×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Contact US

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Cantilever (fixed-free beam)with point load - shear deformation

Cantilever (fixed-free beam)with point load - shear deformation

Cantilever (fixed-free beam)with point load - shear deformation

(OP)
Why for a cantilever (fixed-free beam) with a point load at the end,
the cross section rotations are equivalent between a Timoshenko and Euler Bernoulli Beam?

RE: Cantilever (fixed-free beam)with point load - shear deformation

The derivations shared here by Celt83:

https://www.eng-tips.com/viewthread.cfm?qid=484554

and those on wikipedia seem to be sufficient to understand why that’s the case. Do you have any specific doubts regarding those formulas ?

RE: Cantilever (fixed-free beam)with point load - shear deformation

(OP)
Mathematically speaking, I understand.
But physically speaking, I cant see why it is right

RE: Cantilever (fixed-free beam)with point load - shear deformation

Quote (Batzo)

But physically speaking, I cant see why it is right

If you draw elevations of the beam deflected shape for flexural and shear deflection it should become clear.

For flexural deflection the top and bottom surfaces change in length, and the vertical sections rotate.

For shear deflection the top and bottom surfaces remain the same length. The top and bottom surfaces have the same inclination, and the vertical sections remain vertical, so the rotation due to shear deflection is zero. It is the rotation of the vertical sections that is transferred to connected beams, so the shear deflection does not contribute to that rotation.

For sloping or vertical beams, substitute longitudinal and transverse for "top/bottom" and "vertical" respectively.


Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Cantilever (fixed-free beam)with point load - shear deformation

Dear Batzo,

Please note the Timoshenko's Beam Theory is the most rigorous mathematical model widely used to describe the lateral deformation of beams in the commercial FE packages.

The beam theory according to Bernoulli-Euler, also known as the Classical beam theory, is a simplification of the Linear Theory of Elasticity to calculate deformations in beams. It applies to the case of small deformations in beams subject only to lateral loads. We could say that it is a special case of Timoshenko's Beam Theory.



Best regards,
Blas.

~~~~~~~~~~~~~~~~~~~~~~
Blas Molero Hidalgo
Ingeniero Industrial
Director

IBERISA
48004 BILBAO (SPAIN)
WEB: http://www.iberisa.com
Blog de FEMAP & NX Nastran: http://iberisa.wordpress.com/

RE: Cantilever (fixed-free beam)with point load - shear deformation

The only difference between Euler-Bernoulli and Timoshenko beam theory is that Timoshenko includes shear deflections. Both assume that axial loads do not affect transverse displacements, and ignore the displacement of the free end in the axial direction, so are only applicable to small deflections.

The diagram above is a bit misleading. If the intention is to show the deflected shape for an equal applied deflection at the right hand end, the Timoshenko curve should not be exactly horizontal at the left hand end, and the centre lines should only match at the two ends. Also Q and M will obviously be smaller for the Timoshenko curve than the Euler-Bernoulli.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Cantilever (fixed-free beam)with point load - shear deformation

(OP)
Axial loads? Did u mean transverse loads?
I think I asked a simple question surprise
If this is the explanation for cantilever beam with point load at the end, so im fine and understood.

Quote (IDS )


For flexural deflection the top and bottom surfaces change in length, and the vertical sections rotate.

For shear deflection the top and bottom surfaces remain the same length. The top and bottom surfaces have the same inclination, and the vertical sections remain vertical, so the rotation due to shear deflection is zero. It is the rotation of the vertical sections that is transferred to connected beams, so the shear deflection does not contribute to that rotation.

RE: Cantilever (fixed-free beam)with point load - shear deformation

Batzo - my reference to axial loads was purely in response to the statement that "Timoshenko's Beam Theory is the most rigorous mathematical model widely used to describe the lateral deformation of beams in the commercial FE packages". The main point was that both theories are only applicable to small deflections.

My second sentence is referring to the diagram immediately above, which is a cantilever with a transverse point load at one end.

Did you try drawing some sketches of deflection shape due to flexural and shear deformation?

It would be instructive to draw a corrected version of the diagram posted by BlasMolero:
1. Assuming equal deflection at the right hand end.
2. Assuming equal transverse point load at the right hand end.
3. Assuming a point moment applied at the right hand end (so constant moment and zero shear).

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

RE: Cantilever (fixed-free beam)with point load - shear deformation

(OP)
Yes, I have tried.
That is why I wrote this post,
because I couldn't see it

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members! Already a Member? Login



News


Close Box

Join Eng-Tips® Today!

Join your peers on the Internet's largest technical engineering professional community.
It's easy to join and it's free.

Here's Why Members Love Eng-Tips Forums:

Register now while it's still free!

Already a member? Close this window and log in.

Join Us             Close