Lug Joint Strength — Maddux Section 9

Methodology: Maddux et al., Stress Analysis Manual, Section 9 (AFFDL-TR-69-42, 1969). Public-domain USAF reference. Three-element clevis-and-tang topology (Outer 1 / Center / Outer 2); each outer lug carries half the joint load (modified by the optional center moment).

Failure modes computed:

• Lug bearing (axial) — Eq 9-1, 9-2, 9-3 with the four-way MIN: K-curve ult, K-curve yield×1.304, MMPDS-table ult, MMPDS-table yield×1.304.
• Lug net-section (axial) — Eq 9-4, 9-5, 9-6 with K_n from Maddux Fig 9-4 (three F_ty/F_tu master charts × seven F_tu/(E·ε_u) sub-curves; bilinear interpolation across the 7×3 grid evaluated at the lug's D/w).
• Lug transverse — Eq 9-28, 9-29, 9-30 with K_tru/K_try from Fig 9-8.
• Lug oblique — Eq 9-31 with exponent 1.6: (P/P_u,L)^1.6 + (P_tr/P_tru,L)^1.6 = 1.
• Pin shear — Eq 9-12 generalised for hollow pin: P_us,p = 2·(π/4)·(D_p²−D_p,ID²)·F_su,p.
• Pin bending — Eq 9-15 generalised for hollow pin, with k_bp gated on pin elongation: k_bp = 1.56 if ε_u,p ≥ 5%, else 1.0 (Cozzone 1950 / ANC-5a).
• Balanced design — Eq 9-16/9-17/9-18: when P_ub,p < min(P_uLB, P_us,p), the pin is weak and effective bearing widths b_1,min, 2b_2,min reduce active engagement — tool reports both, plus the geometry-limited cap P_ub,p,max.
• Bushing bearing — Eq 9-8 (F_bru,B = 1.304·F_cy,B) with engagement length MIN(L_bush, t_lug).
• Lug root — combined σ_axial + σ_bend,trans + σ_bend,side at the lug-to-parent transition with k_bT gated on lug ε_u ≥ 5%.

Margin form: MS = P_allow / P_applied / (FS · FF · ECF) − 1.

Improvements over the baseline workbook (per lug_references_comparison.md):

• k_bp is gated on pin ε_u (V.2.2 fix).
• Balanced-design pin path (Eq 9-16) properly gated against P_ub,p < min(P_uLB, P_us,p) per Maddux 9-19a/b. b_1,min, 2b_2,min exposed.
• Default FS_ult = 1.50 (FAA standard) rather than 1.25 (project-specific).

Limitations: D/t ≤ 5 only (K-curve quadratic; Fig 9-3 family for D/t > 5 not yet digitised — tool warns). Symmetric-hole only (no eccentric correction per Ekvall 1986). No explicit lubrication-hole derate. No lug-tang ductility derate (B factor, Maddux §9.15 for lug ε_u < 5%). For single-shear configurations use the dedicated single-shear tool.

References: Maddux et al. (1969) AFFDL-TR-69-42 §9; Stenman (2008) RPI MEng project; Cozzone, Melcon, Hoblit (1950) Product Engineering 21; Melcon, Hoblit (1953) Product Engineering 24; Ekvall (1986) J. Aircraft 23(5).