A prismatic steel bar of length $L = 3\text{ m}$ and cross-sectional area $A = 288\text{ mm}^2$ is subjected to an axial tensile force of $P = 48\text{ kN}$. If Young's modulus $E = 200\text{ GPa}$, what is the total axial elongation of the bar in mm?

Answer Key:

2.48,2.52

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept & Domain Context:** * This question evaluates **Stress and Strain Tensors & Generalized Hooke's Law** under *Strength of Materials & Elasticity* in GATE AE. 2. **Stage 2: Mathematical Derivation:** * Using Hooke's Law: $\delta = \frac{P L}{A E}$. Converting to consistent SI units (N and mm): $P = 48 \times 10^3\text{ N}$, $L = 3 \times 10^3\text{ mm}$, $A = 288\text{ mm}^2$, $E = 200 \times 10^3\text{ N/mm}^2$. Thus $\delta = \frac{(48 \times 10^3)(3 \times 10^3)}{(288)(200 \times 10^3)} = 2.5\text{ mm}$. 3. **Stage 3: Distractor Elimination Forensics:** * The evaluated correct answer is derived using standard physical equations. * Distractor values correspond to typical unit conversion omissions or inverted formulas. 4. **Stage 4: Common Student Trap:** * *Trap:* Omitting the $10^3$ conversion factor between meters and millimeters. *Reference: T.H.G. Megson, Aircraft Structures for Engineering Students (Butterworth-Heinemann).*

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