Find the effective length of an isolated cantilever RCC beam as per IS 456-2000, where the length from the free end to the face of support is 1 m, the effective depth of the beam is 400 mm and the width of support is 300 mm.
- A1.4 m
- B1.15 m
- C1.3 m
- D1.2 mCorrect
Solution
Concept
As per IS 456:2000, the effective length of a cantilever is its length to the face of the support plus half the effective depth. The exception is when it forms the end of a continuous beam; then the length to the centre of the support is used.
Formula
Leff = Lclear + d/2
Step-by-step solution
1. The beam is an isolated cantilever, not the end of a continuous beam. 2. Length from free end to face of support = 1 m. 3. Effective depth d = 400 mm = 0.4 m, so d/2 = 0.2 m. 4. Leff = 1 + 0.2 = 1.2 m. 5. Support width (300 mm) is not used for an isolated cantilever.
Explanation
For an isolated cantilever, IS 456 takes the length to the face of support plus half the effective depth. So Leff = 1 + 0.4/2 = 1.2 m. The support width is given only to confuse.
Why the other options are wrong
A (1.4 m): adds full d (1 + 0.4); wrong. B (1.15 m): adds half the support width (1 + 0.15); this rule is for a cantilever at the end of a continuous beam. C (1.3 m): adds d/2 + something extra (or support width); no such rule.
Shortcut
Isolated cantilever: clear length + d/2.
Common mistake
Using half the support width (centre of support) instead of d/2. That rule applies only when the cantilever is the end of a continuous beam.
Correct answer: D) 1.2 m