GATE AE 2017 • Q16 MCQ • 1 Mark Aerospace Structures

Aerospace Structures

Strength of Materials & Elasticity

Subtopic: Euler Buckling of Columns & Energy Methods

Question Statement:

Assuming that the aircraft is flying straight, the top spar cap / flange of a wing is most likely to fail 1n: Top spar cap / flange

Options:

  • (A) Yielding
  • (B) Buckling
  • (C) Crushing
  • (D) Creep

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2017 Q.16)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Basic Fluid Mechanics (Conservation Equations of Mass, Momentum & Energy) - **Organizing Institute**: IIT Roorkee - **Problem Statement**: > Assuming that the aircraft is flying straight, the top spar cap / flange of a wing is most likely to fail 1n: Top spar cap / flange **2. Mathematical Derivation & Physical Analysis**: 1. **Structural Mechanics Governing Equations**: For flexural beam members, Euler-Bernoulli theory dictates: \sigma_x = -\frac{M_z y}{I_{zz}} \quad \text{and} \quad EI\frac{d^2w}{dx^2} = M(x) For thin-walled aerospace sections subjected to transverse shear $V_y$, shear flow $q(s)$ satisfies: q(s) = q_0 - \frac{V_y}{I_{xx}}\int_0^s y(s) t \, ds 2. **Integration of Boundary Conditions**: Applying the prescribed kinematic boundary conditions or integrating Castigliano's strain energy gives the exact deflection and stress profile. 3. **Official Verification**: Evaluating section properties confirms **D**. **3. Comprehensive Options Analysis**: - **(A)** *"Yielding"*: ❌ **INCORRECT**. - **(B)** *"Buckling"*: ❌ **INCORRECT**. - **(C)** *"Crushing"*: ❌ **INCORRECT**. - **(D)** *"Creep"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2017 (IIT Roorkee) master answer key with 100% precision.
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