# Inelastic Buckling/Buckling in short columns

roanoar
Hey I was wondering how you're supposed to calculate the buckling force for a short column. Is there even a way? If there is, is it accurate and how do you use it? And finally how do you know when to use it?

## Answers and Replies

john.phillip
If the column is "short" (below slenderness ratio limit) there is no global elastic buckling before the material yields, so global elastic buckling theory will not be useful for predicting material failure.

To verify whether a column is "short" or not, you must know the material, how it is being loaded, how it's being supported (fixed, fixed-fixed, pinned-fixed, pinned-guided...), the effective buckling length, the least section's radius of gyration and the limiting slenderness ratio for your beam-column in the design code you are working with.

roanoar
That's interesting so I guess I shouldn't be looking at buckling for these short scenarios. I have calculated all the things you mentioned and have verified it is short. I was simply looking at buckling originally because I came across something called Johnson's equation which supposedly can solve buckling for short beams. But it requires a tangent modulus and this threw me off.

john.phillip
Most engineering designs are within the elastic limit and Euler's critical buckling load is included here. Johnson's approach applies to inelastic buckling, where the material already yielded with little strain or shows no significant elastic behaviour, hence the need for the tangent modulus.

Homework Helper
So I guess I shouldn't be looking at buckling for these short column scenarios.
You should be looking at buckling. You were right to look at that.

The Johnson formula applies to short columns. Notice the peak stress in the Johnson formula is the compressive yield strength, Scy. Hence, the Johnson formula prevents inelastic behavior. Furthermore, you divide the Johnson formula by a factor of safety, making the peak stress below the yield strength. Also, the Johnson formula uses modulus of elasticity, not tangent modulus.

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john.phillip
nvn is right, you can apply Johnson's approach to short columns, but it is not limited to this condition.