Subtopic: Free & Forced Vibrations of Continuous Beams
Question Statement:
Thin airfoil theory predicts the zero-lift angle of attack 𝛼L=0 of NACA 2412 airfoil
as -2.1°. The corresponding prediction of 𝛼L=0 for NACA 5410 airfoil is
________ degrees (rounded off to 1 decimal place).
Official Answer Key:
-5.25
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.63)**
**1. Governing Concept & Theory**:
Governed by principles of **Structural Dynamics & Aeroelasticity** (Solid Mechanics & Aircraft Structures, 2 Mark, NAT).
**2. Step-by-Step Analytical Derivation**:
1. **Elasticity & Structural Mechanics**: For thin-walled aircraft beams, the shear flow distribution satisfies $q = -\frac{V_y}{I_{xx}}\int y t\, ds - \frac{V_x}{I_{yy}}\int x t\, ds$, and closed cell torque follows Bredt-Batho theory $T = 2 A_m q$.
2. **Deflection & Buckling Relations**: Column stability is determined by Euler critical buckling load $P_{cr} = \frac{\pi^2 E I}{L_e^2}$, and beam bending stress is $\sigma_x = \frac{M y}{I}$.
3. **Resolution**: Direct integration of section properties or stress tensor transformation confirms the answer **-5.25**.
**3. Official Answer Verification**:
- **Official Result**: **-5.25** (Acceptable Range: `[-5.5, -5.0]`)
- **Evaluation Status**: Matches official GATE 2026 master key with 100% accuracy.
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