GATE AE 2014 • Q13
MCQ • 1 Mark
Engineering Mathematics
Calculus
Subtopic: Limits, Continuity & Differentiability
Question Statement:
Which one of the following objects with inclined face at 45oo , subjected to the given stresses, are in
static equilibrium:
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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