GATE AE 2017 • Q16
MCQ • 1 Mark
Aerodynamics & Fluid Mechanics
Basic Fluid Mechanics
Subtopic: Conservation Equations of Mass, Momentum & Energy
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
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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