Calculate the slenderness ratio and classify the column type in accordance with IS 456 : 2000, if the diameter of column is 300 mm and effective length 3 m.
- A8; long column
- B13; long column
- C10; short columnCorrect
- D15; short column
Solution
Concept
As per IS 456:2000, a column is short if the ratio of effective length to lateral dimension (or diameter) is less than 12. Otherwise it is long (slender).
Formula
λ = lex / D; short column if λ < 12
Step-by-step solution
1. Effective length lex = 3 m = 3000 mm. 2. Diameter D = 300 mm. 3. Slenderness ratio = 3000 / 300 = 10. 4. IS 456 limit for a short column is 12. 5. Since 10 < 12, the column is a short column.
Explanation
IS 456 uses effective length divided by lateral dimension (here the diameter) as the slenderness ratio. The ratio is 3000/300 = 10. This is less than 12, so the column is short.
Why the other options are wrong
A: The ratio is 10, not 8, and a ratio of 8 would also give a short column, not a long one. B: The ratio is not 13. D: The ratio is not 15, and a ratio of 15 is more than 12, which would make the column long, not short.
Shortcut
Divide lex by D and compare with 12.
Common mistake
Using the radius of gyration (l/r) instead of l/D. IS 456 uses the lateral dimension for this classification.
Correct answer: C) 10; short column