Short Answer:

The neutral axis is an imaginary line that passes through the cross-section of a beam or structural member which experiences no tension or compression when the beam is subjected to bending. It separates the portion of the section under compression from the portion under tension.

In simple words, when a beam bends under load, the upper layers are compressed and the lower layers are stretched. Between these two regions lies the neutral axis, where the fibers neither elongate nor shorten — their stress and strain are zero.

Detailed Explanation :

Neutral Axis

When a beam or any structural member is subjected to a bending moment, it bends into a curved shape. During this bending action, different fibers (or layers) of the material experience different strains and stresses. Some layers get compressed, while others are stretched. Between these two regions lies a layer of fibers that does not change in length. The line joining all these fibers, which neither expand nor contract, is known as the neutral axis of the beam.

Thus, the neutral axis (N.A.) is defined as:

“The line in the cross-section of a beam where the bending stress and strain are both zero when the beam is subjected to bending.”

The neutral axis always passes through the centroid of the cross-section in the case of homogeneous (same material) and symmetric sections. It plays a vital role in determining the distribution of stress within the beam under bending loads.

Concept of Neutral Axis during Bending

To understand the concept of the neutral axis clearly, consider a straight beam subjected to a pure bending moment. When the moment acts on the beam:

The top fibers of the beam are compressed (shortened).
The bottom fibers are stretched (elongated).
Somewhere between these two zones, there is a fiber that does not experience any change in length.

All such unstressed fibers form a neutral surface, and the intersection of this surface with the plane of bending forms a neutral axis.

This means:

Above the neutral axis → compressive stress exists.
Below the neutral axis → tensile stress exists.
On the neutral axis → no stress or strain exists.

Position of Neutral Axis

The position of the neutral axis depends on the shape and material of the beam cross-section.

For homogeneous and symmetric sections (like rectangular, circular, or I-sections made of the same material), the neutral axis passes through the centroid of the section.
For non-homogeneous or composite sections (like reinforced concrete beams), the neutral axis does not pass through the centroid. Its position must be found using equilibrium of forces and bending theory.

The location of the neutral axis is crucial because it helps calculate the moment of inertia (I) and bending stresses (σ) within the beam.

Relation between Neutral Axis and Bending Stress

From the bending equation,

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

From this equation,

At the neutral axis, .
Hence,

This clearly shows that the bending stress is zero at the neutral axis and increases linearly as the distance from the neutral axis increases, reaching maximum values at the outermost fibers of the beam.

Therefore:

The neutral axis is the reference line for measuring distances () to calculate bending stresses in a beam.
The fibers farther from the neutral axis experience higher bending stresses.

Neutral Axis in Different Beam Sections

Rectangular Beam:
The neutral axis passes through the center of the rectangle (centroid).
Circular Beam:
The neutral axis passes through the center of the circle.
I-Section or T-Section Beam:
The neutral axis passes through the centroid of the section, which may not necessarily be at the geometric center.
Composite or Reinforced Beam:
For beams made of different materials (like steel and concrete), the neutral axis position depends on the ratio of elastic moduli of the materials and their cross-sectional geometry.

Mathematical Representation of Neutral Axis

For any section, the distance of the neutral axis from a reference axis can be found using the formula for the centroid:

where,

= area of each component part,
= distance of the centroid of that area from the reference axis.

For homogeneous sections, this gives the location of the neutral axis directly. For composite sections, the areas are converted into equivalent areas based on the modular ratio (n = E_1 / E_2) before calculating the centroid.

Importance of Neutral Axis

Determination of Bending Stresses:
The neutral axis serves as the reference line for determining tensile and compressive stresses in a beam using the bending equation.
Stress Distribution:
It separates the tensile and compressive zones in the beam, helping in understanding stress variations.
Design of Beams:
Knowing the position of the neutral axis helps in designing efficient beam sections that can carry the required loads safely.
Reinforced Concrete Design:
In reinforced concrete beams, locating the neutral axis is important to ensure that steel and concrete share the load properly according to their strength and stiffness.
Structural Safety:
It helps engineers assess whether a beam will fail due to excessive compression or tension.

Example Explanation

Consider a simply supported rectangular beam subjected to a uniform load.

The upper fibers of the beam shorten under compression.
The lower fibers elongate under tension.
The line midway between them, where there is no extension or compression, is the neutral axis.

As the load increases, the stresses above and below this axis increase proportionally, but the axis itself remains unchanged in position until the material’s elastic limit is reached.

Conclusion

In conclusion, the neutral axis is an imaginary line in the cross-section of a beam where the bending stress and strain are zero. It divides the beam into two regions — one under tension and the other under compression. The neutral axis is essential in understanding the behavior of beams under bending, as it forms the reference for calculating bending stresses and designing safe and efficient structures. Its position depends on the geometry and material of the section, making it a fundamental concept in strength of materials and structural analysis.