Difficulty: Easy
Correct Answer: pass through the centroid of the section
Explanation:
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:
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:
Common Pitfalls:
Final Answer:
pass through the centroid of the section.
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