Design of Beams MCQ with answer and solution

Concept

As per IS 456:2000 Cl. 22.2, the effective length of a cantilever is its length to the face of the support plus half the effective depth.

Formula

L_eff = L_clear + d/2

Step-by-step solution

1. IS 456:2000 Cl. 22.2 gives the effective span for different beams. 2. For a cantilever, the effective length = length to the face of support + d/2. 3. Here d is the effective depth of the beam. 4. Exception: if the cantilever is the end of a continuous beam, take the length up to the centre of the support. 5. So the answer is option B.

Explanation

For a cantilever, IS 456 takes the effective length as the clear projection from the support face plus half the effective depth. This accounts for the support reaction acting a little inside the support face. If the cantilever is the end part of a continuous beam, the length is measured to the centre of the support.

Why the other options are wrong

A: Half the support width is not used for a normal cantilever. Centre of support is used only for the end of a continuous beam. C: The code adds d/2, not the full effective depth d. D: The full support width is not added in any IS 456 rule.

Shortcut

Cantilever: clear length + d/2.

Common mistake

Mixing up the cantilever rule with the simply supported beam rule, which takes the lesser of (clear span + d) and c/c distance of supports.