Bending sign convention:\nAcross the neutral axis of a beam under bending, the fibres on one side are in tension and on the other side are in compression. Do you agree?

Introduction / Context:
When beams bend under transverse loads, internal normal stresses develop that vary from compression on one side to tension on the other, with a zero-stress surface known as the neutral axis in between. Understanding this distribution is fundamental to sizing members and checking serviceability.

Given Data / Assumptions:

• Euler–Bernoulli beam assumptions (plane sections remain plane).
• Linear elastic, homogeneous material.
• Conventional sagging moment (concave up) places top in compression and bottom in tension for prismatic, horizontally oriented beams.

Concept / Approach:
From the flexure formula sigma = M * y / I, stress is proportional to the distance y from the neutral axis. The sign depends on the curvature and the side of the axis. Hence, one side experiences positive (tension) and the opposite negative (compression) stress, separated by the neutral axis where sigma = 0.

Step-by-Step Solution:

Verification / Alternative check:
Deflection shape visualization: fibres on the concave side shorten (compression), while those on the convex side lengthen (tension), confirming the opposite nature of stress.

Why Other Options Are Wrong:

• Disagree / conditional options: The statement holds broadly for beams in bending regardless of support type, provided material is homogeneous and within elastic range.

Common Pitfalls:
Confusing sign conventions or misidentifying the neutral axis location in non-homogeneous or composite sections.

Final Answer:
Agree