Structural components of wings and fuselage

Why it matters

An aircraft is a thin-walled shell stiffened by a skeleton of beams and frames, and each member has a definite job in the load path. Knowing which part carries bending, which carries shear and which carries torsion is what lets you size a structure, find where it will fail first and simplify it for hand analysis. Every later topic in this subject (shear flow, idealisation, torsion boxes, buckling) assumes this picture.

Key ideas

Semi-monocoque construction. A monocoque carries all loads in its skin, like an eggshell; it is efficient but a thin unstiffened skin buckles at low compressive stress and is badly weakened by cut-outs. Aircraft use semi-monocoque construction: a thin skin stiffened by longitudinal members (stringers, longerons, spar caps) and transverse members (frames, ribs, bulkheads). The stiffeners carry most of the direct (axial) stress and keep the skin from buckling early; the skin carries shear.

Wing. The primary structure is the wing box, a closed cell formed by the front and rear spars and the upper and lower skin panels.

• Spars: spanwise beams. The spar caps (flanges) carry the axial tension and compression produced by wing bending; the spar webs carry the vertical shear force as shear flow.
• Skin: provides the aerodynamic surface, takes the air pressure loads and passes them to stringers and ribs. Together with the spar webs it forms the closed torsion box that resists twisting moment through a constant shear flow q = T/(2A). With its stringers it also carries a large part of the bending stress.
• Stringers: spanwise stiffeners attached to the skin. They carry axial load from bending and split the skin into small panels that buckle at higher stress.
• Ribs: chordwise members. They hold the aerofoil shape, transfer the air load from skin and stringers to the spars, limit the buckling length of stringers, and introduce concentrated loads (engine pylons, landing gear, flap tracks). Closely spaced, heavy ribs sit wherever large point loads enter.

Fuselage.

• Skin: carries shear from fuselage bending and torsion and the hoop and longitudinal tension from cabin pressure.
• Stringers and longerons: longitudinal members carrying the axial stress from fuselage bending. Longerons are heavier and fewer; they run along edges of large cut-outs.
• Frames: transverse rings that keep the cross-section shape, limit stringer buckling length and spread concentrated loads into the skin.
• Bulkheads: frames with a web across the section. The pressure bulkheads at each end of the cabin react the pressure end load; others carry wing, tail or gear loads.

Load path. Air pressure → skin → stringers and ribs → spars → wing root fittings → fuselage frames → fuselage shell. Bending appears as direct stress in caps and stringers, shear force as shear flow in webs, torque as shear flow around the closed cell.

Cut-outs. Doors, windows and access panels interrupt the shear and direct-stress paths, so they are framed by heavy edge members and doublers. Rounded corners avoid stress concentrations that start fatigue cracks.

Formulas

P = M / h

• P: axial force in each spar cap (N), M: bending moment at the section (N·m), h: distance between cap centroids (m). Two-flange idealisation where the web carries no bending.

q = S / h and τ = q / t

• S: shear force carried by the web (N), q: shear flow (N/m), t: web thickness (m), τ: shear stress (Pa). Constant web shear flow when caps carry all the bending.

q = T / (2·A)

• T: torque (N·m), A: area enclosed by the mid-line of a closed cell (m²), q: shear flow (N/m). Bredt–Batho, single closed thin-walled cell.

σ_h = p·r / t and σ_L = p·r / (2·t)

• p: cabin pressure differential (Pa), r: fuselage radius (m), t: skin thickness (m), σ_h: hoop stress, σ_L: longitudinal stress (Pa). Thin cylinder, r/t > 10, away from frames and ends.

σ = F / A

• Average axial stress (Pa) in a member of area A (m²) carrying force F (N).

Worked examples

Example 1 (standard): sizing a two-flange spar. Given: at one station a spar carries M = 200 kN·m and S = 80 kN. Distance between cap centroids h = 0.50 m, web thickness t = 2.0 mm, allowable cap stress 400 MPa.

1. Cap force: P = M / h = 200 000 / 0.50 = 400 000 N.
2. Cap area required: A = P / σ_allow = 400 000 / 400 × 10⁶ = 1.0 × 10⁻³ m² = 1000 mm².
3. Web shear flow: q = S / h = 80 000 / 0.50 = 160 000 N/m = 160 N/mm.
4. Web shear stress: τ = q / t = 160 N/mm / 2.0 mm = 80 N/mm². Answer: cap area = 1000 mm², web τ = 80 MPa.

Example 2 (GATE level): fuselage skin and wing torsion box. Given: fuselage radius r = 2.0 m, pressure differential p = 60 kPa, skin t = 1.6 mm. A wing box with enclosed area A = 0.40 m² and skin thickness 1.5 mm carries T = 50 kN·m.

1. Hoop stress: σ_h = p·r / t = 60 000 × 2.0 / 0.0016 = 75 × 10⁶ Pa.
2. Longitudinal stress: σ_L = p·r / (2·t) = 37.5 × 10⁶ Pa.
3. Wing box shear flow: q = T / (2·A) = 50 000 / (2 × 0.40) = 62 500 N/m = 62.5 N/mm.
4. Skin shear stress: τ = q / t = 62.5 / 1.5 = 41.7 N/mm². Answer: σ_h = 75 MPa, σ_L = 37.5 MPa, wing-box skin τ = 41.7 MPa.

Common mistakes

• Saying ribs carry wing bending. They carry chordwise shape and local loads; bending goes to spar caps, stringers and skin.
• Using the overall spar depth instead of the distance between cap centroids in P = M/h.
• Forgetting that a torsion box needs a closed cell: an open section (one spar plus skin with a slit) is very weak in torsion.
• Taking longitudinal pressure stress as equal to hoop stress; it is half.
• Treating the skin as non-structural. In a semi-monocoque it carries all the shear and much of the bending.
• Mixing N/mm (shear flow) with N/mm² (stress); divide by thickness to get stress.

For GATE AE

Questions are mostly conceptual: which member carries bending, shear or torsion, monocoque versus semi-monocoque, purpose of ribs, frames and bulkheads. Short numericals use P = M/h for spar caps, q = S/h for webs, q = T/(2A) for a closed box and pr/t for pressurised fuselages. Practise these and keep shear flow and shear stress units separate.

Quick check

1. Which wing member carries most of the bending stress in a two-spar wing?
2. What closes the torsion box of a wing?
3. Name two jobs of a wing rib.
4. A cabin with r = 1.5 m, t = 1.2 mm and p = 50 kPa has what hoop stress? Answers: 1. spar caps with the stiffened skin; 2. the upper and lower skins joined to the front and rear spar webs; 3. hold the aerofoil shape and transfer air loads to the spars (also limit stringer buckling length, introduce point loads); 4. σ_h = 50 000 × 1.5 / 0.0012 = 62.5 MPa.