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What is a cantilever beam and how can we calculate its deflection?

You may have read our previous article about beams and their deflection.  The article talked about deflection in general – what it is and how can it be determined.  Now we’re going to dive a little deeper and focus on cantilever beams and their deflection.

What is a cantilever beam?

Cantilever beams are beams that are constrained at one end and free at the other.  At the fixed, or restrained, end of the beam the slope and deflection must be zero.  Deflection increases as we move towards the free end, with maximum deflection at the tip.

Some examples of cantilever beams in construction are:

example of a cantilever beam
example of a cantilever beam
example of a cantilever beam

Cantilever beams can be either end-loaded or uniformly loaded.  There’s a great video here giving us details on the slope and deflection along the beam.

End-loaded cantilever beams

Here the load is applied at a single point on the beam.  The first diagram below shows a cantilever beam with a deflected shape.  The second diagram shows a cantilever beam carrying a point load at its free end.

cantilever beam with a deflected shape
a cantilever beam carrying a point load at its free end

Uniformly loaded cantilever beams

These types of beams have the force acting uniformly along its length.  An example of a cantilever beam carrying uniformly distributed load (UDL) would be a balcony.

example of a cantilever carrying UDL

The diagram below shows a schematic representation of this type of cantilever beam.

schematic representation of a cantilever beam

Standard data table for cantilever beam deflection and slope.

The most practical and fastest way to calculate the deflection and slope of a beam is to use standard tables.  There are quite a few beam deflection tables that can be used.

For a cantilever beam subjected to a single type of loading, for example a point or concentrated load, uniformly distributed load, deflection and slope can be determined using the formulae in the table below:

standard table to calculate beam deflection

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