# Bending stiffness

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The bending stiffness is equal to the product of the elastic modulus ${\displaystyle E}$ and the area moment of inertia ${\displaystyle I}$ of the beam cross-section about the axis of interest. In other words, the bending stiffness is ${\displaystyle EI}$. According to elementary beam theory, the relationship between the applied bending moment ${\displaystyle M}$ and the resulting curvature ${\displaystyle \kappa }$ of the beam is
where ${\displaystyle w}$ is the deflection of the beam and ${\displaystyle x}$ the coordinate. In literature the above definition is sometimes used with a minus sign depending on convention.