Strength • Section 9.2.3
Lug Transverse Efficiency Factors ($K_{tru}$ & $K_{try}$)
AFFDL-TR-69-42 Section 9.2.3 transverse allowable, Figure 9-8 curves, and yield vs ultimate governing rules
1. Mechanics of Transverse Lug Loading
When the applied load $P_{tr}$ acts perpendicular to the longitudinal axis of the lug, the connection undergoes complex combined stresses:
- Bearing and compressive crushing directly beneath the pin on the loaded side.
- High shear stresses causing diagonal shear tear-out along the $45^\circ$ forward section ($h_1$).
- Bending and tensile cracking on the trailing ligament ($h_3$) due to pin moment rotation.
To resolve these three coupled mechanisms without requiring 3D finite element simulation, Section 9.2.3 of USAF AFFDL-TR-69-42 consolidates the transverse capacity through the harmonic mean dimension $h_{avg}$ and Figure 9-8.
2. USAF Transverse Strength Formulations (Equations 9-8a & 9-8b)
The calculation engine evaluates whether the alloy's ultimate tensile strength or yield strength governs:
| Condition | Governing Allowable Formula | Efficiency Factor Used |
|---|---|---|
| Case 1: $F_{tu} \le 1.304 \cdot F_{ty}$ (Ductile alloys, e.g. 7075-T6, Ti-6Al-4V) |
$P_{tru,L} = K_{tru} \cdot F_{tu} \cdot D \cdot t$ | $K_{tru}$ (Ultimate transverse efficiency from Fig. 9-8) |
| Case 2: $F_{tu} > 1.304 \cdot F_{ty}$ (High yield-spread alloys, e.g. annealed stainless) |
$P_{tru,L} = 1.304 \cdot K_{try} \cdot F_{ty} \cdot D \cdot t$ | $K_{try}$ (Yield transverse efficiency from Fig. 9-8) |
In both cases, if an inner bushing is installed, the bushing allowable compressive load is also checked ($P_{tru,B} = 1.304 \cdot F_{cy,bush} \cdot D_p \cdot t$). The governing transverse allowable is:
3. Characteristics of USAF Figure 9-8
Figure 9-8 plots both $K_{tru}$ (upper curve) and $K_{try}$ (lower curve) against the dimensionless ratio $h_{avg}/D$:
- Range: $0.0 \le h_{avg}/D \le 1.6$.
- Initial Steep Slope ($0 \le h_{avg}/D \le 0.8$): Transverse strength grows almost linearly with effective edge material.
- Plateau ($h_{avg}/D > 1.2$): The efficiency curves flatten out asymptotically near $K_{tru} \approx 1.0 - 1.1$. Adding more material beyond $h_{avg}/D \approx 1.2$ yields little additional transverse capacity.