# 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.

## References

• Russell C. Hibbeler: Structural Analysis, Third Edition, 1995 (p. 345, Elastic Beam Theory)