What is Cantilever Beam? | Shear Force and Bending Moment diagram of Cantilever

The beams are most commonly used all over the world to support different loads. A cantilever is a rigid structural member that extends horizontally. One end of the cantilever is fixed while the other end is free. Like other structural beams, the cantilever may also form as a slab, truss, plate, or beam. These beams usually extend from a flat vertical surface (such as a wall). The beam should be connected firmly to the vertical surface.  

When a cantilever experiences structural loading at its unsupported distal end, it transmits the load to support on which it exerts bending moments and shear stresses.

What is Cantilever Beam?

A cantilever beam is a rigid bar or beam whose one end is free while the other end is fixed to a support (usually a vertical wall or structure). The load acting on the beam’s free end creates a bending moment and reaction force on the fixed end. The cantilever beams serve to produce a bending effect within specific limits.

Cantilever beam

These types of beams transfer the load to the support, where they can manage shear force and bending moment. Shear stress is a force applied parallel to the material surface. The bending moment is the ability of the beam to rotate or twist the object.

A swimming pool diving platform is one of the best examples of a cantilever beam. The aircraft wings that carry wind force are also a most popular example of cantilever beams.

In a bridge, a cantilever is part of a cantilever girder, and in the buildings, a cantilever is constructed as an extension of the continuous beam.

In building construction, cantilever beams are used for multiple purposes, such as they use to carry a roof, gallery, or runway for an overhead traveling crane. They also use in armories, exhibition buildings, large halls, shelves, and sheds.

For large lengths in some special sites, cantilever construction is particularly ideal for bridge construction and heavy loads on the Scottish Forth Bridge, which consists of three cantilever spans and two connected cantilever spans.

Structural Behavior of Cantilever Beam

Cantilever beams bend downwards when a vertical load puts on them. These beams have the ability to carry uniform loads, point loads, or variable loads.

Structural Behavior of Cantilever Beam

Regardless of the load type, the beam bends down and forms a convexity upward. This bending causes compression in the lower fiber and tension in the upper fiber. Therefore, the high tensile stress places on the main reinforcement to the concrete beam’s upper fiber.

Shear Force (SF) and Bending Moment (BM) Diagram of Cantilever Beam

The shear force at any section of the cantilever beam is the sum of the loads between the free end and the section. The bending moment at a given section of the cantilever is the sum of the moments acting on the section from all loads between the free end and the section.

Shear Force and Bending Moment diagram of the cantilever Beam

Let’s explain with an example. Consider a cantilever beam AB of length ‘L.’ A load ‘W’ is applied on the free end B. The beam is divided into two sections. A section X-X from the end B is placed. This section has a distance ‘x’ from the end B. A shear force Rx is applied on sections X-X. This shear force is equal to W. Section X-X has Mx bending moment. This bending moment is equal to W.x.

The shear force and bending moment on the fixed end A are calculated by fixing the section at A. According to the above given S.F diagram and B.M diagram, the shear force and bending moment at A are given below

Bending Moment = Ma = W.l

Shear force = Ra = W

The cantilever has the lowest bending moment at the free end, while it has the highest bending moment at the fixed end. To make a cantilever beam for a structure, first, you need to determine the shear force and bending moment diagram for all possible loads. According to design standards, the load employed to a beam is the combination of static and live loads.

Design of Cantilever Beam

Cantilever beams under the action of structural load generate shear stress and bending moment. The main purpose of the beam design process is to shift shear stresses to the reinforcement carefully.

The cantilever has the lowest bending moment at its free end while it has the highest bending moment at the fixed end. Therefore, to design a cantilever beam, the main support is placed in the concrete beam upper fiber to safely bear the tensile stress.

The maximum span of a cantilever usually depends on the below-given parameters:

  1. Type and quality of the material
  2. Depth of cantilever
  3. The load location, type, and size

The span of the small cantilever beam varies from 2 m to 3 m. However, you can increase the span by improving the depth or prestressed structural member or using steel. The span may be built longer by considering that the structure can counter the moment produced by the cantilever and safely transmit it to the ground. Detailed structural analysis and design may assist to explore the potential of the long-span cantilever.

To minimize the overturning impact, you must properly attach your beam to the support or wall.

Advantages Of Cantilever Beam

  1. The cantilever beam has simple and easy construction.
  2. The cantilever has high stiffness due to its depth.
  3. It requires only one support to fix one end, while the other end doesn’t require support.
  4. These types of beams are less invasive.
  5. Because the beam is only mounted on the arm, it is fairly easy to maintain ground motion and thermal expansion.
  6. The cantilever generates negative bending moments, which help to counter the positive bending moments generated somewhere else. 

Disadvantages Of Cantilever Beam

  1. The cantilever beam has a large deflection.
  2. It has larger bending moments.
  3. The beam has maximum load at the fixed end when the load is applied at one end. Therefore, your beam may break from the support if you apply more load.
  4. For this beam, you need a back span or fixed support and inspection for the uplift of the far support.

Applications of Cantilever Beams

The cantilever beams are most commonly used for the following applications:

  1. Furniture and Shelving
  2. Overhanging roofs such as stadium roofs
  3. Buildings
  4. Cantilever bridges
  5. Plants and machinery such as cranes
  6. Overhanging elements and projections
  7. Balconies

FAQ Section

What is a cantilever beam?

A cantilever beam is a rigid bar or beam whose one end is free while the other end is fixed to a support. Steel or concrete is most commonly used to construct cantilever beams. One end of the beam is attached to vertical support or wall. This is a horizontal beam that contains a vertical load at the free end.

How does a cantilever beam behave under loads?

Cantilever beams bend in a downward direction under vertical loads. These beams have the ability to bear uniform loads, point loads, and variable loads.

Regardless of the load type, the beam bends down and forms a convexity upward. This bending causes compression in the lower fiber and tension in the upper fiber. Therefore, the high tensile stress places on the main reinforcement to the concrete beam’s upper fiber.

What is the maximum span of cantilever beams?

The small cantilevers have a span between 2 m and 3 m. However, you can increase the span by improving the depth or prestressed structural member or using steel.

The span can be built longer by considering that the structure may counter the moment produced by the cantilever and safely transmit it to the ground. Detailed structural analysis and design may assist to explore the potential of the long-span cantilever.

What are the examples of the cantilever beam?

The balcony is one of the most common examples of the cantilever beam. One end of the balcony is free, while the other end is attached to a support. The swimming pool diving platform is another example of a cantilever.

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