Beam equations: Difference between revisions

Latest revision as of 02:41, 22 October 2024

Euler–Bernoulli beam equation - basic theory based on geometry of deformation
Timoshenko beam theory - extended theory that takes into account shear deformation

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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

@@ Line 1: / Line 1: @@
-== Internal Forces ==
+== Beam Theories ==
-<tex>
+* [[Euler–Bernoulli beam equation]] - basic theory based on geometry of deformation
-\frac{dV}{dx} = - w(x)
+* [[Timoshenko beam theory]] - extended theory that takes into account shear deformation
-</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 ==
-* <tex>w(x)</tex> ... distributed load along the girder
+* <math>w(x)</math> ... distributed load along the girder
-* <tex>v</tex> ... deflection
+* <math>v</math> ... deflection
-* <tex>\theta</tex> ... slope of elastic curve
+* <math>\theta</math> ... slope of elastic curve
-* <tex>M</tex> ... moment
+* <math>M</math> ... moment
-* <tex>V</tex> ... shear
+* <math>V</math> ... shear
-* <tex>EI</tex> ... flexural rigidity
+* <math>EI</math> ... flexural rigidity
-== See Also ==
+== External links ==
-* [[Euler–Bernoulli beam equation]]
+* [http://virtual.cvut.cz/beams/ Beam Deflection formulas for cantiveler and simply supported beams]
-* [[Timoshenko beam theory]]
 {{Traditional Analysis Methods}}
+[[Category:Beam]]