Subtopic: Bending of Unsymmetrical Thin-Walled Sections
Question Statement:
The cross-section of a long thin-walled member is as shown in the figure. When subjected to pure
twist, point A
Options:
(A) does not move horizontally or axially, but moves vertically
(B) does not move axially, but moves both vertically and horizontally
(C) does not move horizontally, vertically or axially
(D) does not move vertically or axially, but moves horizontally
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.16)**
**1. Problem Statement & Parameters**:
- **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ)
- **Topic**: Basic Fluid Mechanics (Conservation Equations of Mass, Momentum & Energy)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> The cross-section of a long thin-walled member is as shown in the figure. When subjected to pure twist, point A
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Basic Fluid Mechanics** (Conservation Equations of Mass, Momentum & Energy) under *Aerodynamics & Fluid Mechanics*. 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"does not move horizontally or axially, but moves vertically"*: ❌ **INCORRECT**.
- **(B)** *"does not move axially, but moves both vertically and horizontally"*: ✅ **CORRECT**.
- **(C)** *"does not move horizontally, vertically or axially"*: ❌ **INCORRECT**.
- **(D)** *"does not move vertically or axially, but moves horizontally"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.