# Euler-Bernoulli Beam Equation

## Theorem

$q = \map {\dfrac {\d^2} {\d x^2} } {E I \dfrac {\d^2 w} {\d x^2} }$

where:

$q$ is the bending moment
$E$ is Young's modulus
$\dfrac {\d^2 w} {\d x^2}$ is the curvature
$I$ is the moment of inertia of the cross-section about an axis through the center of mass and perpendicular to the plane of the couple.

## Also known as

The Euler-Bernoulli Beam Equation is also known as the Euler-Bernoulli Law.

## Source of Name

This entry was named for Leonhard Paul Euler and Daniel Bernoulli.