Euler Method 2

[alphanumericname]

Hello,

Does Euler's Formula for buckling generally give a good, quick estimate of the critical buckling load, or should it be disregarded in exchange for modern buckling formulas provided by AISC or ACI? I am studying for my PE and am trying to decide whether or not it can be used as a time saver when solving multiple-choice problems.

Thanks.

 

[271828]

The Euler buckling strength is theoretical only. For long skinny columns, it overestimates the strength by a little. For more normal columns, it overestimates the strength by a lot, sometimes by many multiples.

In AISC, the Euler buckling strength, Fe, is an intermediate value that you need for computing the nominal strength, Fn (or Fcr prior to 2022). After you get Fn, the design strength of the member is phi*Pn = 0.9 * Fn * A.

 

[alphanumericname]

Thanks! That was the confirmation I needed. I will stick to AISC code.

 

[lexpatrie]

Euler buckling doesn't "cap" at the squash load (where the full section reaches Fy, i.e. P = AgFy, that's another way of restating what 271828 said. It's really more of an energy method, it's going to give you a failure load, but it's an upper limit, at best. It's presuming a deflected shape (a sine curve), and doesn't account for residual stress, out of plane, or initial out-of-plumb, or full section yielding. It presumes elastic buckling occurs.

So it will give you a "correct" answer if none of those items are influential, so for say, Kl/r of 200 it's fairly correct.

When you get into intermediate/short columns the formula is still "valid" but it won't control. Plastification effects (inelastic buckling), tangent modulus, dual modulus, or section crushing (short column) will control before the Euler buckling load is achieved. It a multiple choice situation it's probably safe to cross off any option that's higher than the euler buckling load, provided they don't do anything tricky with bracing or effective lengths.

There's a 0.877 on the Euler buckling load in AISC, if you look far enough back.

AISC Flexural Buckling Equation

Side note - generally concrete columns are very stout, Euler buckling is unlikely to be of much use there. Plus you have to transform the section due to the differing E in the concrete/steel.

Regards,
Brian

 

[SE2607]

I think you would be better served being familiar with the allowable compression capacities of various materials. The capacity of short, stiff columns (smaller l/r ratios) have a different failure mechanism than longer l/r ratios. While the longer ratios look much closer like a Euler mode of failure, but they have also built in factors of safety and other issues such as fabrication tolerance, etc. It shouldn't take too much time to become familiar with them.

This is just my two cents, but I think if you go into a PE exam looking for these kinds of shortcuts, you probability of success will be disappointing. This approach may be more appropriate for a FE exam, but a PE exam is, hopefully, more "real world".

 

[IDS]

I totally agree with the comments above on the need to follow the code provisions for any practical buckling problem, but the Euler equation provides an upper limit to the buckling load of a column and is worth further examination to understand the basis (but perhaps after the exam!).

For my discussion of the basis of the equation, and how it links to the time taken for a ball to fall through a hole to the middle of the Earth) see:

https://newtonexcelbach.com/2010/06...and-the-hole-through-the-middle-of-the-earth/

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/