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# Bending stiffness

The bending stiffness $E I$ of a beam (or a plate) relates the applied bending moment to the resulting deflection of the beam. It is the product of the elastic modulus $E$ of the beam material and the area moment of inertia $I$ of the beam cross-section. According to elementary beam theory, the relationship between the applied bending moment $M$ and the resulting curvature $kappa$ of the beam is

$M = E I kappa = E I frac\left\{mathrm\left\{d\right\}^2 w\right\}\left\{mathrm\left\{d\right\} x^2\right\}$

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.

* Beam theory
* Bending
* Applied mechanics

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

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