Bernoulli's assumptions
The Bernoullian assumptions are simplifications of the beam theory , which, as a branch of engineering mechanics, deals with the behavior of loaded beams . They are named after Jakob I Bernoulli , who set them up and then transferred them to theory.
Content of the assumptions
- The beam is slim : its length is much greater than its cross-sectional dimensions .
- It follows from this that one can assume rigidity
- Beam cross-sections that were perpendicular to the beam axis before the deformation are also perpendicular to the deformed beam axis after the deformation.
- It follows from angle conservation that shear rigidity is required
- Cross-sections remain even after deformation.
- Taking balance into account, it follows that shear rigidity is required
application
In the rigid beam theory of the first order there are the following differential equations for the transverse components under the Bernoulli assumptions :
With
- the running coordinate x along the beam axis
- the modulus of elasticity E
- the geometrical moment of inertia I (x)
- V (x) is the shear force
- q (x) the uniform load (transverse load per unit length)
- M (x) is the bending moment
- m (x) the section moment (bending load per unit length)
- φ (x) of the twist
- κ ^{e} (x) of the impressed curvature
- w (x) the deflection.
Individual evidence
- ↑ ^{a } ^{b } ^{c } ^{d } ^{e} Pichler, Bernhard. Eberhardsteiner, Josef: Structural Analysis VO LVA no.202.065 . Ed .: TU Verlag. SS2016 edition. TU Verlag, Vienna 2016, ISBN 978-3-903024-17-5 , linear bar theory of planar bar structures (520 pages, Grafisches Zentrum at the Technical University of Vienna [accessed on September 8, 2016]). Grafisches Zentrum at the Technical University of Vienna ( Memento of the original from March 13, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.