Define simply supported beam.

Short Answer:

A simply supported beam is a type of beam that is supported at both ends, usually with one end resting on a hinge (or pin) and the other on a roller. These supports allow the beam to freely rotate and prevent translation in vertical directions but not in horizontal directions.

It is the most common and basic type of beam used in engineering. The simply supported beam carries loads that act perpendicular to its length and transfers the reactions to its supports. It can easily resist bending moments and shear forces caused by applied loads such as point loads and uniformly distributed loads.

Detailed Explanation:

Simply Supported Beam

A simply supported beam is one of the most fundamental and widely used beam types in structural and mechanical engineering. It consists of a horizontal beam supported at its two ends — one with a hinged or pinned support and the other with a roller support. These supports allow the beam to rotate but do not permit vertical movement, which means the beam can bend under loads but cannot move up or down at the supports.

This type of beam is simple in design and easy to analyze because its reactions can be determined using the basic equilibrium equations of statics:

Since the beam is free to rotate at both ends, no moment is developed at the supports. The bending moment is maximum somewhere between the supports, depending on the load position.

Construction and Support Conditions

A simply supported beam usually has two supports:

  1. Pinned or Hinged Support:
    • It prevents both vertical and horizontal movements but allows rotation.
    • Commonly used as one end support in beams to hold the structure firmly in position.
  2. Roller Support:
    • It prevents vertical movement but allows both rotation and horizontal movement.
    • This helps the beam adjust to any expansion or contraction due to temperature or load changes.

The combination of these two supports allows the beam to bend freely under load while maintaining overall stability. This simple arrangement makes it one of the most used structural elements in buildings, bridges, and machines.

Loading Conditions on a Simply Supported Beam

A simply supported beam can be subjected to different types of loads depending on the application. The main types include:

  1. Concentrated or Point Load:
    • A load acting at a specific point on the beam.
    • It produces a triangular bending moment diagram, with the maximum bending moment occurring under the point load.
  2. Uniformly Distributed Load (UDL):
    • Load spread evenly over the entire length or part of the beam.
    • Produces a parabolic bending moment diagram with maximum bending moment at the center.
  3. Uniformly Varying Load (UVL):
    • Load intensity varies from one end to the other.
    • Common in beams subjected to wind or fluid pressure.
  4. Combination of Loads:
    • In real-life applications, beams may experience a combination of point loads and distributed loads simultaneously.

Each load type affects the beam differently, and engineers calculate bending moment (M), shear force (V), and deflection (δ) to ensure safety and design efficiency.

Shear Force and Bending Moment in a Simply Supported Beam

When a beam is loaded, two main internal forces develop:

  1. Shear Force (V):
    • It is the force that acts along the cross-section of the beam to resist sliding of one layer over another.
    • It is maximum near the supports and zero at the point of maximum bending moment.
  2. Bending Moment (M):
    • It is the moment that causes the beam to bend due to external loads.
    • In a simply supported beam, the bending moment is zero at both supports and maximum at the point where shear force changes sign.
    • For a uniformly distributed load, the maximum bending moment occurs at the mid-span and is given by:

where w = load per unit length and L = span of the beam.

The analysis of shear and bending helps in determining the required beam dimensions to avoid failure.

Deflection of a Simply Supported Beam

When a load is applied to a simply supported beam, it bends downward, causing deflection. The amount of deflection depends on:

  • The magnitude and type of load.
  • The span length (L).
  • The material properties (Elastic Modulus, E).
  • The cross-sectional shape (Moment of Inertia, I).

The deflection for a simply supported beam with a uniformly distributed load is given by:

where,
w = load per unit length,
L = length of beam,
E = modulus of elasticity,
I = moment of inertia.

To ensure safety, the deflection should not exceed permissible limits as specified by design codes.

Advantages of Simply Supported Beam

  1. Easy Design and Analysis:
    • Reactions can be calculated easily using basic equilibrium equations.
  2. Simple Construction:
    • Easy to fabricate and install with minimal material requirements.
  3. Economical:
    • Reduces cost compared to fixed or continuous beams.
  4. Adaptable:
    • Suitable for a wide range of materials, including wood, steel, and reinforced concrete.
  5. Efficient for Short Spans:
    • Ideal for small to medium span structures such as bridges and floors.

Disadvantages of Simply Supported Beam

  1. Higher Deflection:
    • Compared to fixed or continuous beams, simply supported beams bend more under the same load.
  2. No Moment Resistance at Supports:
    • Since supports allow rotation, the beam cannot resist bending moments at the ends.
  3. Less Rigid:
    • Not suitable for very long spans or heavy loads.
  4. More Material Required for Long Spans:
    • To control deflection and bending, larger beam sections are needed for longer spans.

Applications of Simply Supported Beam

  1. Bridge Girders:
    • Used to support bridge decks with loads from vehicles or pedestrians.
  2. Building Structures:
    • Used in floors, roofs, and lintels over doors and windows.
  3. Cranes and Machinery:
    • Used in overhead beams that support hoisting equipment.
  4. Railway Platforms:
    • Used to support covering sheds and canopies.
  5. Small Span Structures:
    • Ideal for footbridges and lightweight structures.
Conclusion

A simply supported beam is a basic structural member supported at both ends, free to rotate but restricted in vertical movement. It is one of the simplest and most widely used beam types due to its easy analysis, economical design, and adaptability. It effectively resists bending and shear forces and is commonly used in buildings, bridges, and machines. Although it deflects more than fixed beams, its simplicity and efficiency make it a fundamental element in structural and mechanical engineering.