Bending fundamentals: In an elastic, homogeneous beam under pure bending, which statement about the neutral plane (neutral axis in section) is correct?

Introduction / Context:
The neutral plane (and its intersection with a section—the neutral axis) is the locus of zero longitudinal strain in bending. Identifying its location is essential for stress distribution and reinforcement detailing in beams.

Given Data / Assumptions:

• Beam is homogeneous, isotropic, prismatic.
• Plane sections remain plane (Bernoulli–Euler hypothesis).
• Pure bending or bending-dominant behavior without significant shear warping.

Concept / Approach:
For homogeneous sections in pure bending, the neutral axis passes through the centroid of the section and is perpendicular to the plane of bending. This follows from the linear strain distribution and the zero resultant axial force condition, which places the NA at the centroid.

Step-by-Step Solution:
Zero axial resultant requires ∫σ dA = 0 with σ = E * κ * y, where y is measured from the NA.Setting the reference so that ∫y dA = 0 places the NA through the centroid by definition of centroidal axis.Thus the correct statement is that the neutral plane passes through the C.G. of the cross-section.

Verification / Alternative check:
For composite or non-homogeneous sections, the elastic neutral axis passes through the transformed-section centroid; for homogeneous sections it is the geometric centroid.

Why Other Options Are Wrong:
'May be its centre': vague and not general; the NA is at the centroid for homogeneous sections.'Does not change during deformation': its orientation/location is fixed for a given section and bending plane, but this statement is ambiguous and not the standard defining property.

Common Pitfalls:
Confusing geometric centre with centroid for non-uniform sections; applying composite-section logic to homogeneous beams.

Final Answer:
It passes through the centroid (C.G.) of the cross-sectional area