Drag the section to resize, drag the moment arrow to change load. Toggle elastic vs plastic to see the stress distribution shift.
In elastic bending, stress is linear: σ = My/I. The extreme fibers carry the most stress and the neutral axis carries none. Once the outer fibers reach yield, the section can still carry more moment by progressively yielding inward — that's the plastic state, and M_p = F_y · Z is the full plastic moment. Toggle between elastic and plastic to see how the stress distribution changes.
When a beam bends, one side compresses and the other stretches. At the neutral axis — the line through the centroid — stress is zero. Moving away from the neutral axis, stress increases linearly: σ = My / I, where y is the distance from the neutral axis. The extreme fiber (top or bottom) sees the highest stress. This is why I-shaped beams put material in the flanges, far from the center — maximum stress, maximum efficiency.
When the extreme fiber stress reaches Fy (yield strength), the section has reached its elastic moment: My = Fy × S (where S = I/c is the elastic section modulus). But the beam doesn't collapse — the interior fibers haven't yielded yet. As load increases, yielding spreads inward until the entire section has yielded. This is the plastic moment: Mp = Fy × Z (where Z is the plastic section modulus). For a W-shape, Mp is typically 10–15% higher than My.