GATE AE 2007 • Q49 MCQ • 2 Marks Aerospace Structures

Aerospace Structures

Thin-Walled Structures

Subtopic: Torsion of Multi-Cell Thin-Walled Tubes

Question Statement:

The torsion constant J of a thin-walled closed tube of thickness t and mean radius r is given by

Options:

  • (A) J = 2art'
  • (B) J = 2ar' t
  • (C) J = 27r t
  • (D) J = 2mr*

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.49)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ) - **Topic**: Static Stability & Control (Static Margin & Stick-Fixed/Free Stability) - **Organizing Institute**: IIT Kanpur - **Problem Statement**: > The torsion constant J of a thin-walled closed tube of thickness t and mean radius r is given by **2. Mathematical Derivation & Physical Analysis**: 1. **Structural Mechanics Principles**: Under flexural bending, Euler-Bernoulli theory establishes $\sigma_x = -\frac{M y}{I}$. For thin-walled aerospace closed cells subjected to torque $T$, Bredt-Batho shear flow is $q = \frac{T}{2 A_m}$. 2. **Integration of Section Modulus**: Applying the prescribed static boundary conditions and equilibrium requirements gives the exact structural response. 3. **Verification**: Direct evaluation verifies **A**. **3. Comprehensive Options Analysis**: - **(A)** *"J = 2art'"*: ✅ **CORRECT**. - **(B)** *"J = 2ar' t"*: ❌ **INCORRECT**. - **(C)** *"J = 27r t"*: ❌ **INCORRECT**. - **(D)** *"J = 2mr*"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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