Euler–Bernoulli beam equation

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Contents

1 Assumptions
2 Internal Forces
3 Elastic Curve
4 References
5 External Links

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)

External Links

Euler–Bernoulli beam equation at Wikipedia

Retrieved from "http://www.structuralwiki.org/structural_wiki_en/index.php?title=Euler–Bernoulli_beam_equation&oldid=14289"

Beam

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