Flexure formula insight:\nWhen a beam is subjected to bending moment, the normal stress at any point varies how with the distance of that point from the neutral axis?

Introduction / Context:
The classic flexure formula sigma = M * y / I underpins most beam stress calculations. It tells us exactly how normal stress varies from the neutral axis to the extreme fibres and is key to sizing sections efficiently.

Given Data / Assumptions:

• Euler–Bernoulli beam theory (plane sections remain plane).
• Homogeneous, isotropic material; linear elasticity.
• Pure bending or regions where shear is negligible.

Concept / Approach:
The strain distribution is linear: epsilon = y / rho. Using Hooke’s law, sigma = E * epsilon = E * y / rho. Combining with the curvature relation M / I = E / rho yields sigma = (M / I) * y, explicitly showing direct proportionality between stress magnitude and distance from the neutral axis.

Step-by-Step Solution:

Verification / Alternative check:
Maximum stress occurs at extreme fibres where |y| is largest; zero stress at y = 0 (neutral axis). This matches both theoretical derivation and experimental strain gauge data.

Why Other Options Are Wrong:

• Equal to / independent of distance: contradict linear variation.
• Inverse or quadratic dependence: not supported by the flexure formula under standard assumptions.

Common Pitfalls:
For composite or cracked sections, the neutral axis location changes; still, within each transformed section, the variation remains linear with local y.

Final Answer:
Directly proportional to the distance