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Bending stress

In a beam that is bent, normal stress arises that varies linearly across the section: zero at the neutral axis, tension on one side and compression on the other. Navier's formula gives the stress at a given distance $y$ from the neutral axis.

\sigma = \dfrac{My}{I}

bending stress (Navier's formula)

Symbols

$M$	bending moment	Nm
$y$	distance from the neutral axis	m
$I$	second moment of area	m⁴

Example

A beam with $I = 20\cdot10^6$ mm⁴, $M = 5$ kNm, $y = 75$ mm:

$\sigma = 5\cdot10^6\cdot 75/(20\cdot10^6) = 18.75$ MPa.

The maximum stress is always in the outer fibers, farthest from the neutral axis.

Practise torsion and bending for free →

← Angle of twist · Hollow cross-sections →

Part of Strength of Materials: Torsion and bending.