Rivet Crushing Stress⚠ unverified
Mechanical / Joints · Compute the bearing (crushing) stress in a riveted joint
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| F | F | N | 1.0 | Bearing load on the rivet |
| d | d | m | 1.0 | Rivet diameter |
| t | t | m | 1.0 | Plate thickness |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | σc | Pa | Bearing/crushing stress, in pascals (Pa). Returns 0.0 when the projected bearing area ``d * t`` is not positive |
The science & history
Understanding the Parameters
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Projected area $d\,t$ — the contact between a cylindrical rivet and a hole is a curved half-cylinder, but bearing stress is conventionally referred to the projected rectangle: diameter $\times$ plate thickness. This flat-area convention is what makes the simple $F/(dt)$ formula work.
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Plate thickness $t$ — the thinner plate governs, since it presents the smaller bearing area. In a multi-plate stack, check each plate against the load it carries.
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Rivet diameter $d$ — larger diameter spreads the bearing load, lowering $\sigma_c$ — but a larger hole also removes more plate net section (the tension check) and demands wider spacing. The three checks trade off.
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Allowable bearing stress — bearing allowables are higher than tension or shear allowables (often $1.5$–$2\times$ the plate tensile allowable) because the surrounding material confines the contact zone; codes tabulate them.
Derivation (Approaching a Proof)
The rivet shank pushes against the inside of the hole over a half-cylindrical surface. Rather than integrate the true (cosine-distributed) contact pressure around that curved surface, bearing analysis uses the projected area: the load $F$ is taken as acting uniformly over the rectangle formed by the rivet diameter $d$ and the plate thickness $t$. The nominal bearing (crushing) stress is then force over projected area:
$$\sigma_c = \frac{F}{A_{\text{proj}}} = \frac{F}{d\,t}.$$
This projected-area convention is exact in the sense that it defines a consistent, tabulated "bearing stress" for design; the true peak contact pressure is higher, which the elevated bearing allowables account for.
Dimensional check. $\sigma_c = \dfrac{F}{d\,t} = \dfrac{\text{N}}{\text{m}\cdot\text{m}} = \dfrac{\text{N}}{\text{m}^2} = \text{Pa}$ — a stress, as required.
History and Development
Bearing (crushing) stress is one of the three founding checks of riveted-joint design — rivet shear, plate bearing, and net-section tension — codified for boilers, bridges, and ships in the 19th century and carried forward into the AISC steel and ASME pressure-vessel rules for bolted and riveted connections. The projected-area convention, dating from that era, remains the standard definition of bearing stress for bolts and pins today.
Related Concepts: Rivet Shear Stress, Shear Stress, Bolt Tensile Stress Area, Principal Stresses, Bolt Proof Load
Notes: Uses projected area $d\,t$ (not the curved contact area). Thinner plate governs. Bearing allowables exceed tension/shear allowables (confined contact). One of the three riveted-joint checks (shear / bearing / net-section tension).