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Qwestrum Engineering360 · Aerospace & Aeronautical · Aircraft Structures

Bending and Torsion in Wings

Wing bending-torsion analysis treats the wing as a cantilever beam with coupled elastic response under aerodynamic loads.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • Wing as cantilever: max bending moment at root in level flight
  • Torsion from offset thrust or aerodynamic centre vs elastic axis
  • Sweep reduces effective bending moment component normal to spar

Topic details

Introduction

University numericals often ask root bending moment, twist angle, and stress check at critical spar cap locations.

Key relations & formulas

EId2wdx2=M(x)EI d^{2}\frac{w}{dx^{2}} = M(x)
(beam bending deflection, w = deflection)
GJdϕdx=T(x)GJ \frac{d\phi}{dx} = T(x)
(torsion of circular/thin-walled section)
σf=MhW\sigma_{f} = M \frac{h}{W}
(flange stress in wing box, W = section modulus)

Notation and sign conventions

Relation 1 —
EId2wdx2=MEI d^{2}\frac{w}{dx^{2}} = M
EId2wdx2=M(x)EI d^{2}\frac{w}{dx^{2}} = M(x)
(beam bending deflection, w = deflection)
Write this relation with symbols exactly as in Megson Aircraft Structures — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
GJdϕdx=TGJ \frac{d\phi}{dx} = T
GJdϕdx=T(x)GJ \frac{d\phi}{dx} = T(x)
(torsion of circular/thin-walled section)
Write this relation with symbols exactly as in Megson Aircraft Structures — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
σf=MhW\sigma_{f} = M \frac{h}{W}
σf=MhW\sigma_{f} = M \frac{h}{W}
(flange stress in wing box, W = section modulus)
Write this relation with symbols exactly as in Megson Aircraft Structures — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

Bending stiffness EI controls vertical deflection while torsional stiffness GJ controls aerodynamic twist. Coupling becomes critical for swept or flexible high-aspect-ratio wings.

Assumptions and validity limits

State assumptions explicitly before using any relation for bending and torsion in wings — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Aircraft Structures viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Aircraft Structures papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to bending and torsion in wings.
4. Use equation 1:
EId2wdx2=MEI d^{2}\frac{w}{dx^{2}} = M
.
5. Use equation 2:
GJdϕdx=TGJ \frac{d\phi}{dx} = T
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Bending and Torsion in Wings appears in airframe design and certification. In Indian aerospace curricula this topic is tested because it connects theory to thin-walled and composite structures.
GATE and semester exams often combine bending and torsion in wings with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use bending and torsion in wings?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Many students confuse geometric twist with elastic twist generated by aerodynamic loading.

Quick revision checklist

Before attempting bending and torsion in wings problems, confirm you can:
1. Wing as cantilever: max bending moment at root in level flight
2. Torsion from offset thrust or aerodynamic centre vs elastic axis
3. Sweep reduces effective bending moment component normal to spar
Revise the solved examples in Megson Aircraft Structures — Standard reference and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Wing twist from torque

Problem

Given T = 1500 N m, span segment length L = 2 m, and GJ = 6 x 10^4 N m^2, estimate twist phi.

Solution

phi = TL/GJ = 1500 x 2 /(6 x 10^4) = 0.05 rad, about 2.86 degree.

Conceptual check — Bending and Torsion in Wings

Problem

In a Aircraft Structures semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of bending and torsion in wings." What should a complete answer include?

Exams & GATE

Megson — distinguish bending axis, elastic axis, and aerodynamic centre.

📖 Standard books (India)

  • Megson Aircraft Structures — Standard reference

    Read: Syllabus unit

    Referenced in Indian B.Tech syllabus

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