Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2012 Q.47)**
**1. Problem Statement & Parameters**:
- **Module**: Flight Mechanics & Space Dynamics (2 Mark, MCQ)
- **Topic**: Atmospheric Flight Mechanics (Drag Polar & Aircraft Performance Equations)
- **Organizing Institute**: IIT Delhi
- **Problem Statement**:
> Buckling of the fuselage skin can be delayed by
**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: **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"increasing internal pressure."*: ✅ **CORRECT**.
- **(B)** *"placing stiffeners farther apart."*: ❌ **INCORRECT**.
- **(C)** *"reducing skin thickness."*: ❌ **INCORRECT**.
- **(D)** *"placing stiffeners farther and decreasing internal pressure.
2012 AEROSPACE ENGINEERING - AE
AE 7/12
Common Data Questions
Common Data for Questions 48 and 49:
A wing and tail are geometrically similar, while tail area is one-third of the wing area and distance between
two aerodynamic centres is equal to wing semi-span ( b/2). In addition, following data is applicable:
0.3, 1.0, 0.08 / deg., 2.5 , 30 , 0, 1.
acLL M tCC c m b m C
$\alpha \alpha \eta$∈= = = = = = = The symbols have their usual
aerodynamic interpretation."*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2012 (IIT Delhi) master answer key with 100% precision.