Bending sense and fiber stresses — rectangular beam under positive (sagging) bending: With a sagging bending moment, is the upper layer of the beam in tension?

Introduction:
Understanding the sign convention and where tension/compression occur under bending is fundamental to beam design and detailing.

Given Data / Assumptions:

• Rectangular prismatic beam.
• Sagging (positive) bending moment convention.

Concept / Approach:
For a positive (sagging) moment, the beam curves concave upward. The top fibers shorten (compression) while the bottom fibers lengthen (tension). For a negative (hogging) moment, this reverses: top in tension, bottom in compression.

Step-by-Step Solution:

Verification / Alternative check:
Standard bending stress relation σ = M*y/I shows σ sign flips across the neutral axis; with y positive upward and M sagging, σ at top (positive y) is compressive.

Why Other Options Are Wrong:

• True: Contradicts sagging behavior.
• “True only for hogging”: Correct concept but the statement asked about sagging; thus answer remains false.
• Depends on shape only / cantilevers only: Fiber stress sense is governed by moment sign, not just section type.

Common Pitfalls:
Mixing up sagging vs hogging; confusing maximum deflection location (midspan) with the sign of fiber stress at the top surface.

Final Answer: