# Local bending stress calculation in long beams

1. Jul 21, 2011

### guideonl

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

#### Attached Files:

• ###### long beam bending stress calculation.pdf
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2. Jul 23, 2011

### Unrest

My answer to everything - FEA.

But more seriously, I doubt there's an analytic solution to this, which would be why you have that empirical formula for a special beam section. You could get an upper limit to the stress by assuming a beam shorter than the width of the loaded region and use the simple beam equation you did.

3. Jul 23, 2011

### guideonl

Hi Unrest,

I am afraid that your solution to the problem could be used only for estimation purposes, I am still looking for analitical/empirical solutions.

Guideon

4. Jul 26, 2011

### the_red_jeste

for an infinite length beam could you not treat the area under load as being built in at a distance away from the load? or use a plastic analysis approach with the concept of moving hinge point along an infinite beam..
take cuts at the hinges and treat as beam with imaginary built in ends (ie a couple applied to the ends of the cut)
with a theoretical max. moment generated either at cut (hogging moment) or at point of load (assuming point load applied) to give a sagging moment. then calculate your second moment of area for the section and using the Engineers Equation (M/I)=(Sigma/y) you can calculate sigma over a range of y and draw the stress distribution across the section @ point of maximum bending

I hope at that helps somewhat..

5. Jul 26, 2011

### guideonl

Red jeste,

I am sorry, but I didn't understand your idea at all. May be I didn't clarify myself well, attached sketch may be helpful to clarify your claim.

Thank you
Guideon