Yield moment of a cross-section: the bending moment that just brings which fibre of the section to the yield stress?

Introduction / Context:
Yield moment is a fundamental term in flexural design and plastic analysis. It marks the boundary between elastic behavior and the onset of yielding in bending members such as beams and slabs.

Given Data / Assumptions:

• Material follows elastic–perfectly plastic idealization in bending.
• Plane sections remain plane so strain varies linearly across the depth.
• Yield stress is known (e.g., steel yield strength).

Concept / Approach:
Under pure bending, extreme fibres (furthest from the neutral axis) experience the maximum tensile and compressive strains. As bending moment increases from zero, the first location to reach the yield stress is the outermost fibre. The moment at which this first yield occurs is the yield moment, often denoted My.

Step-by-Step Solution:
Relate stress to curvature: σ = E * κ * y, where y is the distance from the neutral axis.Maximum |σ| occurs at |y| = c, the extreme fibre distance.Set |σ| = yield stress to find κ corresponding to first yield.Convert curvature to moment using section flexural rigidity to obtain the yield moment.

Verification / Alternative check:
Strain distribution linearity ensures that yielding must initiate at the largest |y|. This remains true regardless of section shape (rectangular, I-section, T-section) as long as plane sections remain plane.

Why Other Options Are Wrong:

• Innermost fibre / neutral fibre: these are closer to the neutral axis and reach yield later.
• Every fibre simultaneously: that corresponds to a fully plastic state (plastic moment), not first yield.

Common Pitfalls:

• Confusing yield moment (first yield at extremes) with plastic moment (full plastic stress block across the section yielding).

Final Answer:
The outermost fibre of the section.