Bolt Load External⚠ unverified
Mechanical / Joints · Compute the portion of an external load carried by the bolt
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| C | C | — | 1.0 | Joint stiffness ratio (dimensionless) |
| Fe | Fe | N | 1.0 | External load applied to the joint |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Fb | N | Portion of the external load taken by the bolt, in newtons (N) |
The science & history
Understanding the Parameters
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Joint constant $C$ — from Joint Stiffness Ratio. It is the whole story of load sharing: the bolt gets $C F_e$, the members shed $(1-C)F_e$. Design keeps $C$ small (soft bolt, stiff members) so the bolt increment stays low.
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External load $F_e$ — the applied service load per bolt. In fatigue it fluctuates (e.g. $0 \to F_e$), and only its $C$-scaled part becomes cyclic bolt stress.
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Added bolt load $F_b$ — the increment above preload. Its alternating component drives bolt fatigue (see Bolt Fatigue Factor); its peak sets the maximum bolt stress.
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Why not all of $F_e$ — the members were pre-compressed by the preload; applying $F_e$ first unloads that compression, and only the stiffness-weighted share reaches the bolt. Ignoring this (assuming $F_b = F_e$) hugely overpredicts bolt stress.
Derivation (Approaching a Proof)
While the joint stays clamped, the bolt and members share the external load $F_e$ through a common displacement $\delta$ (they act as parallel springs). From the load-sharing derivation of Joint Stiffness Ratio,
$$\delta = \frac{F_e}{k_b + k_m}, \qquad F_b = k_b\,\delta = \frac{k_b}{k_b + k_m}\,F_e = C\,F_e.$$
Superposing this on the preload gives the total bolt tension $F_{\text{bolt}} = F_i + C F_e$ (until the external load grows enough to fully decompress the members, at which point the joint separates and the bolt suddenly carries all of $F_e$).
Dimensional check. $F_b = C\,F_e = (\text{–})\cdot\text{N} = \text{N}$ — a force, as required.
History and Development
The load-sharing rule $F_b = F_i + C F_e$ is the payoff of the elastic joint model (Shigley, VDI 2230). It overturned the intuitive but wrong assumption that a bolt carries the entire external load: recognising that preload lets the members absorb most of a fluctuating load is what made high-cycle bolted joints reliable in engines, pressure vessels, and structures. The companion joint diagram shows $C F_e$ graphically as the small rise in bolt force against the large drop in member force.
Related Concepts: Joint Stiffness Ratio, Member Load External, Bolt Preload, Bolt Fatigue Factor, Bolt Proof Load, Bolted Joint Stiffness Member
Notes: $F_b = C F_e$ is the added bolt load; total bolt tension $= F_i + C F_e$. Valid only before joint separation. The alternating part of $F_b$ drives fatigue. Members shed the complementary $(1-C)F_e$.