Short Answer:

The difference between pure and simple bending lies in the presence of shear force and the variation of bending moment along the beam. In pure bending, the beam is subjected only to a constant bending moment with no shear force acting on it, while in simple bending, both bending moment and shear force are present due to external loads.

In simple words, pure bending is an ideal or theoretical case where only bending moment exists, whereas simple bending is the actual condition found in real structures where both shear and bending occur together.

Detailed Explanation :

Difference between Pure and Simple Bending

When a beam or any structural member is subjected to loads, it bends due to the development of bending moments and shear forces within it. Based on the type of loading and the resulting internal forces, bending is classified into pure bending and simple bending.

Understanding the difference between these two is very important because it helps engineers identify where ideal conditions (pure bending) can be assumed and where actual behavior (simple bending) must be considered during design.

1. Pure Bending

Definition:
Pure bending is a condition in which a beam is subjected to constant bending moment only and no shear force acts on it. This means that the bending moment is the same at all points along the beam length in the portion under consideration.

Explanation:
Pure bending occurs when equal and opposite couples (moments) are applied at two ends of a beam section, without any external transverse load between them. Under this condition:

• The beam bends into a circular arc.
• The neutral axis remains unchanged in length.
• The bending moment is uniform.
• The shear force at every section is zero.

Example:
A cantilever beam subjected to a moment at its free end or a beam having a portion between two equal and opposite couples experiences pure bending.

Stress Distribution:
In pure bending, the stress varies linearly from tensile stress at one side to compressive stress at the other, and is zero at the neutral axis.

2. Simple Bending

Definition:
Simple bending is the condition in which a beam is subjected to both bending moment and shear force due to external transverse loads. The bending moment in this case varies along the beam length.

Explanation:
In practical applications, beams are loaded with point loads, uniformly distributed loads, or varying loads. These loads cause:

• Variable bending moments along the beam, and
• Shear forces at different sections.

Hence, in simple bending, both effects — bending and shear — occur together.

Example:
A simply supported beam carrying a point load or uniformly distributed load is under simple bending because bending moment and shear force vary from one point to another.

Stress Distribution:
In simple bending, the stress distribution remains approximately linear along the depth, but near supports, shear stress slightly alters the distribution. The maximum bending stress occurs where the bending moment is maximum.

3. Major Differences between Pure and Simple Bending

Basis of Difference	Pure Bending	Simple Bending
Definition	Bending due to constant bending moment only.	Bending due to varying bending moment and presence of shear force.
Shear Force	Shear force is zero.	Shear force is not zero.
Bending Moment	Constant along the portion of the beam.	Varies along the beam length.
Loading Condition	Produced by equal and opposite couples at the beam ends.	Produced by transverse external loads (point or distributed loads).
Beam Shape after Bending	Beam bends into a perfect circular arc.	Beam bends into a complex curved shape.
Nature	Ideal or theoretical condition.	Practical condition found in real beams.
Example	Beam subjected to pure moments only (no load between).	Simply supported or cantilever beam under UDL or point load.
Stress Distribution	Linear and symmetrical across the depth.	Slightly affected by shear near supports, still approximately linear.

4. Mathematical Representation

In pure bending,

where  is constant and .

In simple bending,

meaning the bending moment varies along the length and the shear force exists.

Thus, the bending equation is valid for both cases, but pure bending represents a special case of simple bending where the moment is constant.

5. Graphical Difference

Although we are not using graphs here, the concept can be understood easily:

• In pure bending, the bending moment diagram is a horizontal line (constant value).
• In simple bending, the bending moment diagram is curved or triangular, showing variation of moment along the beam.

6. Physical Behavior

1. In Pure Bending:
   • The beam’s curvature is uniform throughout.
   • The deflection shape is a circular arc.
   • There are no shear stresses acting across the cross-section.
2. In Simple Bending:
   • The beam curvature changes continuously.
   • Deflection shape is not a perfect circle but a complex curve.
   • Shear stresses act, particularly near the supports.

7. Practical Importance

1. Pure Bending:
   • Used mainly for theoretical study and derivation of the bending equation.
   • Helps in understanding stress and strain distribution within a beam.
   • Useful in material testing where uniform bending moment is required.
2. Simple Bending:
   • Represents the actual behavior of beams in real-world structures.
   • Used in designing building beams, machine parts, and bridges.
   • Engineers analyze shear force and bending moment diagrams under simple bending to ensure safe design.

8. Examples in Real Life

• Pure Bending Example:
  • A shaft subjected to a pure couple.
  • A beam fixed at both ends and subjected to a moment at one end.
• Simple Bending Example:
  • A simply supported beam under uniformly distributed load.
  • A cantilever beam carrying a load at its free end.

These examples show that pure bending rarely occurs in actual practice, whereas simple bending occurs in almost all real situations.

Conclusion

In conclusion, the difference between pure and simple bending lies mainly in the presence of shear force and the variation of bending moment. In pure bending, the beam experiences only constant bending moment without shear, while in simple bending, both bending moment and shear force act simultaneously. Pure bending is a special theoretical case used for deriving bending equations, whereas simple bending represents the practical condition of beams under real loads. Understanding both helps engineers analyze and design safe and efficient structural members.