Euler-Bernoulli Beam Equation

Theorem

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

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.

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Proof

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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.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Euler-Bernoulli law
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$)