A simply supported beam of span 5 m is reinforced with ‘n’ number of 20φ bars at mid-span placed at an effective depth of 300 mm. If the location of the theoretical cut-off point for curtailing ‘n/2’ bars is found at 1.5 m from the mid-span, then the distance of the actual cut-off point from the support will be
- A1.8 m
- B1.74 m
- C0.76 m
- D0.70 mCorrect
Solution
Concept
According to IS 456 (Clause 26.2.3.3), curtailed reinforcement must extend beyond the theoretical cut-off point by at least 12φ or effective depth 'd', whichever is greater, to provide adequate anchorage.
Formula
Actual cut-off distance from support = Distance of theoretical cut-off from support - max(12φ, d)
Step-by-step solution
1. Identify the span of the simply supported beam = 5 m, hence mid-span is at 2.5 m from the support. 2. Locate the theoretical cut-off point from the mid-span = 1.5 m. Therefore, the distance of the theoretical cut-off point from the support = 2.5 m - 1.5 m = 1.0 m. 3. Determine the required extension beyond the theoretical cut-off point: max(12φ, d) = max(12 × 20 mm, 300 mm) = max(240 mm, 300 mm) = 300 mm = 0.3 m. 4. Calculate the actual cut-off distance from the support = 1.0 m - 0.3 m = 0.70 m.
Explanation
According to IS 456, the actual cut-off point of reinforcement bars must extend beyond the theoretical cut-off point by a distance equal to at least 12 times the bar diameter (12φ) or effective depth of the member (d), whichever is greater.
Why the other options are wrong
A: Incorrect calculation. B: Incorrect calculation. C: Uses 12φ incorrectly instead of max(12φ, d). D: Correct distance from the support.
Shortcut
Remember that the actual cut-off point is shifted away from the zone of maximum bending moment (towards the support) by an amount equal to max(12φ, d).
Common mistake
Adding the extension value to the distance from the support instead of subtracting, or forgetting to check both 12φ and d.
Correct answer: D) 0.70 m