Euler–Bernoulli beam equation

Assumptions

 * Beam cross-sections remain perpendicular to the beam axis after the deformation takes place.

Internal Forces
\frac{dV}{dx} = - w(x)

\frac{dM}{dx} = V


 * These relationships are derived from equilibrium of an infinitesimal portion of the beam.

Elastic Curve
d\theta = \frac{M}{EI} dx

\frac{d^{2}v}{dx^2} = \frac{M}{EI}


 * There relationships are derived from geometry of deformed infinitesimal portion of the beam.