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Bending stress and section modulus

For sizing beams, the maximum bending stress, at the outer edge of the section, is what matters. By combining $I$ and the distance to the outer edge $y_{max}$ into the section modulus $W$ , the formula becomes simple: $\sigma_{max} = M/W$ .

W = I/y_{max}

section modulus

\sigma_{max} = M/W

maximum bending stress

Symbols

$W$	section modulus	m³
$I$	second moment of area	m⁴
$M$	bending moment	Nm

Example

A rectangle $b=50$ , $h=100$ mm: $W = bh^2/6 = 83\,300$ mm³.

With $M = 2$ kNm: $\sigma_{max} = 2\cdot10^6/83\,300 \approx 24$ MPa.

W = bh^2/6

for a rectangle – note the second power on the height, versus the third for

I

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Part of Machine Design: Stress and sizing.