Bending stiffness

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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 $κ$ 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.