Neutral axis behavior: At the neutral axis of a beam under bending, which statement best describes the state of the fibres?

Introduction / Context:The neutral axis (NA) is a central concept in beam theory. It is the locus of points within the cross-section that experience zero normal stress during bending. Correctly identifying conditions at the NA helps in understanding strain distribution and in locating the centroidal axis for homogeneous sections.

Given Data / Assumptions:

• Linear elastic bending assumptions (plane sections remain plane).
• Homogeneous material, no residual stresses.
• Pure bending or general bending with NA defined by zero normal stress.

Concept / Approach:Normal strain varies linearly through the depth: epsilon = y / rho. At y = 0 (the NA), epsilon = 0. By Hooke’s law, sigma = E * epsilon, the normal stress is also zero at the NA. Thus, fibres along the NA neither elongate nor shorten; they undergo no normal strain.

Step-by-Step Solution:

Verification / Alternative check:Experimental strain gauge readings across a beam depth show zero reading at the NA, confirming theory.

Why Other Options Are Wrong:

• Maximum/minimum bending stress occurs at extreme fibres, not at the NA.
• Compression at NA is incorrect; stress changes sign across the NA and is zero at it.

Common Pitfalls:Assuming the NA always passes through the geometric centroid; for composite or non-homogeneous sections, the NA may shift relative to the centroid.

Final Answer:The layers do not undergo any strain