Simple bending theory – Identify the incorrect statement\n\nWhich of the following statements about pure bending of beams is incorrect?

Introduction / Context:
Elementary beam theory rests on specific assumptions that lead to linear strain variation and corresponding stress distribution. Spotting an incorrect statement tests conceptual clarity about neutral axis behavior and section properties.

Given Data / Assumptions:

• Material is homogeneous and isotropic; Hooke's law valid.
• Plane sections remain plane; small deflection theory.
• No shear deformation in the pure bending region.

Concept / Approach:
Strain varies linearly with distance y from the neutral axis, and stress σ = E * ε = (M * y) / I. At y = 0 (neutral axis), both strain and stress are zero; maximum stress occurs at the extreme fibers where |y| is maximum.

Step-by-Step Solution:
Bending stress formula: σ = M * y / I.Neutral axis: y = 0 → σ = 0.Extreme fibers: y = ±c → |σ_max| = M * c / I = M / Z, where Z = I / c is section modulus.Hence bending stress is inversely proportional to Z, consistent with option (d).

Verification / Alternative check:
Plotting the linear stress diagram confirms zero at the neutral axis and maxima at the outermost fibers. Beam design maximizes Z to reduce stresses for a given bending moment M.

Why Other Options Are Wrong:
Option (c) is wrong because stress at the neutral axis is zero. Options (a), (b), and (d) are standard results. Option (e) is consistent with homogeneous materials.

Common Pitfalls:
Confusing neutral axis with centroidal axis location for unsymmetrical sections; forgetting linear distribution under elastic bending.

Final Answer:
At the neutral axis of a beam, the bending stress is maximum.