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.

Concept

Effective span

A. Simply supported beams and slabs (leff)

\({{\rm{l}}_{{\rm{eff}}}} = {\rm{minimum}}\left\{ {\begin{array}{*{20}{c}} {{l_o} + w}\\ {{l_o} + d\;} \end{array}} \right.\)

Here, lo = clear span

w = width of the support

d = depth of beam or slab

B. For continuous beam

i) If the width of support \( < \frac{1}{{12}}\) of the clear span

\({{\rm{l}}_{{\rm{eff}}}} = {\rm{minimum}}\left\{ {\begin{array}{*{20}{c}} {{l_o} + w}\\ {{l_o} + d\;} \end{array}} \right.{\rm{\;}}\)

ii) If the width of support \(> \frac{1}{{12}}\) of the clear span

a) When one end is fixed and other end is continuous or both ends are continuous.

\({{\rm{l}}_{{\rm{eff}}}} = {{\rm{l}}_{\rm{o}}}\)

b) When one end is continuous and another end is simply supported.

\({{\rm{l}}_{{\rm{eff}}}} = {\rm{minimum}}\left\{ {\begin{array}{*{20}{c}} {{l_o} + \frac{w}{2}}\\ {{l_o} + \frac{d}{2}\;} \end{array}} \right.{\rm{\;}}\)

C. Cantilever

i) Normally

\({l_{eff}} = {l_o} + \frac{d}{2}\)

Where lo is the clear span

ii) In form of the end of the continuous beam

\({l_{eff}} = \left( {{l_o} + \frac{w}{2}} \right)\)

Calculation:

l₀ = 1 m

d = 400 mm

w = 300 mm

Hence,

\({l_{eff}} = {l_o} + \frac{d}{2}\) = 1 + (0.400/2) = 1.2 m