A rectangular beam cross-section has width $b = 100\text{ mm}$ and depth $h = 200\text{ mm}$. What is the section modulus $Z$ of the cross-section about its neutral axis?

(A) 666.7 \times 10^3\text{ mm}^3

(B) 1333.3 \times 10^3\text{ mm}^3

(C) 333.3 \times 10^3\text{ mm}^3

(D) 66.7 \times 10^6\text{ mm}^3

Answer Key:

A

### 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:** * For a rectangular beam: moment of inertia $I = \frac{b h^3}{12}$, distance to extreme fiber $y_{\max} = \frac{h}{2}$. Section modulus $Z = \frac{I}{y_{\max}} = \frac{b h^2}{6} = 666.7 \times 10^3\text{ mm}^3$. 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:* Using $b h^3 / 12$ (moment of inertia) instead of $b h^2 / 6$ (section modulus). *Reference: T.H.G. Megson, Aircraft Structures for Engineering Students (Butterworth-Heinemann).*

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