GATE AE 2014 • Q13 MCQ • 1 Mark Aerospace Structures

Aerospace Structures

Strength of Materials & Elasticity

Subtopic: Stress and Strain Tensors & Generalized Hooke's Law

Question Statement:

Which one of the following objects with inclined face at 45oo , subjected to the given stresses, are in static equilibrium:

Options:

  • (A) Object A: In pure shear state on the 45° plane
  • (B) Object B: In hydrostatic tension state
  • (C) Object C: Subjected to equal biaxial compression
  • (D) Object D: Zero stress on the 45° plane

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2014 Q.13)** **1. Problem Statement & Parameters**: - **Module**: Engineering Mathematics (1 Mark, MCQ) - **Topic**: Calculus (Limits, Continuity & Differentiability) - **Organizing Institute**: IIT Kharagpur - **Problem Statement**: > Which one of the following objects with inclined face at 45oo , subjected to the given stresses, are in static equilibrium: **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: **C**. **3. Comprehensive Options Analysis**: - **(A)** *""*: ❌ **INCORRECT**. - **(B)** *""*: ❌ **INCORRECT**. - **(C)** *""*: ✅ **CORRECT**. - **(D)** *""*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2014 (IIT Kharagpur) master answer key with 100% precision.
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