A cantilever
beam is a horizontal, rigid structural component that is supported at one fixed
end and free at the other. They bear load in the form of bending. When a
horizontal force is applied to the free end in the cantilever, it transfers
those forces to the column through the fixed end and then to the foundation and
ultimately to beneath the ground, where those forces are re-distributed among
the soil.

We often observe cantilever beam below our balcony, bridges, etc.

Cantilever beams are made trapezoidal because of the bending moment acting on them. We should provide more depth to the structure where there is more bending moment acting upon. Otherwise, the structure will collapse due to more bending or turning effect of the structure.

1. 1. When
a point force is acted upon a Cantilever beam

Let us consider a weight (W) is acted upon a free end of the cantilever beam of length (l).

∑Fy =0

+w-Ry=0

Ry=W

*W at free end tends to bend the beam
downward. So, there is production of maximum bending moment in the fixed or
support end. Hence to counter the maximum bending moment produced in the fixed
end, more depth is provided in fixed end than in free end. Otherwise, the beam
will collapse or shear off.*

From bending moment
diagram as well, maximum bending moment (Wl) is acted upon the fixed end of the
cantilever beam and zero bending moment is acted on the free end of the
cantilever beam even though weight is applied to the free end of the beam.

Since the bending moment is maximum at the fixed end, more
depth should be provided in the fixed end to avoid collapse of the structure
due to the turning effect and minimum depth should be provided at the free end
of the cantilever beam.

2. When a uniformly distributed load is acted upon the beam

For uniformly distributed load as well, the maximum bending
moment(WL^2/2) will be acted upon on the fixed end of the beam. So, the depth
should be maximum on the fixed end of the cantilever beam.

We often see beams of rectangle shape as well. If we prefer
on putting rectangle beams, then we must construct a beam of relatively more
depth. Otherwise, due to the dead load on the free end, there is a high chance
of collapse. Also, trapezoidal beams are more economical than rectangular
beams. Rectangle beams only increases the cost of project. It does not have any
significance.

1.

nice information....

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