A single-cell thin-walled closed aircraft torque box has an enclosed cross-sectional area $A_m = 0.4\text{ m}^2$. If it is subjected to an applied torsional moment $T = 8000\text{ N}\cdot\text{m}$, what is the shear flow $q$ (in N/m) across the skin according to the Bredt-Batho formula?

Answer Key:

10000

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Bredt-Batho Relation:** For single-cell closed tubes, shear flow $q = \tau t$ is constant around the contour. 2. **Stage 2: Torque Equilibrium:** $T = 2 A_m q$. 3. **Stage 3: Solve for $q$:** $q = \frac{T}{2 A_m} = \frac{8000}{2 \times 0.4} = 10000\text{ N/m}$. 4. **Stage 4: Correct Value:** 10000.

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