A short column of symmetric (rectangular) cross-section of width h, made of a brittle material, carries a vertical load P at an eccentricity e from the centre line. To avoid tensile stress, e should be less than or equal to:
Try it first: pick an option, then read the explanation.
Correct answer: B. h/6
Asked in SSC JE 03/03/2017 (Morning)
Detailed Explanation
Brittle materials (masonry, plain concrete, cast iron) are weak in tension, so the stress on the far face must not become tensile.
\[ \sigma_{min} = \frac{P}{bh} - \frac{Pe}{bh^2/6} = \frac{P}{bh}\left(1 - \frac{6e}{h}\right) \ge 0 \;\Rightarrow\; e \le \frac{h}{6} \]
Why “h/6” Is Correct
The eccentricity must not exceed h/6 — the middle-third rule.
Why the Other Options Are Wrong
- A. h/12: h/12 is safe but over-restrictive — it is not the limit.
- C. h/3: h/3 is the width of the middle third, not the eccentricity limit.
- D. h/2: h/2 puts the load at the edge; heavy tension develops.
Key Point
Rectangle: no tension if e ≤ h/6 (load within the middle third).
Key Concepts for Students
- σmax = (P/A)(1 + 6e/h).
- At e = h/6, stress varies from 0 to 2P/A.
- Circle limit: e ≤ d/8.
Practice more: this is question 35 in Columns and Struts MCQs – Part 3. Try the whole set and check every answer instantly.