743/n$ — the Unified-thread offset from major diameter to the effective tensile diameter (mean of pitch and root diameters). Here $n = 6$ threads/inch is baked in; a different thread (finer $n$) gives a larger $A_t$. This is why the general formula keeps $n$ (or pitch $p$) as a variable.

Derivation (Approaching a Proof)

A threaded bolt fails at an effective diameter equal to the mean of the pitch diameter $d_p$ and the minor (root) diameter $d_r$:

$$A_t = \frac{\pi}{4}\left(\frac{d_p + d_r}{2}\right)^2.$$

For 60° Unified threads, $\dfrac{d_p + d_r}{2} = d - \dfrac{0.9743}{n}$ (the ISO-metric equivalent is $d - 0.9382\,p$). Substituting $n = 6$ reproduces the registry constant:

$$\frac{0.9743}{6} = 0.1624 \;\Longrightarrow\; A_t = \frac{\pi}{4}(d - 0.1624)^2,$$

which is exactly Bolt Tensile Stress Area. The full reasoning — why the average of pitch and root diameters correlates with tensile fracture, and the thread-geometry relations $d_p = d - 0.6495p$, $d_r = d - 1.2269p$ — is given on that page.

Dimensional check. $[A_t] = (\text{length})^2$, valid only if $d$ shares units with the $0.9743/6$ inch constant. Mixing SI and imperial is invalid (see note).

History and Development

See Bolt Tensile Stress Area. The tensile-stress-area relation was calibrated from tension tests and standardised in ASME B1.1 (Unified, $0.9743/n$) and ISO 898-1 (metric, $0.9382p$); tabulated values fill Machinery's Handbook and Shigley.

Related Concepts: Bolt Tensile Stress Area, Bolt Proof Load, Bolt Yield Torque, Bolt Thread Stiffness, Thread Stripping Strength

Notes: Duplicate card (Track B cleanup candidate). Hard-codes $n = 6$ imperial. Prefer tabulated $A_t$ or the pitch-dependent metric form $\frac{\pi}{4}(d - 0.9382p)^2$.