GATE AE 2009 • Q31 MCQ • 1 Mark Aerospace Structures

Aerospace Structures

Thin-Walled Structures

Subtopic: Bending of Unsymmetrical Thin-Walled Sections

Question Statement:

The torque balance equation (Bredt-Batho formula) for this section leads to

Options:

  • (A) 91 - 92 = 2000 N/m
  • (B) 9, + 292 = 2000 N/m
  • (C) 4, + q2 = 2000 N/m
  • (D) 2q, + q2 = 2000 N/m

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.31)** **1. Problem Statement & Parameters**: - **Module**: Aerospace Structures (1 Mark, MCQ) - **Topic**: Strength of Materials & Elasticity (Stress and Strain Tensors & Generalized Hooke's Law) - **Organizing Institute**: IIT Roorkee - **Problem Statement**: > The torque balance equation (Bredt-Batho formula) for this section leads to **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Strength of Materials & Elasticity** (Stress and Strain Tensors & Generalized Hooke's Law) under *Aerospace Structures*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **C**. **3. Comprehensive Options Analysis**: - **(A)** *"91 - 92 = 2000 N/m"*: ❌ **INCORRECT**. - **(B)** *"9, + 292 = 2000 N/m"*: ❌ **INCORRECT**. - **(C)** *"4, + q2 = 2000 N/m"*: ✅ **CORRECT**. - **(D)** *"2q, + q2 = 2000 N/m"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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