Wing Skin, Shear Flow & Torsion

What Is It?

The wing skin is not just an aerodynamic covering — it is a primary structural member. The skin carries shear, torsion and bending as part of the wing box. The stressed-skin design, where the skin participates in the primary load path, is what makes modern wings efficient. The shear flow in the skin — the shear force per unit length around the wing-box section — carries the vertical shear and the torsion. Understanding how the skin carries load through shear flow is essential for analysing the wing structure.

Why It Matters

If the skin were only an aerodynamic covering and did not carry structural load, the wing would need much heavier internal structure to carry the same loads. The stressed-skin design allows the skin to contribute to the structural efficiency — the skin that is already there for aerodynamic reasons is also carrying shear, torsion and bending. This is a major weight saving. But it also means the skin must be analysed as a structural member — its thickness, its stability, its connections to the spars and ribs and its fatigue behaviour all affect the wing performance.

The aerodynamic skin is often a primary structural member. The wing skin carries shear, torsion and bending as part of the closed wing-box section. Treating the skin as a non-structural covering ignores a major part of the wing load-carrying capability.

Stressed-Skin Wing Behaviour

In a stressed-skin wing, the upper and lower skins are integral parts of the wing box. They carry three types of load. In bending, the skins carry axial compression (upper) and tension (lower) — the skin acts as the flange of the wing-box beam. In shear, the skins carry vertical shear as shear flow around the wing-box section. In torsion, the skins carry the torsional shear flow around the closed cell. The skin thickness is therefore determined by the most critical of these three loads — the bending stress, the shear stress or the torsional shear stress — at each location along the span.

Closed-Section Torsion

A closed thin-walled section is extremely efficient in torsion. The torsional shear flow is constant around the closed cell — the shear force per unit length is the same everywhere around the perimeter. The shear flow is determined by the applied torque and the enclosed area of the cell. A larger enclosed area gives a lower shear flow for the same torque — this is why a wider wing box (spars further apart) is more efficient in torsion.

Torsional shear flow in a thin-walled closed section:

q  =  T / (2 · A_m)

where:
q    =  shear flow (N/mm) — constant around the cell
T    =  applied torque (N·mm)
A_m  =  enclosed area of the closed cell (mm²)

The factor 2·A_m comes from the moment equilibrium
of the constant shear flow around the cell

Larger A_m → lower q for same T → more efficient torsion
This is why a wider wing box is better in torsion

Shear Flow Concept

Shear flow is the shear force per unit length along a section. It describes how the vertical shear is distributed around the wing-box section. For an open section (like a channel or an I-beam), the shear flow varies along the section — it is zero at the free edges and maximum at the neutral axis. For a closed section (like the wing box), the shear flow circulates around the cell — it is non-zero everywhere and is the sum of the open-section shear flow and a constant torsional shear flow.

Open-section shear flow (Bredt–Zhuravskii):

q(s)  =  V · Q(s) / I

where:
q(s)  =  shear flow at location s along the section
V     =  vertical shear force
Q(s)  =  first moment of area above (or below) location s
I     =  second moment of area of the section

For closed sections, a constant torsional shear flow is added:

q_total  =  V·Q/I  +  T/(2·A_m)

Skin Shear and Spar Web Shear

The vertical shear is carried by the spar webs and the skins together. In the wing box, the shear flow is distributed around the closed section — the spar webs carry a portion and the skins carry a portion. The distribution depends on the geometry — the spar web thickness, the skin thickness and the wing-box dimensions. In a typical wing box, the spar webs carry the majority of the vertical shear (they are the vertical members), and the skins carry the majority of the torsion (they form the top and bottom of the closed cell). But both contribute to both loads — the distribution is not a simple partition.

Multi-Cell Sections

Some wings have more than two spars, creating multiple cells in the wing box. A three-spar wing has two cells — one between the front and middle spar, one between the middle and rear spar. Multi-cell sections are more efficient in torsion — the torsional stiffness increases with the number of cells. They also provide redundant load paths — if one cell is damaged, the others can carry the load. Multi-cell sections are used for highly loaded wings or wings with special requirements (supersonic, high-torsion). The analysis of multi-cell sections requires solving for the shear flow in each cell simultaneously — the cells share the torsion, and the distribution depends on the relative stiffness of each cell.

Shear Centre and Warping

The shear centre is the point through which a shear load must be applied to produce bending without torsion. If the shear load is applied away from the shear centre, torsion is produced. For a symmetric wing box (symmetric about the vertical axis), the shear centre is on the vertical centreline. For a non-symmetric section, the shear centre may be off-centre. The lift typically acts ahead of the wing-box shear centre (the aerodynamic centre is ahead of the structural centre), producing nose-up torsion. Warping is the out-of-plane deformation of the cross-section under torsion — a closed section warps less than an open section, which is another reason closed sections are efficient in torsion.

Key Takeaways

• The wing skin is a primary structural member — it carries shear, torsion and bending
• Closed-section torsion: q = T/(2Am) — shear flow is constant around the cell
• A wider wing box (larger enclosed area) is more efficient in torsion
• The shear centre is where shear must be applied to avoid torsion — lift offset from shear centre creates torsion
• Multi-cell sections provide higher torsional stiffness and redundant load paths