Bolt Thread Stiffness⚠ unverified
Mechanical / Fasteners · Compute the axial stiffness of the threaded portion of a bolt
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| At | At | m**2 | 1.0 | Tensile stress area of the threaded portion |
| E | E | Pa | 1.0 | Young's modulus of the bolt material |
| L | L | m | 1.0 | Length of the threaded portion |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | k | N/m | Axial stiffness, in newtons per metre (N/m). Returns 0.0 if ``L`` is not positive |
The science & history
Understanding the Parameters
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Tensile stress area $A_t$ — the effective area of the threaded section (mean of pitch and root diameters), used here because the threads reduce the load-carrying cross-section below the nominal shank area. This is why the threaded portion is more compliant than the shank for the same length.
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Young's modulus $E$ — the axial stiffness of the material; the thread stretches in tension, so $E$ applies.
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Threaded length $L$ — the length of threaded material inside the clamped grip (not the total thread length on the bolt). Only the portion between the loaded faces stretches under preload.
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Series combination — because the shank and threaded portion carry the same tension and their stretches add, the whole-bolt stiffness is $1/k_b = 1/k_{\text{shank}} + 1/k_{\text{thread}}$. The softer (threaded) segment dominates the compliance.
Derivation (Approaching a Proof)
Identical in form to any axial bar (see Bolt Shank Stiffness). For the threaded segment treated as a prismatic bar of effective area $A_t$, Hooke's law gives the elongation under force $F$:
$$\delta = \frac{F L}{A_t E} \;\Longrightarrow\; k = \frac{F}{\delta} = \frac{A_t E}{L}.$$
The only modelling choice is using $A_t$ (the tensile stress area) rather than the minor-diameter area or nominal area — a standard approximation that matches measured bolt compliance well. Combining with the shank segment in series (equal force, additive elongations) yields the full bolt stiffness used in the joint constant $C = k_b/(k_b + k_m)$ (see Joint Stiffness).
Dimensional check. $[k] = \dfrac{\text{m}^2 \cdot \text{Pa}}{\text{m}} = \text{N/m}$. ✓
History and Development
The series shank-plus-thread stiffness model is the standard bolt-compliance treatment in Shigley, VDI 2230, and NASA fastener design guides, developed as bolted-joint fatigue analysis matured in the 1960s–70s. Getting the bolt compliance right (including the threaded portion and even a fraction of the threads outside the grip) is essential to predicting the load the bolt actually sees under a fluctuating external load.
Related Concepts: Bolt Shank Stiffness, Bolt Tensile Stress Area, Joint Stiffness, Joint Stiffness Ratio, Bolt Fatigue Endurance
Notes: Uses the tensile stress area $A_t$ for the threaded section. Combine in series with Bolt Shank Stiffness for total bolt stiffness. $L$ is the threaded length within the grip.