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# Bending stiffness

The bending stiffness EI 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 κ of the beam is

### Additional recommended knowledge

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

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

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Bending_stiffness". A list of authors is available in Wikipedia.
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