An eccentric load placed within which of the following central cores of a rectangular column section (width b, depth d) produces no tension in the cross-section?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2011
Detailed Explanation
The book shows four sketches (A)–(D); they are described in words here. In the book's figures (C) and (D) described the same rhombus labelled two ways, so option (c) has been rewritten as the middle-third rectangle, a common wrong idea.
\[ \frac{6e_x}{b} + \frac{6e_y}{d} \le 1 \quad\Rightarrow\quad \text{rhombus with vertices at } \left(\pm\frac{b}{6},0\right),\ \left(0,\pm\frac{d}{6}\right) \]
Why “A rhombus with full diagonals b/3 and d/3” Is Correct
For a load with eccentricities about both axes, no tension requires 6ex/b + 6ey/d ≤ 1 — a rhombus whose full diagonals are b/3 and d/3 (diagram D in the book).
Why the Other Options Are Wrong
- A. A rhombus with full diagonals b/6 and d/6: Diagonals b/6 and d/6 are only half the true core — safe but not the full no-tension zone.
- B. A rhombus with semi-diagonals b/3 and d/3 (full diagonals 2b/3 and 2d/3): Semi-diagonals b/3 and d/3 make the rhombus twice too big; tension would develop near its tips.
- C. A rectangle b/3 × d/3 (the middle-third box): The corners of the middle-third rectangle lie outside the rhombus (6ex/b + 6ey/d = 2 there), so loads near them cause tension.
Key Point
No-tension zone of a rectangle = rhombus with full diagonals b/3 and d/3.
Key Concepts for Students
- Biaxial eccentricity condition: 6ex/b + 6ey/d ≤ 1.
- The middle third applies separately along each axis only.
- Options reworded from the book's sketches.
Practice more: this is question 37 in Columns and Struts MCQs – Part 3. Try the whole set and check every answer instantly.