Beam mechanics – neutral axis concept In the flexural analysis of a simply supported prismatic beam (small deflection theory), which statement best describes the behavior of material fibres exactly along the neutral axis during bending? Provide the most accurate description used in strength of materials.

Introduction / Context:
The neutral axis is a core concept in strength of materials and structural analysis. When a beam bends under transverse loads, fibres above and below a certain line experience compression and tension respectively. Understanding what happens exactly on that line (the neutral axis) is essential for stress–strain distribution, section design, and locating reinforcements.

Given Data / Assumptions:

• Prismatic, homogeneous, and isotropic beam material.
• Linear elastic behavior (Euler–Bernoulli beam theory) and small deflections.
• Plane sections remain plane and perpendicular to the neutral axis after bending.

Concept / Approach:
Under pure bending, normal strain varies linearly with distance from the neutral axis (y = 0 at the axis). The classic relationship is:
epsilon(y) = -k * ywhere k is curvature. Thus, at y = 0 (the neutral axis), the normal strain is zero and the corresponding normal stress is also zero. Above the axis (positive y), compression occurs; below (negative y), tension occurs.

Step-by-Step Solution:
Identify the neutral axis (through the centroid for homogeneous, symmetric cross-sections under bending).Use linear strain distribution: epsilon = -y / R → at y = 0, epsilon = 0.Stress follows sigma = E * epsilon → at the neutral axis, sigma = 0 as epsilon = 0.Therefore, fibres along the neutral axis neither shorten nor elongate; they undergo zero normal strain.

Verification / Alternative check:
The bending stress formula sigma = M * y / I shows sigma = 0 at y = 0 (neutral axis). Experimental strain gauge readings confirm zero strain along this axis for elastic bending.

Why Other Options Are Wrong:
Minimum strain suggests a non-zero extremum, which is incorrect—strain is exactly zero at the neutral axis. Maximum strain occurs at the extreme fibres, not at the neutral axis. None of these is invalid because the correct statement is provided in option A.

Common Pitfalls:
Confusing neutral axis with centroidal axis for non-homogeneous or transformed sections; in composite sections, the neutral axis may not pass through the geometric centroid but still corresponds to zero strain and stress.

Final Answer:
fibres do not undergo strain