Member Load External⚠ unverified
Mechanical / Joints · Compute the portion of an external load carried by the members
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 | Fm | N | Portion of the external load taken by the members, in newtons (N) |
The science & history
Understanding the Parameters
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Joint constant $C$ — from Joint Stiffness Ratio. The members take $(1-C)$; a small $C$ (soft bolt, stiff members) means the members shoulder most of the external load, protecting the bolt.
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External load $F_e$ — the applied tensile load per bolt. It first decompresses the members before it can separate the joint.
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Member share $F_m$ — the loss of clamping force. The residual clamp left on the joint is $F_i - F_m = F_i - (1-C)F_e$; it must stay positive (with margin) to keep the joint sealed and prevent slip.
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Separation load — the external load that fully unloads the members, $F_{e,\text{sep}} = F_i/(1-C)$. Beyond it the members lift off and the bolt abruptly carries the entire load — a design limit to avoid.
Derivation (Approaching a Proof)
Under external load $F_e$ the clamped members and the bolt share a common additional displacement $\delta$ (parallel springs). The change in member force is
$$F_m = k_m\,\delta = \frac{k_m}{k_b + k_m}\,F_e = (1 - C)\,F_e,$$
using $1 - C = 1 - \dfrac{k_b}{k_b+k_m} = \dfrac{k_m}{k_b+k_m}$. This $F_m$ is a reduction in the member's pre-compression, so the remaining clamp force is $F_i - F_m$. The bolt increment $C F_e$ and the member relief $(1-C)F_e$ add back to the full external load, $C F_e + (1-C)F_e = F_e$, as equilibrium demands.
Dimensional check. $F_m = (1-C)\,F_e = (\text{–})\cdot\text{N} = \text{N}$ — a force, as required.
History and Development
The complementary shares $C F_e$ (bolt) and $(1-C)F_e$ (members) are the two outputs of the elastic joint-diagram model (Shigley, VDI 2230). The member share is the one that governs joint separation and sealing: pressure-vessel and gasketed joints are preloaded specifically so that $(1-C)F_e$ never exceeds the preload over the working pressure range, keeping a positive residual clamp. This separation criterion, not bolt strength, often sizes the preload.
Related Concepts: Bolt Load External, Joint Stiffness Ratio, Bolt Preload, Gasket Factor, Bolt Proof Load, Bolted Joint Stiffness Member
Notes: $F_m = (1-C)F_e$ is the loss of clamp; residual clamp $= F_i - (1-C)F_e$ must stay positive. Separation at $F_e = F_i/(1-C)$ — beyond it the bolt carries all the load. Governs sealing/slip.