local bending stress calculation in long beams
local bending stress calculation in long beams
(OP)
Hi everyone,
Recently I faced a problem in calculating bending stress in a long UPN profile "flange" due to concentrated force.
It seems that the regular/familiar formula for bending stress in a finite/short element does not applicable in local bending of long/infinite beam. See sketch attached for clarification.
An example to such calculation I found in elevator's std for "T" rails calculation which express the stress in the "flange" root:
\sigma=\frac{1.85F}{c^2}
My question is how to calculate such local bending stress in a "flange" of std profiles such UPN/IPN...and sources/books in the subject.
Thank you,
Guideon
Recently I faced a problem in calculating bending stress in a long UPN profile "flange" due to concentrated force.
It seems that the regular/familiar formula for bending stress in a finite/short element does not applicable in local bending of long/infinite beam. See sketch attached for clarification.
An example to such calculation I found in elevator's std for "T" rails calculation which express the stress in the "flange" root:
\sigma=\frac{1.85F}{c^2}
My question is how to calculate such local bending stress in a "flange" of std profiles such UPN/IPN...and sources/books in the subject.
Thank you,
Guideon





RE: local bending stress calculation in long beams
RE: local bending stress calculation in long beams
Brian
www.espcomposites.com
RE: local bending stress calculation in long beams
A sketch of your premise might be helpful.
RE: local bending stress calculation in long beams
Thanks for the answers,
Brian,
You are right, I found something like your answer in my notes, with one little correction 2b=x, and the only problem with this assumption is, that the bending stress equation you get is σ=3P/t^2, which is x independable (means that no matter what is the distance of the force P from the "flange" root, the stress has the same value).
Ron,
Upon your request, hereby another sketch which I hope that
explains to you the local bending in a flange of long beam.
Guideon
RE: local bending stress calculation in long beams
The could be modeled easily in FEA, but obviously can be approximated by hand.
As for the beam itself, you should check torsion, particularly if the concentrated load is near an end where the top flange is restrained.
RE: local bending stress calculation in long beams
As far as being x independent, that is the way it works out. Its a bit conservative for small x, and is mostly used at root (corner of your beam).
The aircraft industry has been using this approach for decades, with a total subtended angle usually 90 degrees (45 to both sides of the horizontal).
Brian
www.espcomposites.com
RE: local bending stress calculation in long beams
I found (simple geometry) that you are right, it should be b=2x!
I also lie on your experiance in the aircraft industry and accept the conservative approach you discribed.
Guideon
RE: local bending stress calculation in long beams
The 45 degrees is just a guideline. Some use more, some use less, based on test data, FEM, etc. You can think of it as a method and not necessarily something that captures the exact state of stress (which varies along the width b).
Brian
www.espcomposites.com
RE: local bending stress calculation in long beams
Guideon
RE: local bending stress calculation in long beams
Mike McCann
MMC Engineering
RE: local bending stress calculation in long beams
In aircraft at least, you will have wires and systems installations that run along the length of beams. In these cases, the flange is sufficient to support the load. It wouldn't be economical to add webs everywhere you want to hang a light load.
Forgot to mention, I believe Niu's analysis book has a curve that is based on test data for these types of problems as well. It better addresses the effect of x (i.e. the apparent dilemma Guideon observed). If the load is close to the corner, you get an improved benefit due to the fastener head, etc. The 45 degree rule works better when x is relatively large.
Brian
www.espcomposites.com