An Euler-Bernoulli beam in bending is assumed to satisfy:
Options:
(A) both plane stress as well as plane strain conditions
(B) plane strain condition but not plane stress condition
(C) plane stress condition but not plane strain condition
(D) neither plane strain condition nor plane stress condition
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2011 Q.7)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (2 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Data Interpretation)
- **Organizing Institute**: IIT Madras
- **Problem Statement**:
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**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Quantitative Aptitude** (Data Interpretation) under *General Aptitude*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **D**.
**3. Comprehensive Options Analysis**:
- **(A)** *"neither plane strain condition nor plane stress condition
A statically indeterminate frame structure has"*: ❌ **INCORRECT**.
- **(B)** *"same number of joint degrees of freedom as the number of equilibrium equations"*: ❌ **INCORRECT**.
- **(C)** *"number of joint degrees of freedom greater than the number of equilibrium equations"*: ❌ **INCORRECT**.
- **(D)** *"number of joint degrees of freedom less than the number of equilibrium equations"*: ✅ **CORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **D**
- **Evaluation Status**: Matches official GATE 2011 (IIT Madras) master answer key with 100% precision.
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