# Bending stiffness

The

**bending stiffness**$E\; I$ of abeam (or aplate ) relates the appliedbending moment to the resulting deflection of the beam. It is the product of theelastic modulus $E$ of the beam material and thearea moment of inertia $I$ of the beam cross-section. According to elementarybeam theory , the relationship between the applied bending moment $M$ and the resultingcurvature $kappa$ of the beam is$M\; =\; E\; I\; kappa\; =\; E\; I\; frac\{mathrm\{d\}^2\; w\}\{mathrm\{d\}\; x^2\}$

where $w$ is the deflection of the beam and $x$ the spatial coordinate. In the literature sometimes the above definition is given with a minus sign depending on convention.

**See also***

Beam theory

*Bending

*Applied mechanics **External links*** [

*http://www.efunda.com/formulae/solid_mechanics/beams/theory.cfm Efunda's beam calculator*]

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