For a rectangular beam under transverse loading (sagging), where is the maximum tensile stress located across the depth?

Introduction / Context:
In beam bending, the sign and distribution of normal stress depend on the bending moment sense (sagging or hogging). Correctly locating tensile and compressive zones is vital for reinforcement layout and checking tensile strength.

Given Data / Assumptions:

• Rectangular prismatic beam, linearly elastic.
• Sagging moment (concave up) due to transverse loads.
• Small deflection theory; plane sections remain plane.

Concept / Approach:
Bending stress varies linearly with distance y from the neutral axis: sigma = M y / I. For sagging, the top fibers are in compression (negative y), the bottom fibers in tension (positive y). Maximum magnitudes occur at the extreme fibers farthest from the neutral axis.

Step-by-Step Solution:

Verification / Alternative check:
Sign convention check using sagging positive: compression at top, tension at bottom; textbook stress blocks confirm.

Why Other Options Are Wrong:
Top layer is compressive under sagging.Neutral axis has zero normal stress.Stress is not uniform across section depth.

Common Pitfalls:
Confusing sagging versus hogging; misplacing neutral axis in non-symmetric sections.

Final Answer:

bottom layer