Timoshenko - Euler Bernoulli In Plane Curved Beams


by bugatti79
Tags: beams, bernoulli, curved, euler, plane, timoshenko
bugatti79
bugatti79 is offline
#1
Dec12-12, 03:02 PM
P: 652
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
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
SteamKing
SteamKing is offline
#2
Dec13-12, 02:03 AM
HW Helper
Thanks
P: 5,549
Yes, there's quite a bit. Google 'curved beams'.
Studiot
Studiot is offline
#3
Dec13-12, 06:46 AM
P: 5,462
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...-AUGUST-11.pdf


Register to reply

Related Discussions
Kinematics of Euler Bernoulli and Timoshenko Beam Elements Mechanical Engineering 5
Castigliano's Theorem on Curved Beams Engineering, Comp Sci, & Technology Homework 29
Calculating the deflection on curved beams Engineering, Comp Sci, & Technology Homework 0
deflection of curved beams Mechanical Engineering 0
Radial stress in curved beams Mechanical Engineering 4