Beam equations: Difference between revisions
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* <tex>w(x)</tex> ... distributed load along the girder | * <tex>w(x)</tex> ... distributed load along the girder | ||
* <tex>v</tex> ... deflection | * <tex>v</tex> ... deflection | ||
* <tex> | * <tex>\theta</tex> ... slope of elastic curve | ||
* <tex>M</tex> ... moment | * <tex>M</tex> ... moment | ||
* <tex>V</tex> ... shear | * <tex>V</tex> ... shear | ||
Revision as of 06:15, 20 March 2009
Internal Forces
<tex> \frac{dV}{dx} = - w(x) </tex>
<tex>
\frac{dM}{dx} = V
</tex>
Elastic Curve
<tex> d\theta = \frac{M}{EI} dx </tex>
<tex> \frac{d^{2}v}{dx^2} = \frac{M}{EI} </tex>
Assumptions
Notation
- <tex>w(x)</tex> ... distributed load along the girder
- <tex>v</tex> ... deflection
- <tex>\theta</tex> ... slope of elastic curve
- <tex>M</tex> ... moment
- <tex>V</tex> ... shear
- <tex>EI</tex> ... flexural rigidity
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