Following IS : 2502-1963, determine the approximate total length of bar of 6 mm diameter, measured along centre line, for the stirrup shown in Figure [Circular stirrup with internal diameter 26 cm and two hooks]. (Note: Take the given stirrup dimensions in Figure as internal).
- A0.448 m
- B0.884 mCorrect
- C0.848 m
- D0.440 m
Solution
Concept
Cutting length of a circular stirrup = centre-line circumference + hook allowances.
Formula
L = π (Di + d) + hook allowance
Step-by-step solution
1. Internal diameter Di = 26 cm and bar diameter d = 0.6 cm. 2. Centre-line diameter = 26 + 0.6 = 26.6 cm. 3. Centre-line circumference = π × 26.6 = 83.57 cm. 4. Add hook allowance for two hooks: about 2 × 4d = 2 × 2.4 = 4.8 cm (assumed). 5. L = 83.57 + 4.8 = 88.4 cm, which is about 0.884 m.
Explanation
The length of a bar is measured along its centre line, so half the bar diameter is added on each side of the internal diameter. The circumference at the centre line is then found, and the length of the two hooks is added to it. The result is about 0.884 m.
Why the other options are wrong
A and D: These values are about half of one circumference, which is too small. C: 0.848 m is roughly the circumference alone, with almost no hook length added.
Shortcut
π × 26.6 ≈ 83.6 cm; only option B is a little more than this, which allows for the hooks.
Common mistake
Using the internal diameter (π × 26) instead of the centre-line diameter, or forgetting to add the hooks.
Correct answer: B) 0.884 m