Beam equations: Difference between revisions

From StructuralWiki
Jump to navigation Jump to search
No edit summary
No edit summary
Line 4: Line 4:
* [[Timoshenko beam theory]] - extended theory that takes into account shear deformation
* [[Timoshenko beam theory]] - extended theory that takes into account shear deformation


== Internal Forces ==
<tex>
\frac{dV}{dx} = - w(x)
</tex>
<tex>
\frac{dM}{dx} = V
</tex>
* These relationships are derived from equilibrium of an infinitesimal portion of the beam.
== Elastic Curve ==
<tex>
d\theta = \frac{M}{EI} dx
</tex>
<tex>
\frac{d^{2}v}{dx^2} = \frac{M}{EI}
</tex>
* There relationships are derived from geometry of deformed infinitesimal portion of the beam.
== Assumptions ==
{{To Do}}
== Derivation ==
{{To Do}}


== Notation ==
== Notation ==

Revision as of 23:15, 7 March 2010

Beam Theories


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

 

Home > Topics > Traditional Analysis Methods e
Fundamentals Traditional analysis methods  · Section properties  · Mohr's Circle  · Interaction diagram
Theory Elasticity equations
Forces and Stresses Torsion  · Flexure  · Shear  · Principal stress
Basic Statics Beam equations  · Moment area method  · Vereschagin's rule  · Stiffness matrix  · Fixed end moments  · Determinate statics  · Indeterminate statics  · Maxwell's theorem of reciprocal displacements  · Betti's law
Influence lines  · Muller-Breslau principle
Basic Dynamics Damping  · Mass matrix  · Damping matrix
Energy Methods External work and strain energy  · Principle of work and energy  · Virtual work method  · Unit load method  · Castigliano's Theorem
Approximate Methods Moment distribution method
Graphical Cremona Diagram

See Also Computational analysis methods
Related Categories Traditional Analysis Methods