# Short Steel Columns yielding in compression



## E720 (Mar 7, 2021)

Does anyone have any information on when (what KL/r) you could realistically expect a short column to yield in compression instead of buckle. In the AISC 360-16 code as KL/r goes to zero, Fe will go to infinity, and the Fcr term will go to Fy. Obviously you could solve for the Euler buckling length that would result in a critical buckling stress of Fy, but if you plugged that length into the AISC code then you would get <Fy (you will only get Fcr = Fy when KL/r goes to zero). I am assuming also the column's elements are compact so no local buckling will occur. Any information is appreciated. Thanks


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## EBAT75 (Mar 7, 2021)

I thought L was was always in the denominator of the Fe equation. So it not clear why the 2016 edition would make a difference.

I think this has to do with the critical slenderness.

Euler’s critical stress curve is similar to the Seismic Response curve up to Lr (plastic and elastic range). Above the critical slenderness ratio, Euler works well. Below that theoretically it follows the curve, and was assumed to plateau when it reaches fy(cf Plastic in seismic response). But it does not account for material failure modes such as yield which has been shown to lower the critical buckling stress. This works for slender columns (“long”.

With short columns, below the critical slenderness ratio, the critical buckling stress becomes lower than predicted by Euler. 

Johnson did empirical work in early 1900s and came up with a parabolic transition to fy when slenderness ratio approaches zero. Johnson's formula interpolates between the yield stress of the column material and the critical stress given by Euler's formula.

As an example for 50 ksi steel, critical slenderness ratio below say 65 would not work well with Euler. The Johnson parabolic transition is a better predictor.

When KL/r is zero, wouldn’t the required strength exceed the available strength and no stiffness reduction (Tau) is available?


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## thedaywa1ker (Mar 7, 2021)

The only time I've seen compression yielding be worth worrying about is in my time doing cell tower retrofits...we would reinforce the pipe tower legs with half pipes of larger diameter welded to the outside.

We would check the slivers of unreinforced section of smaller pipe at top and bottom of the leg to see if it would yield before the built up section buckled. 

I don't have anything for your specific question, just my 2c


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## EBAT75 (Mar 8, 2021)

Just a quick addition to my earlier post.

All the Available Compression Strength Tables in the Manual give a strength value for KL=0 that corresponds to the yield strength multiplied by the strength reduction factor, not infinity. Examining the numbers for even other very short column heights, it appears to not follow Euler’s equation up to, I think the critical slenderness ratio. Suggests a gradually but at a varying rate may be parabolic transition to fy strength. Easy to check.

Also, the Note at the bottom of the Stiffness Reduction (Tau) Table in the Manual is of related interest.

Double angles are commonly used as braces in SCBF. If they are stitched in 2 places, they become 3 short columns to be checked. Not to be trivialized.


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