The allowable stress in a long column can be increased by increasing the:
Try it first: pick an option, then read the explanation.
Correct answer: A. radius of gyration
Asked in SSC JE 2012
Detailed Explanation
The safe stress of a long column falls as its slenderness ratio rises: σcr = π²E/λ².
\[ \sigma_{cr} = \frac{\pi^2E}{(l_e/r)^2} = \frac{\pi^2E\,r^2}{l_e^2} \]
Why “radius of gyration” Is Correct
Increasing the radius of gyration reduces λ and raises the allowable stress.
Why the Other Options Are Wrong
- B. eccentricity: Eccentricity adds bending and lowers the safe load.
- C. slenderness ratio: A higher slenderness ratio lowers the allowable stress.
- D. length of the column: A longer column is more slender and weaker.
Key Point
Allowable stress ↑ when r ↑ (λ ↓). Spread material away from the centroid.
Key Concepts for Students
- Tubes and built-up sections maximise r.
- Bracing reduces le and so λ.
- Allowable stress tables (IS 800) are given against λ.
Practice more: this is question 28 in Columns and Struts MCQs – Part 2. Try the whole set and check every answer instantly.