Short Answer:

Pure bending and simple bending are two conditions of beam bending. Pure bending occurs when a constant bending moment acts on a beam without any shear force. It happens in the middle portion of a beam between two equal and opposite moments. Simple bending, on the other hand, occurs when both bending moment and shear force act on the beam due to external loads. Thus, pure bending is a special case of simple bending where the shear force becomes zero.

In simple words, pure bending involves only bending moments, while simple bending involves both bending moment and shear force. Pure bending generally occurs in the middle part of the beam, while simple bending occurs throughout the beam under external loading conditions.

Detailed Explanation :

Difference between Pure and Simple Bending

When a beam is subjected to external loads, it bends due to the development of bending moments and shear forces within its cross-section. The bending of the beam can occur under two main conditions — pure bending and simple bending. Both terms are related to the study of beam strength, but the internal forces acting in each case make them different.

1. Pure Bending

Pure bending is a condition in which a beam is subjected to a constant bending moment along a section of its length, and no shear force acts on that portion. It means that only bending stress is produced, and no shear stress exists.

Pure bending occurs between two points where equal and opposite couples (moments) act on the beam. This condition is generally found in the middle region of a simply supported beam or between two couples applied to a beam.

Example:
Consider a beam acted upon by two equal and opposite couples (moments) at its ends. The portion of the beam between these couples is under pure bending because the bending moment remains constant, and the shear force is zero.

Characteristics of Pure Bending:

• The bending moment is constant throughout the length of the beam section.
• Shear force is zero.
• Stress varies linearly from the neutral axis — maximum at the outermost fibers and zero at the neutral axis.
• Occurs in the region where the bending moment diagram is horizontal.
• The curvature of the beam is uniform.

Mathematical Relation:
In pure bending, the bending equation applies directly as:

where
= constant bending moment,
= moment of inertia,
= bending stress,
= distance from the neutral axis,
= modulus of elasticity,
= radius of curvature of the beam.

2. Simple Bending

Simple bending is the general case of bending that occurs when a beam is subjected to transverse loads, such as uniformly distributed loads or concentrated loads. In this case, both bending moment and shear force exist within the beam at most sections.

Unlike pure bending, the bending moment in simple bending is not constant; it varies along the length of the beam. The shear force also changes at different sections, depending on the loading condition.

Example:
A simply supported beam carrying a uniformly distributed load (UDL) is an example of simple bending. In such a beam, the bending moment is maximum at the center and zero at the supports, while shear force changes sign along the length.

Characteristics of Simple Bending:

• Both bending moment and shear force are present.
• Bending moment varies along the beam’s length.
• The curvature of the beam changes along its length.
• The bending stress is maximum where the bending moment is highest.
• It represents the most common bending condition in practical structures.

3. Key Differences Between Pure and Simple Bending

Feature	Pure Bending	Simple Bending
Definition	Occurs when only a constant bending moment acts without shear force.	Occurs when both bending moment and shear force act on the beam.
Shear Force	Zero throughout the section.	Not zero, varies along the beam.
Bending Moment	Constant along the beam section.	Varies along the beam.
Region of Occurrence	Occurs in the central region or between applied couples.	Occurs throughout the beam under external loads.
Curvature of Beam	Constant curvature.	Varying curvature.
Practical Example	Beam under equal and opposite end couples.	Simply supported beam with a distributed or point load.

4. Physical Meaning

In pure bending, the beam bends smoothly into a circular arc because the bending moment is uniform. There is no distortion due to shear force. This helps in theoretical analysis and in understanding the basic stress distribution in bending.

In simple bending, however, the beam is subjected to varying bending moments and shear forces. The curvature and stress distribution change from section to section. Simple bending is what occurs in real-world structures such as bridges, beams in buildings, and machine frames.

5. Applications

• Pure bending is mainly used in laboratory experiments and theoretical analysis to derive bending equations.
• Simple bending represents actual working conditions of beams under real loading.

Understanding both types helps in designing structural elements to resist bending and avoid failure.

Conclusion :

Pure bending and simple bending are closely related concepts, but they differ in the presence of shear force and the variation of bending moment. In pure bending, the bending moment is constant and shear force is zero, while in simple bending, both bending moment and shear force exist and vary along the beam. Pure bending is mainly a theoretical case, while simple bending represents the practical condition of real beams under loads. Both concepts are essential for understanding the behavior and design of structural and mechanical elements.