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:
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.
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.
The diagram below shows a schematic representation of this type of 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:
Interested in our courses?
Interested in civil engineering? Find out more about all the civil engineering courses we have available by clicking here.
Diploma in Sustainable Construction
Diploma in Structural Engineering
Diploma in Building and Construction Engineering
Higher International Certificate in Civil Engineering
Higher International Diploma in Civil Engineering
Alternatively, you can view all our online engineering courses here.
Recent Posts
Kirchhoff’s current and voltage laws
Kirchhoff’s current and voltage laws In our last article, we looked at the principles and operation of a d.c motor. In this article, we’re going to investigate Kirchoff’s current and voltage laws, as well as how to apply them to engineering problems. Kirchoff’s law of current Kirchoff’s law of current states that the algebraic sum […]
What are the principles of operation of a DC electric motor?
What are the principles of operation of a DC electric motor? In our last article, we looked at the electrical parameters in series and parallel electrical circuits. In this article, we’re going to dive into the principles of operation of a DC electric motor. The motor effect When a current-carrying conductor is placed on a […]
What are the electrical parameters in series and parallel electrical networks?
What are the electrical parameters in series and parallel electrical networks? In our last article, we looked at the principles of operation of electrical cells. In this article we’re going to move on to the electrical parameters in both series and parallel electrical networks. When we have circuits with more than one resistor, we need […]