What is a cantilever beam?

Short Answer:

A cantilever beam is a type of beam that is fixed at one end and free at the other end. It carries loads along its length, which act perpendicular to its axis, creating bending and shear stresses within the beam. The fixed end resists both the bending moment and the shear force caused by the applied load.

In simple terms, a cantilever beam is supported firmly at one end, while the other end projects freely in space. It is commonly used in balconies, bridges, and projecting structures where one end needs to remain unsupported. The main characteristic of a cantilever beam is that all reactions and moments occur only at the fixed end.

Detailed Explanation :

Cantilever Beam

A cantilever beam is a structural member that extends horizontally and is supported rigidly at one end while the other end remains free. It is one of the most common and important beam types used in engineering structures. The loads on a cantilever beam act perpendicular (transverse) to its length, causing bending moments and shear forces in the beam.

The fixed end of the beam provides all the necessary reactions—vertical, horizontal, and moment reactions—to keep the beam stable. The free end of the beam, being unsupported, experiences maximum deflection when the load is applied.

Cantilever beams are widely used in structures where overhanging projections are needed, such as in balconies, canopies, and aircraft wings.

Characteristics of Cantilever Beam

  1. Support Condition:
    One end of the beam is rigidly fixed into a wall or column, and the other end is free.
  2. Type of Loading:
    The load may be a point load, uniformly distributed load (UDL), or varying load acting along the beam length.
  3. Internal Forces:
    • The fixed end develops bending moment, shear force, and axial reaction to resist the applied load.
    • The free end has no reaction because it is unsupported.
  4. Deflection:
    The maximum deflection occurs at the free end of the beam.
  5. Applications:
    Cantilever beams are used in balconies, roofs, bridges, traffic signals, diving boards, and cranes.

Bending Moment and Shear Force in Cantilever Beam

The main internal forces developed in a cantilever beam under load are bending moment (M) and shear force (V).

  1. For a Cantilever Beam with Point Load (W) at the Free End:
    • Shear Force (V): Constant throughout the beam and equal to .
    • Bending Moment (M): Varies linearly from zero at the free end to a maximum at the fixed end.

At the fixed end (x = L),

  1. The negative sign indicates that the bending moment acts opposite to the applied load direction.
  2. For a Cantilever Beam with Uniformly Distributed Load (w) per unit length:
    • Shear Force (V):
    • Bending Moment (M):
  1. The maximum bending moment occurs at the fixed end.

In both cases, the maximum bending moment and maximum shear force occur at the fixed support, making it the most critical section of the beam.

Deflection in Cantilever Beam

When loads act on a cantilever beam, it bends downward (or upward depending on load direction). The deflection (δ) depends on the type of load, beam material, length, and moment of inertia of the cross-section.

  1. For a Point Load (W) at Free End:
  1. For a Uniformly Distributed Load (w):

Where,

  •  = deflection,
  •  = modulus of elasticity,
  •  = moment of inertia of the beam’s cross-section,
  •  = length of the beam.

The deflection is maximum at the free end and zero at the fixed end.

Advantages of Cantilever Beam

  1. No Need for Intermediate Support:
    Cantilever beams can project beyond the support without additional columns, allowing for free space below.
  2. Simple Construction:
    Only one end needs to be fixed, which simplifies the support design.
  3. Architectural Flexibility:
    Suitable for creating extended portions like balconies, canopies, and bridges.
  4. Efficient for Overhanging Structures:
    Ideal where free space or overhanging parts are required.
  5. Can Carry Concentrated or Distributed Loads:
    They are versatile and can handle various load types efficiently.

Disadvantages of Cantilever Beam

  1. High Bending at Fixed End:
    The fixed support experiences very high bending moments, which requires strong reinforcement or support.
  2. Deflection is Large:
    Deflection at the free end is more compared to other beam types.
  3. Complex Design:
    The analysis and design of cantilever beams are more complicated due to combined bending and shear at the fixed end.
  4. Difficult Support Construction:
    Fixing one end firmly into a wall or column demands careful construction and additional reinforcement.

Applications of Cantilever Beam

  • Balconies: Support overhanging platforms without vertical supports.
  • Bridge Girders: Used in cantilever bridges for long spans.
  • Traffic Light Poles: The light arm acts as a cantilever beam.
  • Aircraft Wings: Wings are fixed at the fuselage and free at the outer end.
  • Crane Jibs: The projecting arm of cranes behaves as a cantilever.
  • Building Roofs and Canopies: Used to support projections without pillars.

Cantilever beams are especially preferred where space below the structure must remain unobstructed.

Behavior of Cantilever Beam under Load

  • The top surface of a cantilever beam under downward load is in tension, and the bottom surface is in compression.
  • The neutral axis runs through the center of the beam’s cross-section, where the stress is zero.
  • Failure generally starts at the fixed end due to maximum bending moment.
Conclusion

In conclusion, a cantilever beam is a beam that is rigidly fixed at one end and free at the other. It experiences bending and shear when loads act along its length. The fixed end carries all the reactions, while the free end experiences the maximum deflection. Cantilever beams are widely used in engineering structures like balconies, bridges, and cranes due to their ability to project beyond supports. Proper design of the fixed end and selection of material are crucial for ensuring safety, stability, and performance of cantilever beams.