Deep Beam "Arch Action" Theory for Steel Rods

[PhDE]

I have a 10" steel rod spanning 10" with a uniform load.

If I think about this problem as I would a deep concrete beam utilizing deep beam theory - as a compression arch, I am fine with the combession stresses.

I also evaluated it as a bending member and found my stresses were close to the allowables.

Just to confirm that I was being conservative, I looked this up in my trusty Roark's book (4th Ed page 131). Here, my "arch action" idea is out the door, in addition, to simple bending. Roark indicates there is a penalty in short beam. For a L/d ratio of 1 for my case, I have to decrease my allowable stress (or increase my applied moment) by a factor of 2.725!! Ouch. Any help interpreting this would be greatly appreciated.

 

[flamby]

I would have considered FEA for such structures more than any Roark's juggelery.

However, I guess that your section will fail in PLAIN SHEAR before you have to take any pain of going further with the bending analysis. If the span is short, check the shear first before other things.

 

[corus]

Basically you have no choice other than to accept the results of Roark unless you have access to FEA. As the rod is so small the effects of the end restraints or load application will be significant on the maximum stress due to their proximity to the centre of the beam. Roark indicates that the results of the table have been verified by measurements.
FEA may be of help where contact produces a different load distribution or yielding redistributes the load somehow, otherwise you're on to a loser.
Incidentally, in Roark's 6th ed. the table is referred to on page 203.

 

[PhDE]

Of course I checked shear, that wasn't my question. We also don't have a solids FEM program here - only shells. I am going to increase the size.