Neutral axis properties in homogeneous beams For a homogeneous prismatic beam under bending that obeys the Euler–Bernoulli assumptions, the neutral axis of any cross-section must:

Introduction / Context:
The neutral axis (N.A.) is the line within a cross-section where the bending normal stress is zero. Correctly locating the N.A. is fundamental to computing stresses and deflections. In homogeneous, isotropic materials under pure bending, the N.A. passes through a specific geometric location regardless of section shape.

Given Data / Assumptions:

• Homogeneous, isotropic material with linear stress-strain behaviour.
• Plane sections remain plane; pure bending assumptions.
• No axial force (only bending moment considered).

Concept / Approach:

From compatibility and equilibrium, strain varies linearly with distance from a neutral surface; zero strain line maps to zero stress line. For a homogeneous section with no axial force, the internal compressive and tensile resultants must be equal and opposite, so the centroidal axis is the only location where the first moment of area about the N.A. is zero. Therefore the N.A. must pass through the centroid.

Step-by-Step Solution:

Verification / Alternative check:

For non-homogeneous composite sections, the elastic neutral axis passes through the transformed-section centroid, not necessarily the geometric centroid—highlighting why the homogeneity assumption matters.

Why Other Options Are Wrong:

• “Equidistant from top and bottom” is only true for symmetric sections; not general.
• “Axis of symmetry” may not exist (unsymmetric sections can be used).
• “Always coincide with mid-depth” is again only true when the section is symmetric about that depth.
• “None of these” is incorrect because the centroidal condition is definitive.

Common Pitfalls:

• Confusing geometric centroid with elastic neutral axis for composite materials.

Final Answer:

pass through the centroid of the section.