Fiber stress state at the lower surface of a sagging beam\n\nFor a prismatic beam under typical downward loading causing a sagging (concave-up) bending moment, the lower layer (bottom fiber) of the beam will be in which state?

Introduction / Context:
Identifying which fibers are in tension or compression under bending is essential for detailing reinforcement, checking brittle materials, and preventing cracking where tension capacity is low.

Given Data / Assumptions:

• Beam experiences sagging bending (positive bending moment by common sign convention).
• Plane sections remain plane; linear strain profile across depth.
• Neutral axis passes through the centroid for homogeneous material.

Concept / Approach:
For sagging (concave-up) bending, the top fibers shorten (compression) and the bottom fibers elongate (tension). The neutral axis is where axial stress is zero; stress varies linearly with distance from that axis.

Step-by-Step Solution:
Assume positive bending moment M > 0.Strain distribution: ε = −(κ) y, with curvature κ > 0 and y measured positive upward from neutral axis.Top (y > 0) → ε negative (compression); bottom (y < 0) → ε positive (tension).Stress via σ = E ε follows the same sign pattern.

Verification / Alternative check:
Sketch the deflected shape for a simply supported beam with midspan load: it sags; string analogy shows the underside stretches, confirming tension at the bottom.

Why Other Options Are Wrong:
“Compression” applies to hogging (negative) bending. “Neither” is only true at the neutral axis, not at an extreme fiber. “Pure shear only” and “torsion” are unrelated to the axial fiber stress caused by bending.

Common Pitfalls:
Mixing sign conventions; misreading a hogging region (over a fixed support) as sagging; assuming composite sections always have centroidal neutral axes (they may shift).

Final Answer:
in tension