Short Answer:

A simply supported beam is a type of beam that is supported at both ends, usually by a hinge or pin at one end and a roller at the other. These supports allow the beam to freely rotate and expand or contract horizontally but prevent vertical movement. It mainly resists bending and shear stresses caused by loads applied along its length.

In simple words, a simply supported beam is a freely resting beam that carries transverse loads and transfers them to its two supports. It is the most basic and commonly used beam type in construction and mechanical structures such as bridges, roofs, and floors.

Detailed Explanation :

Simply Supported Beam

A simply supported beam is one of the most fundamental and widely used types of beams in mechanical and structural engineering. It is a horizontal structural member that is supported at both ends, allowing it to rotate freely but not translate vertically. The beam is subjected to loads that act perpendicular (transverse) to its length, causing it to bend and develop internal stresses.

This beam provides simple support conditions, meaning it cannot resist any moment at the supports but can transfer shear force and bending moment along its span. Because of its simplicity and predictable behavior, it is used extensively in buildings, bridges, machine parts, and other structures.

Support Conditions of Simply Supported Beam

A simply supported beam has two main supports:

Pinned (Hinged) Support:
- One end of the beam is provided with a pin or hinge.
- It restricts vertical and horizontal movement but allows rotation.
- It provides both vertical and horizontal reactions.
Roller Support:
- The other end rests on rollers.
- It prevents vertical movement but allows horizontal movement and rotation.
- It provides only a vertical reaction.

These two supports together allow the beam to bend freely under load, avoiding the development of restraint moments at the supports.

Types of Loads Acting on Simply Supported Beam

The beam can be subjected to different types of loads depending on its application, such as:

Concentrated (Point) Load:
- A load acting at a single point along the beam.
- Produces maximum bending moment at the point of load application.
Uniformly Distributed Load (UDL):
- A load distributed evenly along the entire length of the beam.
- Creates a parabolic bending moment distribution.
Uniformly Varying Load (UVL):
- Load intensity varies along the beam length (triangular or trapezoidal pattern).
Combination of Loads:
- A beam may have multiple types of loads acting simultaneously, like UDL and point loads.

Internal Forces in Simply Supported Beam

When loads act on a simply supported beam, internal forces are developed within the beam material to resist deformation. These forces are:

Shear Force (V):
- The internal force that acts parallel to the cross-section of the beam.
- It prevents sliding of one part of the beam over another.
- Maximum shear force usually occurs at or near the supports.
Bending Moment (M):
- The internal moment that causes the beam to bend under applied loads.
- Maximum bending moment generally occurs at the midspan (for symmetrical loading).

The relationship between load, shear force, and bending moment is given as:

where is the load per unit length.

Bending Moment and Shear Force for Common Load Conditions

For a Simply Supported Beam with a Point Load (W) at Midspan:
- Maximum bending moment,

- Reactions at supports,

For a Simply Supported Beam with Uniformly Distributed Load (w):
- Maximum bending moment,

- Reactions at supports,

For a Simply Supported Beam with Uniformly Varying Load:
- Maximum bending moment,

(depending on load variation pattern).

These equations help engineers determine stress distribution and deflection in beam design.

Deflection of Simply Supported Beam

Deflection is the vertical displacement of the beam due to loading. The amount of deflection depends on the load, beam length, material properties, and cross-sectional shape.

For small deflections, the formulas are:

For Point Load (W) at Midspan:

For Uniformly Distributed Load (w):

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

The deflection is maximum at the midpoint of the beam and zero at the supports.

Advantages of Simply Supported Beam

Simple Construction:
Easy to design and install due to its straightforward support conditions.
Economic Design:
Requires fewer materials and simpler supports compared to fixed beams.
Predictable Behavior:
The bending moment and shear force distribution are easy to calculate.
Flexibility:
Allows for rotation at supports, reducing the risk of cracking in structures.

Disadvantages of Simply Supported Beam

Larger Deflection:
Compared to fixed or continuous beams, deflection is greater.
Limited Load Capacity:
Cannot carry heavy loads without increasing beam depth or reinforcement.
Less Stiffness:
Since it cannot resist end moments, it has lower stiffness.
Vibration Problems:
Under moving loads (like vehicles), simply supported beams may experience vibrations.

Applications of Simply Supported Beam

Bridges: To support roads and railway tracks.
Floors and Roofs: As horizontal members supporting slabs or decking.
Machine Frames: For supporting loads in tools and industrial equipment.
Temporary Structures: Used in scaffolding or formwork.
Railway Sleepers and Platforms: Provide stable yet flexible load distribution.

Simply supported beams are chosen for their simplicity, economy, and ease of analysis, especially where moderate loads are expected.

Conclusion

In conclusion, a simply supported beam is a beam supported at both ends, with one end hinged and the other on rollers. It is capable of resisting transverse loads through bending and shear forces. It is widely used in engineering due to its simple design, predictable behavior, and ease of construction. However, it experiences higher deflection compared to fixed beams, making it suitable mainly for moderate load applications such as floors, bridges, and building structures.