Geometry • Section 9.2
Lug Geometry Ratios & Design Boundaries
Non-dimensional ratios that parameterize USAF Chapter 9 empirical curves and stress limits
1. Role of Non-Dimensional Ratios
The USAF AFFDL-TR-69-42 method collapses complex lug geometry into several non-dimensional ratios. These ratios correlate directly to the axes of empirical efficiency factor curves ($K_{bru}, K_{nu}, K_{tru}$) and define the structural boundaries of valid aerospace design practice.
| Geometry Ratio | Definition | USAF Curve Source | Design Validity Range | Structural Significance |
|---|---|---|---|---|
| $e/D$ | Edge distance / Bore diameter | Fig. 9-2 & Fig. 9-3 ($K_{bru}$) | $0.5 \le e/D \le 3.0$ (Target: $1.5 \le e/D \le 2.0$) |
Controls shear tear-out vs. pure bearing. At $e/D \ge 1.5$, full bearing capacity is reached. |
| $D/t$ | Bore diameter / Lug thickness | Fig. 9-2 vs. Fig. 9-3 Threshold | $D/t \le 5.0$ (Thick lug) $D/t > 5.0$ (Thin lug) |
Thick lugs ($D/t \le 5$) exhibit uniform bearing. Thin lugs ($D/t > 5$) suffer localized distortion and require Figure 9-3 knockdowns. |
| $D/W$ | Bore diameter / Net width | Fig. 9-4 ($K_{nu}$) | $0.1 \le D/W \le 0.8$ (Typical: $0.3 \le D/W \le 0.6$) |
Controls net-section tensile stress concentration and plasticity relief across the hole boundary. |
| $h_{avg}/D$ | Effective edge distance / Bore diameter | Fig. 9-8 ($K_{tru}$) | $0.2 \le h_{avg}/D \le 1.6$ | Governs transverse shear and rotational blow-out resistance when carrying cross-loads. |
2. Detailed Examination of Governing Ratios
A. Edge Distance to Hole Diameter Ratio ($e/D$)
The $e/D$ ratio dictates whether the pin will tear through the forward tip in double-shear tearout or fail through compressive crushing:
- $e/D < 1.0$: Dangerous shear tearout zone; allowable strength drops precipitously.
- $1.0 \le e/D < 1.5$: Transition zone; efficiency factor $K_{bru}$ climbs steeply as forward material ligament increases.
- $e/D \ge 1.5$: Full bearing allowable is achieved; further increases in $e/D$ produce diminishing returns in strength while adding parasitic weight.
B. Diameter to Thickness Ratio ($D/t$)
The ratio of hole diameter to plate thickness governs stress distribution across the pin bearing contact face:
- $D/t \le 5$: Thick lug condition. Pin load is distributed uniformly without out-of-plane plate cupping. Governed by Figure 9-2.
- $D/t > 5$: Thin lug condition. Pin bending and lateral flexibility cause stress peaking near the outer corners, accompanied by hole ovalization. Governed by Figure 9-3. In the web app, if $D/t > 5$, a cautionary badge is displayed and Figure 9-3 is engaged automatically.
C. Diameter to Net Width Ratio ($D/W$)
The ratio $D/W$ reflects the ligament proportion resisting axial hoop tension. If $D/W$ is very small, the elastic stress concentration factor ($K_t \approx 3$) cannot fully relieve plastically prior to gross section yield, reducing $K_{nu}$. As $D/W$ increases toward 0.5, ductile plastic redistribution optimizes the net tensile efficiency factor $K_{nu}$.