Aircraft Structures: Loads, Thin Walls & Stressed Skin

How aircraft carry enormous loads with very little weight. Learn the loads on an aircraft (aerodynamic, inertial, pressurisation, landing), shear force and bending moment along a wing, semi-monocoque construction (skin, stringers, ribs, spars, frames), thin-walled beams, shear flow and the Bredt–Batho formula for torsion, skin buckling and stiffeners, fuselage pressurisation stresses, and the FEA workflow — with Python analysing a wing box.

An airliner's structure weighs only about 25–30% of its maximum take-off weight, yet it survives 2.5 g manoeuvres, gusts, landings and tens of thousands of pressurisation cycles. The secret is semi-monocoque design: thin skins that carry shear and pressure, stiffened by stringers and frames that prevent buckling.

Aerospace structural analysis uses the same beam theory as civil and mechanical engineering, adapted for thin-walled open and closed sections where shear flow, not shear stress, is the natural quantity.

An analogy

A wing box is like a hollow aluminium drinks can reinforced from inside: on its own, a thin sheet crumples easily, but formed into a closed tube with ribs and stringers it becomes astonishingly stiff and strong for its weight.

Structural components

Main parts of an airframe:

Loads and load paths

Lift is distributed along the span; subtracting wing weight and fuel (inertia relief) gives shear force and bending moment diagrams, maximum at the root. Pitching moments and offset lift create torque. The fuselage carries tail loads as bending and the cabin pressure as hoop stress. A good design gives every load a direct, continuous path to where it is reacted.

Thin-walled sections and shear flow

In thin walls shear stress is nearly uniform through the thickness, so we use shear flow q = τt. In a closed cell under pure torque q is constant (Bredt–Batho). Open sections (like a C-channel) are very weak in torsion and have a shear centre outside the section — why wings use closed boxes. Multi-cell boxes are solved with compatibility of twist.

Buckling, pressurisation and FEA

Thin compression skins buckle at low stress; stringers divide them into narrow panels (buckling ∝ (t/b)²), and many designs allow skin buckling at limit load while stringers carry the compression (post-buckling, tension-field webs). Fuselage pressurisation (Δp ≈ 55–60 kPa) cycles on every flight — a key fatigue driver. Detailed sizing uses finite element models (NASTRAN, Abaqus) with thousands of load cases and margins of safety MS = allowable/(applied × factor) − 1 ≥ 0.

Formulas

Worked example: Hoop stress

Given: Δp = 58 kPa, r = 1.95 m, t = 1.6 mm

Find: Hoop and longitudinal stress.

Answer: 70.7 MPa hoop, 35.3 MPa longitudinal

Worked example: Shear flow

Given: T = 50 kN·m, A = 0.36 m²

Find: q.

Answer: 69.4 kN/m

Worked example: Skin buckling

Given: Al (E 72 GPa, ν 0.33), t = 2 mm, stringer pitch b = 150 mm, k = 4

Find: σ_cr.

Answer: ≈ 47 MPa — hence closely spaced stringers

Wing box under torsion and bending

# Closed single-cell wing box under torque (Bredt-Batho) and bending
T = 50e3             # N*m torque
b, h = 1.2, 0.3      # box width and depth, m
t_skin, t_web = 3e-3, 5e-3
A = b * h
q = T / (2 * A)                     # shear flow, N/m
print(f"enclosed area {A:.2f} m2, shear flow q = {q/1000:.1f} kN/m")
print(f"shear stress: skin {q/t_skin/1e6:.1f} MPa, spar web {q/t_web/1e6:.1f} MPa")
# Bending: M = 400 kN*m carried by skins (flanges) only, I ~ 2 * (b*t) * (h/2)^2
M = 400e3
I = 2 * b * t_skin * (h / 2) ** 2
sigma = M * (h / 2) / I
print(f"skin bending stress ~ {sigma/1e6:.0f} MPa (7075-T6 yield ~ 500 MPa)")
# enclosed area 0.36 m2, shear flow q = 69.4 kN/m
# shear stress: skin 23.1 MPa, spar web 13.9 MPa
# skin bending stress ~ 370 MPa (7075-T6 yield ~ 500 MPa)

In a closed cell the shear flow is constant around the wall, so thinner walls carry higher shear stress. The bending estimate treats skins as flanges of an I-beam; real analysis includes stringers, spar caps and effective skin width, and checks compression skins for buckling long before yield.

Common mistakes

Applications

Key takeaways

Going further