Timoshenko - Euler Bernoulli In Plane Curved Beams

[bugatti79]

Folks,

Searches of Timoshenko and Euler Bernoulli Beam Theory show differential equations for straight beams.

Is there any material out there illustrating differential equations for "curved in plane beams"..?

Thanks

 

[SteamKing]

Yes, there's quite a bit. Google 'curved beams'.

 

[Studiot]

First and foremost you need to distinguish between beams curved in plan ie those subject to out of plane forces and those initially curved in longitudinal section.

Consideration of torsion is essential with the first type.

I am assuming you mean the second.
This type of beam can be examined under two headings

Those for which the initial Radius is >> the cross section dimensions (small curvature)

Those for which the initial Radius is of the same order as the cross section dimensions (larfe curvature)

Both require variations from simple straight beam theory.

Names associated with this tyype of curved beam theory are

Winkler and Bach
Gibson and Ritchie
Wilson and Quereau
Dolan and Levin

You might find this document (2011) interesting as it lists some analystical theory and some results that you can calibrate your work against.

http://duebjri.pci.org/view_file.cfm?file=JL-80-JULY-AUGUST-11.pdf