# Short Beam Stress Concentration

1. Apr 7, 2013

### elsikre

Hi there

Are any one familiar with tables of stress concentration factors, or the like for short beams for different span/depth ratios.

My beam is technically not a beam, but I would still like to estimate maximum bending stresses related to normal stresses caused by bending moment (sigma = Mc/I) near the fixation. According to Roarks Formulas for Stress and Strain (7th edition p167) span/depth ratios of less than 3 does no longer give accurate results with Mc/I, but the stress distribution changes depending on the manner of loading and support. I kind of need tables with these factors or the like.

My "beam" is classic example of a short cantilever beam fixated at the left end, transverse point load at the tip.
lengt/span = 0.2
height/depth = 0.2
thickness/width = 0.04

Any one can give me a hint on this one ?

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2. Apr 12, 2013

### odmart01

3. Apr 13, 2013

### elsikre

Hi odmart01

Thank you for your interest in this subject an your reply. I actually know it is not a beam because it does not fulfill the span/depth ratio to use Euler Bernoulli etc. That is also why I wrote: "My beam is technically not a beam", buty still Roarks Formulas for stress and strain uses the term "Beam" even for extremely short and deep beams, so I just didn't know what to call it.

But anyway, let us say that you were given the task to estimate highest bending stresses in this short structure with length/depth ratio of 1, due to the given constraint and transverse force applied. My question is whether it might be possible to calculate analytical, or will it be only possible to do by FEA.

The case is, that Roarks formulas has a table with stress concentration factors, but that is (as I can see) only for simply supported extremely short beam.

- And thanks a lot for the link.

4. Apr 15, 2013

### timthereaper

Stress concentration only comes into play where you have a sudden change in geometry or shape, such as near a fillet, a hole, etc. In your problem, you don't have that.

The size of the beam does complicate things, but you still can use Mc/I to get a ballpark of stress due to bending. Sure, it's not accurate, but if you want accuracy, throw it into some analysis software or do some strain testing.

One more thing, you probably want to look at the shear due to bending in this problem. The VQ/It stress will play a large role in the problem due to the shortness of the "beam".

5. Apr 16, 2013

### elsikre

Great. It is nice to hear that this guess should be close enough. I will do some guesses at the axial stresses related to the bending of the profile, and include Timoshenko effects in an analytical calculation of deformation as well. Of course some FEA. That should do the trick then. Thanks.