The core of a circular section short column of diameter d is a concentric circular area having a diameter of:
Try it first: pick an option, then read the explanation.
Correct answer: A. d/4
Asked in SSC JE 01/03/2017 (Evening)
Detailed Explanation
The core (kern) is the region within which a compressive load can act without causing tension anywhere. Its boundary is where P/A = Pe/Z, i.e. e = Z/A.
\[ e_{max} = \frac{Z}{A} = \frac{\pi d^3/32}{\pi d^2/4} = \frac{d}{8} \quad\Rightarrow\quad \text{core diameter} = 2\times\frac{d}{8} = \frac{d}{4} \]
Why “d/4” Is Correct
The core is a concentric circle of diameter d/4.
Why the Other Options Are Wrong
- B. d/3: d/3 resembles the rectangle's middle-third diagonal, not the circle's core.
- C. d/2: d/2 is far too large — tension would develop.
- D. d/8: d/8 is the core radius (max eccentricity), not its diameter.
Key Point
Solid circle: core diameter d/4 (e ≤ d/8). Rectangle: rhombus b/3 × d/3.
Key Concepts for Students
- Core boundary: e = Z/A = r²/y.
- Hollow circle: e ≤ (D² + d²)/(8D).
- Masonry chimneys and piers are checked with the core.
Practice more: this is question 33 in Columns and Struts MCQs – Part 3. Try the whole set and check every answer instantly.