| name | aircraft-structures |
| description | Aircraft structural analysis — wing bending/torsion, shear flow, semi-monocoque, idealized sections, flutter, fail-safe/damage tolerance, FAR 25 loads, structural weight estimation. |
| metadata | {"priority":7,"promptSignals":{"phrases":["aircraft structure","wing structure","shear flow","semi-monocoque","aircraft loads","wing bending","FAR 25","damage tolerance"],"minScore":3}} |
Aircraft Structures — Complete Skill
Load Cases
Design Load Factors (FAR/CS 25)
Limit load: maximum load expected in service
Ultimate load = limit × 1.5 (safety factor)
n_z = load factor (g units): +2.5g limit (large transport); +3.8g (small GA); -1.0g negative
V-n diagram:
Maneuvering (A): n = n_max at V_A (maneuvering speed)
Gust envelope: n = 1 ± U_e V_EAS m/(2W) × (dC_L/dα) × a_lf [gust load factor]
Wing Structure
Semi-Monocoque Construction
Spars: carry bending moment (flanges) and shear (webs)
Stringers/longerons: carry direct stress from bending
Skin: carries shear flow; stabilized by frames/ribs
Simplified wing box: two-cell or single-cell closed section
Bending: N_b = M × y/I [direct stress in stringers, N/m]
Shear: q = VQ/I + twist shear flow q₀
Wing bending moment:
Root BM = ∫ p(y)(y-0)dy + W_fuel (y) + W_engine — inertia relief
p(y) = aerodynamic load distribution (elliptic approximation for baseline)
Shear Flow in Thin-Walled Sections
Open Section
q(s) = -∫₀ˢ (V_y Q/I_x + V_x Q/I_y) ds [from shear center]
Q = first moment of area = ∫ y t ds (statical moment)
Closed Section (Torsion + Shear)
Torsion shear flow: q_T = T/(2A_enclosed) (Bredt-Batho)
A_enclosed = enclosed area of box
Combined: q_total = q_open + q₀ (constant) + q_T
q₀ found by: twist compatibility (rate of twist equal in all cells for multi-cell box)
Shear center: point about which applied load produces no torsion
For symmetric section: shear center on axis of symmetry
Idealized Section (Boom Theory)
Concentrate skin area into discrete booms (stringers + associated skin)
B_i = t_i d_i + b_{i-1} t_{i-1}/6 × (2 + σ_{i-1}/σ_i) + b_{i+1} t_{i+1}/6 × (2 + σ_{i+1}/σ_i)
Reduces section to N booms connected by shear-only webs
Shear flow between booms: q_{ij} = q_{i-1,j} + B_i σ_i V_y/I_x (recurrence relation)
Aeroelasticity and Flutter
Divergence (Static Aeroelasticity)
Wing twisting under aerodynamic loads → increased angle of attack → more lift → more torsion
Divergence speed: q_D = GJ / (e × L × ∂C_L/∂α × c) [dynamic pressure]
e = distance from aero center to elastic axis (positive if AC is forward of EA)
Design: EA must be ahead of or at AC to avoid static divergence (swept forward wings susceptible)
Flutter
Dynamic instability from coupling of bending and torsion modes
Classical binary flutter: V_F = f(m, f_bending, f_torsion, b, a, x_α, r_α)
Theodorsen theory: unsteady aerodynamic coefficients C(k)
Flutter speed determined by V-g (damping vs. speed) method in aeroelastic analysis
Rule of thumb: f_torsion / f_bending ≥ 2-3 to avoid flutter in subsonic transport range
Damage Tolerance (FAR 25.571)
Design Philosophies
Fail-safe: multiple load paths; structure can sustain loss of one member
Damage tolerant: cracks grow slowly; detectable before critical size; inspection intervals set by K_I < K_IC and da/dN
Residual strength diagram:
Critical crack size: a_c = 1/π (K_IC/(σ √π))²
Inspection interval: N such that crack grows from a_detect to a_c
Typical inspection: a_detect = 12.5mm (visible); a_c depends on material and stress
2024-T3: K_IC = 30 MPa√m; 7075-T6: K_IC = 25 MPa√m (lower K_IC, higher strength)
Structural Weight Estimation (Raymer Method)
Wing: W_wing = 0.0051(W_dg n_z)^0.557 S_w^0.649 AR^0.5 (t/c)^(-0.4)(1+λ)^0.1 cos(Λ_25)^(-1.0) S_csw^0.1
(W_dg = design gross weight, n_z = ult load factor, S_w = wing area [ft²], λ = taper ratio)
Fuselage: W_fus = 0.3280 k_door K_Lg (W_dg n_z)^0.5 L^0.25 S_f^0.302 ...
Output
Provide: limit and ultimate loads [kN], wing root bending moment [kN·m], shear flow q [N/m] at critical section, flutter speed V_F [m/s], critical crack size a_c [mm], inspection interval [flight cycles], wing structural weight estimate [kg].
