GATE AE 2012 • Q24
MCQ • 1 Mark
Flight Mechanics & Space Dynamics
Dynamic Stability
Subtopic: Short Period & Phugoid Longitudinal Modes
Question Statement:
In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary
carriers of
Options:
-
(A) shear stresses due to an aerodynamic moment component alone.
-
(B) normal (bending) stresses due to aerodynamic forces.
-
(C) shear stresses due to aerodynamic forces alone.
-
(D) shear stresses due to aerodynamic forces and a moment component.
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.24)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ)
- **Topic**: Dynamic Stability (Short Period & Phugoid Longitudinal Modes)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> In a semi-monocoque construction of an aircraft wing, the skin and spar webs are the primary carriers of
**2. Mathematical Derivation & Physical Analysis**:
1. **Structural Analysis & Beam Theory**:
Under flexural bending, normal stress and curvature follow Euler-Bernoulli theory:
$\sigma_x = -\frac{M_z y}{I_{zz}} \quad \text{and} \quad \frac{d^2w}{dx^2} = \frac{M(x)}{EI}$
For thin-walled aerospace sections subjected to torque $T$, the closed-cell shear flow follows Bredt-Batho theory:
$q = \frac{T}{2 A_m}$
2. **Integration of Section Properties**:
Evaluating section modulus and enforcing equilibrium yields the stress distribution.
3. **Official Verification**:
Matches the verified answer: **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"shear stresses due to an aerodynamic moment component alone."*: ❌ **INCORRECT**.
- **(B)** *"normal (bending) stresses due to aerodynamic forces."*: ❌ **INCORRECT**.
- **(C)** *"shear stresses due to aerodynamic forces alone."*: ❌ **INCORRECT**.
- **(D)** *"shear stresses due to aerodynamic forces and a moment component."*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.
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