Bending theory – Neutral axis in a rectangular beam under transverse load\nWhen a rectangular beam is transversely loaded, is the bending (normal) stress zero at the neutral axis?

Introduction / Context:
In pure bending theory for prismatic beams, the neutral axis (NA) passes through the centroid and separates tension and compression zones. Understanding stress distribution relative to the NA is foundational in beam design.

Given Data / Assumptions:

• Rectangular, homogeneous, prismatic beam.
• Elastic, small deflections; Bernoulli–Euler assumptions.
• Transverse loading causing bending and shear.

Concept / Approach:
The bending (normal) stress varies linearly with distance y from the NA: σ = (M/I) * y. At y = 0 (on the NA), σ = 0. While shear stress may be maximum near the NA, the normal bending stress is zero exactly at the NA.

Step-by-Step Explanation:
Identify NA at the centroid for a symmetric rectangular section.Bending stress distribution is linear: tension on one side, compression on the other, zero at NA.Shear stress distribution is parabolic and peaks at the NA but is a different stress component.

Verification / Alternative check:
Plot σ(y) = (M/I) * y; at y = 0, σ = 0. Superimpose shear distribution to see that shear does not alter the zero bending stress at NA.

Why Other Options Are Wrong:
Stating false unless shear is zero confuses normal and shear stresses. The condition holds for general transverse loading within elastic theory, not just for cantilevers or “symmetric loading only”.

Common Pitfalls:
Mixing the concepts: maximum shear occurs at the NA, but bending stress there is still zero. Students often conflate these two stress types.

Final Answer:
True