Bending Stress

This equation gives the normal stress at a specific point in a beam cross-section when the beam is bent. It comes from the idea that, under pure bending, cross-sections stay plane, so fibres farther from the neutral axis stretch or compress more; the stress varies linearly with distance y and is larger when the bending moment M is larger. The moment of area I measures how strongly the cross-section resists that bending, so a larger I spreads the stress out and reduces the peak value.

Use this for beams, shafts, and structural members when you need the bending stress at a particular location in the cross-section. It is especially useful in design checks, failure analysis, and comparing how changing a section shape affects stress.

• Mixing units, such as using N·m with mm^4 without converting consistently
• Using the overall beam depth instead of the point’s distance y from the neutral axis
• Confusing the second moment of area I with mass moment of inertia