Bending Stress

When a beam bends, one side is stretched and the other is compressed, and the normal stress varies linearly with distance from the neutral axis. The formula \(\sigma = \frac{Mc}{I}\) comes from combining that linear strain distribution with Hooke’s law and the internal moment balance of the cross-section. It shows that larger bending moment increases stress, while a larger second moment of area makes the section stiffer and lowers stress for the same load.

Use this when you need the bending stress at a particular point in a beam cross-section under a known bending moment, such as in beam design, failure checks, or verifying whether a member can safely carry a load. It is especially useful in structural, mechanical, and civil engineering problems involving prismatic beams.

• Using the beam depth instead of the distance from the neutral axis for c
• Mixing units, especially kN·m with mm^4 without converting consistently
• Assuming the formula gives the same sign everywhere instead of tension on one side and compression on the other