Strength • Section 9.2.1
Lug Bearing & Shear-Out Efficiency ($K_{bru}$)
AFFDL-TR-69-42 Section 9.2.1 bearing allowable formulation, Figures 9-2 & 9-3, and aluminum grain cutoffs
1. Fundamentals of Lug Bearing & Shear-Out Failure
When an axial tension load pulls a pin against a lug hole, the contact interface experiences intense compressive bearing stresses. Depending on the edge distance ratio ($e/D$), failure manifests in one of two ways:
- Shear Tear-Out / Splitting ($e/D < 1.5$): The pin shears through the forward cylindrical cap along two parallel shear planes tangential to the hole, or splits the forward ligament open.
- Plastic Bearing Crushing ($e/D \ge 1.5$): The forward ligament is sufficiently deep that shear tear-out cannot occur; the material directly beneath the pin yields and mushrooms in plastic compressive flow.
2. USAF Mathematical Formulation (Equations 9-3a & 9-3b)
Per USAF AFFDL-TR-69-42 Section 9.2.1, the ultimate bearing strength of the lug plate ($P_{bru,L}$) is calculated as:
where the reference allowable strength $F_{min}$ is defined as:
The factor $1.304$ enforces an empirical cutoff ensuring that excessive plastic deformation (yielding) does not cause joint unserviceability before ultimate tensile failure occurs.
3. Thick Lugs vs. Thin Lugs ($D/t$ Threshold)
The calculation engine differentiates between thick and thin lugs based on the $D/t$ ratio:
| Regime | Criterion | Design Curve | Calculation Details |
|---|---|---|---|
| Thick Lug | $\frac{D}{t} \le 5.0$ | USAF Figure 9-2 | Uses the axial bearing efficiency curve $K_{axial}(e/D)$. For short edge distances ($e/D < 1.5$), the forward ligament knockdown factor $\frac{a}{D} = \frac{e - D/2}{D}$ is applied per Eq. (9-1a/b). |
| Thin Lug | $\frac{D}{t} > 5.0$ | USAF Figure 9-3 | In thin lugs, pin bending and out-of-plane distortion peak the contact stresses near the plate faces. Figure 9-3 families parameterize $K_{bearEff}$ directly against $e/D$ across discrete $D/t$ curves ($D/t = 6, 8, 10$). |
4. Aluminum Grain Direction Cutoffs
In high-strength wrought aluminum alloys (such as 7075-T6 plate or forgings), transverse grain orientations exhibit reduced fracture toughness and notch ductility. Section 9.2.1 establishes optional grain direction caps:
- Curve A (Short Transverse ST): Caps maximum bearing efficiency at conservative limits to protect against grain delamination.
- Curve B (Long Transverse LT): Caps maximum bearing efficiency at $K_{bru} \le 2.00$.
- Longitudinal (L): Uncapped standard Figure 9-2 / 9-3 curves.
5. Bushing Bearing Strength ($P_{u,B}$)
If an interference-fit or slip-fit bushing is installed inside the lug bore, the bushing itself must react the pin contact load. Per USAF Equation (9-9):
where $F_{cy,bush}$ is the bushing material compressive yield strength and $D_p$ is the inner pin diameter. The allowable axial bearing capacity of the lug-bushing assembly is: